does component sharing help or hurt reliability? an ...faculty.london.edu/kramdas/ramdas and...

Does Component Sharing Help or Hurt Reliability? An Empirical Study in the AutomotiveIndustryAuthor(s): Kamalini Ramdas and Taylor RandallSource: Management Science, Vol. 54, No. 5 (May, 2008), pp. 922-938Published by: INFORMSStable URL: http://www.jstor.org/stable/20122441 .

Accessed: 01/10/2014 08:16

Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at .http://www.jstor.org/page/info/about/policies/terms.jsp

.JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range ofcontent in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new formsof scholarship. For more information about JSTOR, please contact [email protected].

.

INFORMS is collaborating with JSTOR to digitize, preserve and extend access to Management Science.

http://www.jstor.org

This content downloaded from 163.119.96.156 on Wed, 1 Oct 2014 08:16:41 AMAll use subject to JSTOR Terms and Conditions

http://www.jstor.org/action/showPublisher?publisherCode=informs

http://www.jstor.org/stable/20122441?origin=JSTOR-pdf

http://www.jstor.org/page/info/about/policies/terms.jsp


MANAGEMENT SCIENCE hCK Vol. 54, No. 5, May 2008, pp. 922-938

DOI i0.i287/mnsc.l070.0791 issN 0025-19091 EissN 1526-55011081540510922 ? 2008 INFORMS

Does Component Sharing Help or Hurt Reliability? An Empirical Study in the Automotive Industry

Kamalini Ramdas Darden Graduate School of Business, University of Virginia, Charlottesville, Virginia 22906,

[email protected]

Taylor Randall David Eccles School of Business, University of Utah, Salt Lake City, Utah 84112,

[email protected]

Component sharing?the use of a component on multiple products within a firm's product line?is widely

practiced as a means of offering high variety at low cost. Although many researchers have examined trade

offs involved in component sharing, little research has focused on the impact of component sharing on quality. In this paper, we examine how component sharing impacts one dimension of quality?reliability?defined as

mean time to failure. Design considerations suggest that a component designed uniquely for a product will result in higher reliability due to the better fit of the component within the architecture of the product. On the other hand, the learning

curve literature suggests that greater experience with a component can improve

conformance quality, and can increase reliability via learning from end-user feedback. The engineering literature

suggests that improved conformance in turn increases reliability. Sharing a component across

multiple products increases experience, and hence, should increase reliability Using data from the automotive industry,

we find

support for the hypothesis that higher component reliability is associated with higher cumulative experience with a component. Further, we find support for the hypothesis that higher component reliability is associated with a component that has been designed uniquely for a product. This finding suggests that the popular design strategy of component sharing

can in some cases compromise product quality, via reduced reliability

Key words : empirical study; benefits of specific design; quality; component sharing History: Accepted by Christoph Loch, R&D and product development; received June 11, 2004. This paper was

with the authors 2 years and 4 months for 2 revisions. Published online in Articles in Advance March 27, 2008.

1. Introduction In this paper, we examine the impact of component

sharing?the use of a component across multiple end

products within a firm's product line?on component

reliability. A component's reliability is defined as its mean time to failure.

Consider the following design scenario relating a

firm's component-sharing strategy to the reliability of

the components used in its products. When designing an assembled product, designers repeatedly evaluate

whether to create a unique component specifically for

the product or to reuse an existing component. Spe cific design allows the designer greater flexibility in

tailoring the component specifications to the needs of the product, which should lead to higher reliability.

For any component, however, unanticipated defects

may arise in its manufacture, assembly, or use. Over

time, the occurrence of such defects is reduced via

improvements in manufacturing and assembly pro cesses for the component, and engineering improve

ments to the component itself based on feedback from

downstream firm functions and from end users. The benefit of using an existing component is that many

reliability problems may already have been identi fied and corrected via this improvement process. The downside to using an existing component is that

design fit can be compromised, leading to decreased

reliability. The tension described in this scenario leads us to the central questions of this paper. Does greater

reliability result when a component is used in a prod uct for which it was specifically designed? Is higher component reliability associated with increased expe rience with a particular component, in manufacturing, assembly, and field use? Finally, if both the specific design effect and the experience effect exist, which

might have the greatest relative impact, and in what situations?

We believe that these are important questions both for practitioners engaging in component shar

ing and for researchers studying this topic. Auto

industry executives we interviewed claimed that the economic incentive to share components increases

when after-sales warranty costs are factored into the

design decision. Our work examines whether, and in what situations, component sharing has the poten tial to reduce failures, and hence warranty costs. If

922



Ramdas and Randall: An Empirical Study in the Automotive Industry Management Science 54(5), pp. 922-938, ?2008 INFORMS 923

component sharing compromises product reliability, this detrimental effect on quality could negate the

widely touted benefits of component sharing, which

include reduction in product design, manufactur

ing and distribution costs, and increased responsive ness to consumer demand, as documented by Ulrich

(1995), Swaminathan and Tayur (1998), Ramdas and

Sawhney (2001), Ramdas (2003), Rutenberg (1971), Fisher et al. (1999), Gupta and Krishnan (1999), Krishnan and Gupta (2001), Desai et al. (2001), Kim

and Chhajed (2001), Ramdas et al. (2003), Thonemann

and Brandeau (2000), and Yano and Dobson (1998).

Conversely, if component sharing enhances product

reliability in addition to its more widely known ben

efits, this could lead companies to encourage more

component sharing.

Although a few researchers have prescriptively modeled how component sharing can be effectively used to satisfy market segments with differing qual

ity needs (Desai et al. 2001, Heese and Swaminathan

2006, Ramdas et al. 2003), the reliability trade-off we

described above remains unaddressed. Using empiri cal data in the domain of automotive braking systems,

we examine how component sharing impacts reliabil

ity. Examining the impact on reliability of tailoring a

component's design specifically to a product applica tion is one major contribution of our work. Another

key contribution is that we shed light on how differ

ent ways to increase the cumulative experience with a

component?experience on a single car model versus

experience via sharing the component across multi

ple models?improve reliability. Finally, we are able

to highlight design contexts where either the unique

design or experience effects dominate.

In ?2, we describe the industry context for our study. In ?3, we develop our hypotheses. In ?4, we discuss

the data and variable definitions. In ?5, we present

methodology, and in ?6, we present results. In ?7, we

discuss our findings and their implications for prac tice. Section 8 contains limitations and conclusions.

2. Industry Context The context for our study is the automotive industry.

We focus specifically on one component of the auto

motive braking system?the brake rotor?and study brake rotor sharing strategies at Ford Motor Com

pany. We chose to focus on braking systems because

brake reliability is of critical importance to the con

sumer, brake-related quality issues are a critical deter

minant of warranty costs (Automotive News, June

1999), and there is considerable sharing of braking

system components at Ford and other auto makers.

Within braking systems, we chose to focus on brake

rotors because, based on our discussions with indus

try experts, reliability problems associated with brake

rotors are most easily identified as occurring due to

rotor design decisions, as opposed to decisions about some other components in the braking system or the

automobile.

An automotive braking system is a hydraulic sys tem that converts human foot pressure applied at the

pedal into a much higher braking pressure applied at the wheels via the braking system components. The pressure applied at the wheels forces stationary brake components?brake pads that are attached to

the calipers?to rub against rotating components?the brake rotor, thus converting the kinetic energy of a

moving car into heat energy via friction. The pressure

applied to the rotor by the brake pads causes wear

on the brake rotor. Common rotor problems that arise

from use include warping, scoring, or even cracking of the rotor.

Automotive braking system design is initiated only after vehicle design has been broadly specified, via

"system-level parameters" such as vehicle weight, top

speed, and stopping distance. Given these inputs, the

components of the braking system must be designed so as to provide adequate torque to stop a car

from top speed within the desired stopping distance. In addition, all braking components are designed for "maximum loading" conditions: for example, the

brake pedal should not crack if the driver steps excep

tionally hard on it in a panic stop. Further, sev

eral constraints arise due to the interaction between

braking components: for example, the hydraulic ratio

(ratio of areas of master cylinder and caliper pis tons) must lie within prespecified limits to eliminate

excessive pedal "travel," which could cause the brake

pedal to hit the floor of the car. Braking system design parameters like rotor radius, desired pedal force, and area of the caliper pistons and master cylinder piston are manipulated to meet these different ends. In the context of our study, the challenge for the designer is to balance the constraints of each unique braking sys tem with the potential benefits of component sharing.

3. Theory and Development of

Hypotheses Our hypotheses rely on prior research in design the

ory and learning curve theory, as well as insights

gained from interviewing senior executives, man

agers, and engineers in the auto industry. The

first hypothesis addresses the question of whether

uniquely designed components produce better relia

bility outcomes. The second hypothesis addresses the

question of whether and how greater experience with a component impacts reliability.

Design theory suggests that designing unique com

ponents for each specific product application will

result in higher product quality. Ulrich (1995) dis cussed the role of components within modular and



Ramdas and Randall: An Empirical Study in the Automotive Industry 924 Management Science 54(5), pp. 922-938, ?2008 INFORMS

integral product architectures. In a pure modular

architecture, the interfaces among components are

standardized, and so multiple products can be config ured by mixing and matching from a base set of com

ponents. In a pure integral product architecture, the

complex interactions among components require that

components be specifically designed for each prod uct (Ulrich and Ellison 1999). In practice, products are

often a blend of modular and integral architectures.

The elements of the architecture that are integral lead

designers to uniquely design components for each

end product rather than share components across end

products. An implication of this theory is that sharing

components inappropriately will result in poor fit of

the component with the product, and hence will hurt

quality. In probing exactly how quality may be affected

when design fit is compromised, it is useful to think

of the impact of design fit on multiple dimensions

of quality. We posit that a compromise in design fit

can negatively impact both performance and reliabil

ity. As a simple example, suppose that while design

ing a scissors intended for cutting cloth, designers at

a stationery company borrow blades from an exist

ing scissors that was designed to cut paper. (In actu

ality, scissors manufacturers typically advocate that

paper scissors not be used for cutting cloth, and vice

versa.) One possible outcome is that the scissors per forms poorly from the start, because the blade is just not what is needed for cutting cloth. Another possible outcome is that the scissors performance is acceptable at first, but deteriorates over time, so that at some

point the performance is longer acceptable. This effect

is called "perf or manee degradation/' and it is more

likely to occur if the fit of the design to the particular

application in which it is used is compromised. Such

performance degradation in turn impacts reliability. To our knowledge, this important effect of compo

nent reuse has not been documented in the literature.

One possible reason for this oversight is that in the

traditional engineering literature, reliability has had

a binary definition: a product has either failed, or it

has not. Only recently have researchers proposed a

continuous-state reliability model, in which gradual

degradation in performance occurs over time (Yang and Kapur 1997). Degradation can occur even in cases

where there is a distinct switch over to the "failure"

state?for example, a light bulb fails because its ele

ment is gradually evaporating over time. It is reason

able to expect that lack of design fit of a component to

the specific application in which it is used will accel

erate such performance degradation over time, thus

reducing reliability. This basic notion is complicated by industrial prac

tice. Auto manufacturers often choose to design a new

rotor for use on multiple models at once, rather than

on a single new model. We argue that doing this

dilutes the specificity of the design to any particular model in the use set. Therefore, for any vehicle, if the

rotor used on it was designed for the specific model

and model year of that vehicle, and furthermore if

that was the only vehicle for which it was designed, we expect the fit and therefore the reliability to be

higher than if that rotor was designed for use on sev

eral different models in that particular model year. In our empirical model, we expect that the positive

impact on reliability associated with using a rotor that

was designed for the model and model year of a vehi

cle will be moderated by the total number of models

on which that rotor was used in its first year.1 These

arguments lead to our first hypothesis.

Hypothesis 1. The greater the specificity of a compo nent's design to a product application, the greater the reli

ability of the component in that application. However, the

larger the set of products a component was designed for, the

poorer the specificity of the design to any one product in

that set, and hence the poorer the component's reliability.

In the automotive braking context, we expect that

the reliability of a brake rotor in a vehicle will be

higher if the rotor was designed for the specific model

and model year of the vehicle than if it had been orig

inally designed for another model or even another

model year of the same model. This effect will be neg

atively moderated by the number of models for which

the brake rotor was designed. The literature on learning curves provides empiri

cal evidence that product costs decrease in the cumu

lative production volume of a product.2 More recently, researchers have examined the impact of learning on

different aspects of quality. Reagans et al. (2005) con

sider the impact of learning on surgical outcomes.

In an airline industry study, Lapr? and Tsikriktsis

(2006) link learning to customer dissatisfaction, an

outcome measure of quality evaluated by consumers.

Fine (1986) and Ittner (1996) link learning curve

theory to improvements in conformance quality. Fine (1986) models conformance quality improve

ment over time as a function of both "learning-by

doing," as described by Anzoni and Simon (1979), and induced learning; that is, consciously engaging in

improvement activities. Lapr? and van Wassenhove

(2001) empirically identify factors that facilitate "for

mal" or induced learning. Mukherjee et al. (1998)

1 We assume that if a rotor was used on multiple models in its first

year, it was designed for use on all of these models.

2 See Hatch and Mowery (1998) for a comprehensive list of the

many studies that document the learning curve phenomena in

various industries. See, as examples, Wright (1936), airplanes; Baloff (1971), automobiles; Dick (1991), semiconductors; Lieberman

(1984), semiconductors.



Ramdas and Randall: An Empirical Study in the Automotive Industry

Management Science 54(5), pp. 922-938, ?2008 INFORMS ^

925

report on empirically observing two types of learn

ing: operational learning, which comes from develop

ing specific solutions to specific problems faced in a

factory, and conceptual learning, which relies on con

ceptual models to understand why problems occur,

resulting in more general solutions.

The engineering literature suggests that an improv ement in conformance quality in turn improves prod uct reliability. Kececioglu (1991) states that quality con

trol assures conformance quality, i.e., conformance to

specifications. This reduces manufacturing variance, which can degrade reliability. Kececioglu (1991, p. 35) maintains that "no product can perform reliably with

out the inputs of quality control because quality parts and components are needed to go into the product so that its reliability is assured." Dasgupta and Pecht

(1991) indicate that a component can fail if its man

ufacturing tolerance requirements are not met. Wong (1995) graphs production quality of semiconductors

against their reliability in the field, and finds a clear

positive relationship. To understand why production experience and

conformance quality impact reliability, it is useful to

consider how product flaws affect reliability. For a

product in use, reliability problems can very often be

attributed to "built-in flaws," which are introduced

in the course of the manufacturing or assembly pro cess (Wong 1995). Wong distinguishes such built-in

flaws from "design flaws," which are introduced in

the course of the design process. Design flaws can be

very damaging to reliability, but are typically discov

ered early and corrected before the product is in use

(see Figure 1). The engineering literature suggests that reliability

improves with greater manufacturing experience, due

to a reduction in built-in flaws. Specifically, in the

context of brake rotors, an example of a built-in flaw

is overtightening of wheel lug nuts during assembly. Such overtightening can distort the rotor, inducing lateral runout, a condition where the surface of the

Figure 1 The Impact of Design Flaws and Built-in Flaws on Quality

Design flaw Built-in flaw

Where is flaw is

introduced? Design process Manufacturing

process

What dimensions

of quality does the flaw affect?

Performance

j (over time) Reliability

Conformance

I Performance

| (overtime)

Reliability

Where is the

flaw identified? Design, manufacturing,

manufacturing testing, or in field use

Manufacturing,

manufacturing

testing, or in field use

rotor wobbles from side to side as it rotates. Accord

ing to General Motors Corporation, undertorquing a

single lug nut can create as much as 0.003 inch of lat

eral runout (Carley 2002). A rotor with lateral runout

will not wear evenly, increasing the likelihood of fail ure over time. With improved manufacturing based on greater experience and learning by doing, con

formance quality, and in turn reliability, are likely to improve. Kececioglu (1991, p. 192), notes that

improvements in conformance quality reduce infant

mortality, and also improve reliability in the normal

life and end-of-life portions of a product's life cycle. As experience with a product increases, aside from

learning by doing in manufacturing, the firm also

has an opportunity to learn from end-user feedback.

For example, as products are used in the field, failed

products under warranty are returned to the firm, and undergo FMEA3 analysis, which can expose both

design flaws and built-in flaws. Modifications made to products based on this type of feedback and anal

ysis can improve component reliability. Thus, greater experience should improve reliabil

ity, be it via learning by doing in manufacturing, or

learning from end-user feedback.

A stream of research on learning transfer focuses on whether and how the learning accumulated in the course of production at one production site transfers to other production sites or to other products at the same site. Hatch and Mowery (1998) report that losses in semiconductor yield occur as processes are trans

ferred from development facilities to manufacturing facilities. Adler (1990) shows that not all productiv

ity gains associated with learning by doing are trans

ferred to new manufacturing situations.

Similarly, the empirical research that investigates

knowledge transfer across products suggests that

knowledge transfer occurs?but to an incomplete degree (Argote 1999). For example, Benkard (2000) finds in the context of aircraft production that only a

partial transfer of knowledge occurs across different models built at the same production site.

Based on these arguments, we expect that although the use of a component on a new model will increase

overall experience with the component, the shift to

the new model will likely be accompanied with a

discontinuity in the learning curve, in the form of an initial loss of quality. Multiple models that use

the same component may have slight differences that

make some of the learning from one model irrel

evant to another. Models that share a component

may be assembled on different lines within a plant, or in totally different geographical locations, further

impeding knowledge transfer. Argote (1999) provides an example of how an automotive plant using a

3 Failure modes and effects analysis.




Figure 2 Annual Volume and Cumulative Volume for a Brake Rotor Used on the Ford Mustang from 1994 to 2001

200,000

180,000

160,000

O 140,000 E = 120,000 O

? 100,000

i 80,000

60,000

40,000

20,000

O

Annual volume

Cumulative total

1,200,000

1,000,000

-1-800,000 i O >

600,000 >

3

400,000 E O

200,000

1994 1995 1996 1997 1998 1999 2000 2001

Year

particular assembly system may discover a way to

improve its performance, but if sister plants do not use the same system, the improvements may not be

transferable. Of course, the efficiency of knowledge transfer is likely to vary across firms, because it is a

function of organizational structure and knowledge management capability

Focusing on brake rotors, Figures 2 and 3 show

examples in our data from Ford of how the cumu

lative experience with a specific brake rotor can be

attained in different ways?via sharing the rotor over

time on a single model, or via sharing the rotor over

multiple models, over time. In practice, different mod

els that share a component are often made at different

plants or on different assembly lines, and this trend

will increase as companies move towards implement

ing global product platforms.4 We expect that the

cumulative experience gained with a specific brake

rotor via its use on a single model will have a greater

positive impact on reliability than experience gained via its use on multiple models.

The above discussion leads us to our second

hypothesis.

Hypothesis 2. Higher component reliability will be

associated with higher cumulative production experience, but the magnitude of the relationship will decrease in the

number of products used to attain any particular level of

experience.

4. Data and Variables We obtained data from several sources. The data on reliability focuses specifically on the reliability of

automotive brake rotors. This data was obtained from

the Department of Transportation of the U.S. govern ment, and records consumer complaints about front

brake rotor quality problems. This data is used by the U.S. government to guide product recall deci

sions. Like the data on customer dissatisfaction used

by Lapr? and Tsikriktsis (2006), our data is based on

performance in the field, as opposed to internal eval

uation of quality within the firm. Our data on brakes

component sharing was obtained from an automo

tive research company. From this data, we can deter

mine all of the unique braking components in use

on vehicles sold on the U.S. market in the period of our study, and what vehicles used each unique brake. We obtained data on individual model vol umes and vehicle characteristics such as weight and

horsepower from Ward's Automotive (Ward's Automo

tive Yearbooks 1965-2003) and Automotive News, and

data on brake characteristics via direct measurement, Internet sources, and Motor Vehicle Manufacturer's

Association specification sheets. We obtained data on

control variables from public sources. For example,

precipitation data was obtained from the National

Weather Service, and population data from the U.S.

Census.

The unit of analysis in our study is an individ

ual vehicle on the road, identified by its vehicle

identification number (VIN). The VIN label, which

is often printed on the underside of the dash

board, uniquely identifies every vehicle on the road.

It can be used to track ownership, standard and

optional factory-installed equipment, and other indi

vidual vehicle-specific details. The original data set

from the government on brake failures contained 990

observations from Ford Motor Company for individ

uals reporting a first-time rotor failure. Of these, 297

observations were dropped due to incomplete data.

The primary reason for the incomplete data was lack

of precise rotor information to match the VIN. The

pattern of missing rotor information appears random,

reducing the potential for sample bias. This leaves 693

observations on which to test our hypotheses. Fifty six different brake rotors were used on the vehicles in

our data set. We describe below the variables used in our hypothesis tests. Refer to Table 1 for descriptive statistics.

4.1. Dependent Variable

4.1.1. Miles to Failure. We use miles to failure of

the brake rotor as our measure of rotor reliability, the dependent variable in our study. Miles to failure

is the number of miles driven in a particular vehi

cle from zero miles to the miles at the time of the

first reported failure of the brake rotor. A rotor fail ure is defined as a case in which the rotor requires

repair or replacement because it appears abnormal, either in the way in which it is operating or in its

4 A platform is defined most broadly as a set of resources that is

shared across products, ranging from components to production

processes.




Figure 3 Annual Volume by Model and Cumulative Volume for a Brake Rotor Shared over Multiple Models and over Multiple Years

500,000 i-r 8,000,000

000,000

1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994

Year

physical condition. Our data indicates that rotor fail ure results from problems such as scoring, warping, or cracking of the rotor. The mean miles to failure is

31,673 (median = 27,000) with the minimum miles to

failure reported at 2 miles and the maximum miles to

failure reported at 134,000 miles. Figure 4 presents a

histogram of miles to failure.

Table 1 Descriptive Statistics {N = 693)

Mean Median Std. dev. Min. Max.

Continuous variables

Miles to failure 31,673 27,000 24,330 2 134,000 Cumulative volume 845,205 511,395 1,112,285 7,869 7,568,420

Time in use 1.75 1 2.55 0 15

Number of models 2.33 2.00 1.12 1.00 9.00

Horsepower 151.76 140 33.21 84 310

Swept area per ton 119.34 120 12.18 85.19 198.79

Precipitation 38.48 41 14.85 7 110

Population density 3,300.57 2,478 3,198.27 12.8 34,916

% Positive weight 7.72 6.21 6.59 0.03 30.13

difference

(/7 = 554)(%) % Negative weight 7.62 7.12 6.42 0.05 32.78

difference

(A7 = 82) (%) Suggested retail 13,587 12,440 4,328 5,893 28,987

price

Dichotomous variables (% of sample)

Year-specific design 36%

Carryover design 49%

Vented 88% Trucks 24%

4.2. Study Variables

4.2.1. Measures of Cumulative Experience. Exist

ing literature uses cumulative production volume as

a proxy for cumulative experience effects (Macher

2003). Although alternative measures such as time

and engineering resources have been explored (Hatch and Mowery 1998), cumulative volume is the stan

dard proxy. We measure the cumulative volume of a rotor used in a VIN as the total volume from its

time of first use up to the model year of that VIN.5

We calculated cumulative volumes for each brake

rotor by summing the volumes of all the models over

which the rotor had been used, up to and including the model year of the car. We obtained individual

model volumes from Ward's Automotive and Auto

motive News, and adjusted for cases in which mul

tiple rotors had been used on a model. The mean

cumulative volume for brake rotors is 845,205 rotors

(median =

511.395), with a minimum cumulative vol ume of 7,869 and a maximum of 7,568,420. Figure 5

shows the cumulative volumes over time for the 56

unique Ford brake rotors in our study. It is common

convention in the learning curve literature to take the

natural log of cumulative volume for estimation pro cedures (Hatch and Mowery 1998). We follow this

convention.

5 As a robustness check, we also measure volume using midyear

production volumes rather than end-of-year volumes. We report no significant differences in results using this alternative volume

measure.




Figure 4 Histogram of Miles to Failure

25,000 50,000 75,000 100,000 125,000

Miles to failure

Aside from cumulative volume, we also use a mea

sure of learning based on the time that has passed since the first use of the component. The time in use

for each rotor-VIN combination is defined as the time

from when that rotor was first introduced until the

model year of the VIN in question. The mean time

in use is 1.75 years (median =

1). We note a rela

tively high correlation between cumulative volume

and time in use (Table 2, r ? 0.67, p < 0.01). We believe it is an empirical question as to whether

it is cumulative volume or time in use that better cap tures learning effects in the data. We show results

with both measures in our model specification.

4.2.2. Number of Models. The number of models

represents the number of different vehicle models on

which a particular brake was shared up to the time of

manufacture of the vehicle in question. This variable serves as the moderating variable in our hypothe ses. Rotors are shared on an average of 2.33 models

(median =

2) with a minimum of 1 model (no shar

ing) and a maximum of 9 models. We defined each

unique name

plate?e.g., Ford Taurus versus Mercury

Sable?as a distinct model. Although these vehicles

share a platform, there are some significant differ

ences; for example, in vehicle weight, which is an

important factor in brakes design. This is the reason

for our choice of definition. However, we obtain sim

ilar results when we classify models such as the Ford

Taurus and Mercury Sable as being the same model.

4.2.3. Measures of Product Specificity of Com

ponent's Design. We measure whether a brake was

designed specifically for a model in two different

ways. An indicator variable, year-specific design, cap tures whether or not the brake rotor used in a VIN

was designed specifically for the model and model

year of that VIN. If the rotor used on a VIN was intro

duced prior to the model year corresponding to that

VIN, then year-specific design equals zero. If instead

the rotor used on a VIN was introduced in the same

model year as that VIN, year-specific design equals one regardless of how many other models the rotor

was used on in its first year of use. In our sample, 36%

of the observations had rotors designed specifically for the model and model year of the VIN in ques tion. Another indicator, carryover design, is set equal to one if the brake used in a VIN is designed specifi

cally for the model corresponding to that VIN, but not

for its specific model year. This variable enables us

to examine the reliability benefits of sharing rotors on

the same model across time. For example, if a rotor is

Figure 5 Cumulative Volumes for the 56 Unique Ford Front Brake Rotors in Our Study

8,000,000

1983 1985 1987 1989 1991 1993 Model year

1995 1997 1999 2001




Management Science 54(5), pp. 922-938, ?2008 INFORMS 929

Table 2 Correlation Matrix (N = 693)

Miles to failure

Cumulative

volume

Time in use

Number

of

models Horsepower

Swept area

per ton Precipitation Population

density

% Positive weight

difference

% Negative Suggested weight retail

difference price

Miles to failure Cumulative volume

Time in use

Number of models

Horsepower

Swept area per ton

Precipitation Population density % Positive weight

difference % Negative weight

difference

Suggested retail

price

1 -0.03

-0.13***

0.03

-0.19***

0.03

0.12***

-0.06

0.04

0.01

-0.09**

1

0.67*'

0.68*'

-0.35*'

0.08*'

0.04

0.03

0.23*'

-0.05

-0.26*'

1

-0.54*'

-0.19*'

0.07*'

0.03

0.03

0.12*=

0.05

-0.15*'

1

-0.30*'

0.02

0.09*'

0.02

0.28*'

0.10*=

-0.11*'

1

-0.24

-0.09

-0.10*

-0.30

0.08

0.56

1

0.03

0.04

0.37

-0.23

-0.34

1

-0.08*'

0.01

0.01

0.01

1

0.07*

-0.01

-0.11*

1

-0.26

-0.48

1

0.24*=

, *

coefficient significant at the p < 0.01, 0.05, and 0.10 levels, respectively.

used on a model in 1993 (the design year), 1994, and

1995, carryover design equals 0 in 1993 (the design

year) and 1 in each subsequent year. Forty-nine per cent of our observations used a carryover design.

4.3. Control Variables

4.3.1. Vented. Rotors may be vented or solid.

Vents alleviate heat generated as calipers come in con

tact with the rotor during braking. The reduced heat

keeps rotors from warping easily. We use an indicator

variable to indicate a vented rotor. We expect vented

rotors to have lower hazard rates than solid rotors, other things being equal. Eighty-eight percent of the

observations in our sample have vented rotors.

4.3.2. Horsepower. Automobiles with higher

horsepower can accelerate faster, placing higher

requirements on the brakes. We expect automobiles with higher horsepower to have a higher failure rate.

The mean horsepower was 151.76 HP (median =

140 HP).

4.3.3. Swept Area per Ton. The swept area is the area of contact between a brake caliper and brake rotor. All else being equal, the larger this swept area, the greater the braking ability. Heavier cars typically

have a larger rotor swept area. The rotor swept area

per ton controls for the relation between the weight of the vehicle and the compensating swept area, and

is a commonly used metric of braking potential. We

expect a higher swept area per ton to result in higher miles to failure. We report a mean swept area per ton

of 119.34 square inches per ton (median = 120 square

inches per ton).

4.3.4. Population Density. We use the population

density of the county of driver residence as a proxy for general driving conditions. We expect the hazard

rate to increase with population density because city

driving results in greater use of the brakes. We report a mean population density of 3,300 people per square

mile (median =

2,478). Population density exhibits considerable skewness. We mitigate this problem by taking the natural log of population density.

4.3.5. Precipitation. Interviews with brake ex

perts suggested that weather conditions associated with precipitation can reduce the longevity of brakes and brake rotors. We use the average precipitation of the county of driver residence to control for wet

weather conditions. The mean precipitation per year is 38 inches (median

= 41 inches).

4.3.6. Percent Positive Weight Difference. Inter views with industry personnel suggest that when a brake rotor is reused across multiple models, to ensure reliability the rotor selected might be overspec ified. In this case, we would expect the rotor per formance to increase when reused. Although there are many dimensions of performance specification, our interviews indicated that it is easier to share a

rotor across models if the new automobile weighs less than the weight of the car that the rotor was origi

nally designed for (design weight6). We use the pos itive percent weight difference, calculated below, as a proxy for the potential overspecification of shared

brake rotors. For each VIN,

Percent positive weight difference

(design weight ?

weight of VIN)

design weight = if design weight >

weight of VIN,

0 else.

6 If a rotor was used on multiple models in its first year of use, we

define design weight as the weight of the heaviest of these models.




We report an average positive percent weight dif

ference of 7.72% (median =

6.21%). Note that 554, or

80%, of our observations exhibit a positive difference,

indicating that rotors are typically reused on models

that weigh less than their design weight.

4.3.7. Percent Negative Weight Difference. Inter

views with industry personnel also indicated that a

brake might also be reused in instances where the

weight of the automobile is higher than the original

design weight. To control for potential quality prob lems caused due to underspecification, we include a

variable that captures underspecification. We define

the percent negative weight difference as follows.

Percent negative weight difference

[ (weight of VIN ? design weight)

design weight = i if design weight < weight of VIN,

[ 0 else.

We report an average percent negative weight dif

ference of 7.62% (median =

7.12%). Note that only 82 observations have a negative weight difference,

whereas 57 observations display no weight difference.

4.3.8. Suggested Retail Price. We proxy for the

overall quality of the automobile design by using sug

gested retail price adjusted for inflation. We expect cars of higher price to have a higher quality. The

average inflation-adjusted price is $13,587 (median

$12,440).

4.3.9. Early Epoch. To control for potential

changes in brake technology over time, we divide

the brake introduction time period into epochs. We

present results with an early epoch (prior to 1985). However, results are robust to different specifica tions of the epoch variable. Eight percent of our

observations occur on brakes designed before 1985.

Finally, we use indicator variables to control for

the specific assembly plant that produced a VIN.

MacDuffie et al. (1996) reported significant differ ences in quality across automobile assembly plants.

Although we found significant coefficients for several

of the assembly plant dummies, for brevity we omit

these variables in reporting our results. We also use

an indicator variable to control for whether the vehi

cle is a passenger car or a truck. Twenty-four percent

of the observations are trucks.

Table 2 presents Pearson correlation coefficients

among the study variables. We highlight several of

the significant correlations. We note that our depen dent variable, miles to failure, is negatively asso

ciated with horsepower and suggested retail price, but positively associated with precipitation. It is not

significantly correlated with our variables of interest.

Second, we notice that cumulative volume is highly correlated with the number of models.

5. Methods Because we are dealing with survival data, a haz

ard rate model should be used rather than standard

regression analysis (Helsen and Schmittlein 1993). We

specify the hazard function used to test our hypothe ses as follows:

hi(t/X) =

A0(f).exp{a1(experience/) + a2(number of models,)

+ a3(experience^ (number of models/)

+ a4(specific design^)

+ a5(specific designz)(number of models,)

4- ? (control variables, )},

where h^t/X) represents the hazard of failure for the

zth observation (VIN in our study) at mileage t, given a set of covariates X, A0(?) represents a baseline haz

ard that is a function of miles driven but does not

vary by individual VIN, the as are the coefficients of

the study variables, "control variables" represents a

vector of control variables, and ? represents a vector

of coefficients of the control variables. The variable

"experience" refers to either ln(cumulative volume) or time in use, discussed earlier. The variable "spe cific design" refers to either year-specific design or

carryover design, discussed earlier.

An important issue we considered was what type of hazard model to estimate. There are a wide array of

models and the choice of models depends to a great extent on the purpose of the study (Allison 1995). In

our study, we are interested in understanding what

drives the differences in failure rates across different

models at any mileage, rather than how the hazard

rate varies with mileage. In other words, we are not

interested in estimating A0(f). One hazard model, the

Cox proportional hazards model, requires no strict

assumption about A0(f) (Cox 1972). The Cox model

assumes that the ratio of hazards for any two indi

viduals is constant over time. Using this assump tion, a method of partial likelihood estimation may be

used. During estimation the baseline hazard, A0(?), is

eliminated. Practically speaking, the model eliminates

potential biases introduced by assuming a specific functional form for the distribution of the baseline

hazard. In our application, it is reasonable to assume

that all brakes share a similar pattern of hazard A0(?) with regard to miles driven, and that relative differ

ences in reliability at any mileage are a function of

differences in the study variables and control vari

ables included in our analysis. For this reason, we

believe the Cox model to be most appropriate for our

situation. Further, Allison (1995) states that the Cox

model is commonly used for hazard rate analysis and





has become a standard in hazard regressions. Regres sion coefficients in the Cox model have a relatively

straightforward interpretation. The coefficient is inter

preted as a risk ratio. By subtracting 1 from the risk

ratio and then multiplying by 100, one can interpret the coefficient as the percentage change in the haz

ard ratio for a one unit change in the independent variable.

One further methodological issue arises due to our

specific sample and self-reported nature of the data.

Because we have data only on those individuals who

experienced a rotor failure and who also chose to

report this failure, the hazard distribution for our data

could be different from that in the general popula tion. However, under the reasonable assumption that

the probability of reporting a failure is not a function

of any of the variables of interest in our study, it can

be shown that the coefficients of our study variables

have the same interpretation as they would if we had

in fact analyzed data representing both reported and

unreported failures (see the appendix).

6. Results Table 3 presents results of estimates obtained using the Cox proportional hazard model. Note that higher

reliability is associated with a lower hazard (nega tive coefficient) and lower reliability is associated with a higher hazard (positive coefficient). The chi-square statistics for all models in the table are significant at

the 0.01 level. The r-square values calculated based

on Allison (1995) range from 20.69% to 23.00%. The

first column presents results of a model with con

trol variables only As expected, higher proportional hazard rates are associated with higher horsepower,

higher population density, and brakes designed in the

early epoch. We see no significant association between

vented rotors, positive or negative percent weight dif

ference, the truck dummy variable, and the hazard

rate. Unexpectedly we see a significant negative asso

ciation between our precipitation variable and the

hazard rate. This result is not a function of influen

tial points in the data set. Further research yielded an alternative explanation for this result. When rain

ing, drivers often slow average speed. This results

in lower braking demands leading to lower failure

rates rather than the higher hypothesized rates of fail ure. We also see an unexpected positive association

between suggested retail price and the hazard rate.

These results suggest that cars with higher price are

of lower brake rotor reliability. The price variable may be associated with the propensity to report: owners

of higher-priced cars may report at lower mileages than owners of lower-priced cars (see the appendix).

Unfortunately, we cannot distinguish between these

two alternative explanations. We also notice a posi tive association between swept area per ton and the

Table 3 Cox Proportional Hazard Regression Estimating the Hazard of Brake Rotor Failure

I II III IV

Horsepower 0.005*** 0.004** 0.004** 0.004**

Swept area per ton 0.01** 0.01 0.01 0.01 Vented -0.13 -0.06 -0.12 -0.04

% Positive weight 0.32 0.56 0.92 0.76 difference

% Negative weight 0.77 0.68 1.36 1.12 difference

Suggested retail price 0.0001*** 0.0001*** 0.0001*** 0.0001***

Early epoch 0.74*** 0.81*** 0.88*** 0.82***

Truck -0.05 -0.12 -0.26 -0.14

Precipitation -0.006** -0.006** -0.007** -0.006**

ln(population density) 0.10** 0.10** 0.10** 0.10**

ln(cumulative volume) -0.23** ?

-0.23**

Time in use 0.01

Number of models -1.60** -0.24*** -1.62*

ln(cumulative volume) 0.10** ?

0.10*

xnumber of models

Time in use 0.01

xnumber of models

Year-specific design -1.18*** -0.65** -1.17*

Carryover design ? ?

-0.004

Year-specific design 0.53*** 0.31** 0.55**

xnumber of models

Carryover design ?

0.04

xnumber of models

Wald chi-square 160.20*** 179.72*** 175.18*** 181.13***

statistic

fl-squared (%) 20.69 22.84 22.34 23.00 N 693 693 693 693

***, **, *

coefficient significant at the p < 0.01, 0.05, and 0.10 levels,

respectively.

hazard rate. However, this variable is not significant in subsequent models.

Columns II and III present models containing our

two alternative measures of experience, ln(cumulative

volume) and time in use. In column II, we report results of a model using ln(cumulative volume) as

a measure of learning. We report a negative and

significant coefficient for year-specific design and a

positive and significant coefficient for the interaction

between year-specific design and number of models.

This finding is consistent with Hypothesis 1, which

states that the reliability of a brake will be higher on cars that are among the set of models the brake

was designed for, but that this effect will decrease

as the number of models the brake was designed for increases. We also report a negative and signifi cant coefficient for ln(cumulative volume) and a posi tive significant coefficient for the interaction between

ln(cumulative volume) and the number of models.

This finding is consistent with Hypothesis 2, which

states that reliability is increasing in cumulative expe rience, but that this effect is mitigated by the num

ber of models over which the experience is gained. In column III, we report results of a model in which




time in use is the measure of experience. Consistent

with column II and Hypothesis 1, we report a sig nificant negative coefficient for year-specific design and a positive significant coefficient for the interac

tion between year-specific design and the number of

models. However, we find no significant coefficients

for our second measure of experience, time in use, or

for the interaction between time in use and the num

ber of models.7 This suggests that cumulative volume

better captures the effect of experience in our data.

Schoonhoven (1981) suggests analyzing the deriva

tive of the estimated equation for more careful exam

ination of interaction effects when the main effect and interaction effect have opposite signs. For ease

of exposition, we ignore the subscript / that refers to

specific VINs, in our regression model. Our regression model using ln(cumulative volume) is

h(t/X) =

A0(f). expja^ ln(cumulative volume)

+ a2(numDer of models)

+ a3 In (cumulative volume)

(number of models) + a4 (specific design)

+ a5 (specific design) (number of models)

+ /3(control variables)}.

Taking the derivative of the hazard rate h with respect to volume, and setting this to zero, we have

dh(t/X) ?(cumulative volume)

= h(t/X)(_^_ i a3(number of models)\ =Q

\ cumulative volume cumulative volume /

Solving for the number of models at which dh(t/X)/d cumulative volume =

0, number of models = ? ax/a3.

For our data set, with ax = ?0.23 and a3

= 0.10,

the proportional hazard rate decreases with cumula

tive volume when the number of models over which

the volume is spread is less than 2.30, and starts to

increase with cumulative volume when the number

of models is greater than 2.30. In our data, roughly 50% of all observations have brake rotors that are

shared across more than two models. By similar logic, we analyze the interaction term between year-specific

design and number of models. Here, the benefits of

designing for a specific set of models are eliminated

when the number of models equals 2.22. In our data,

roughly 50% of all observations have brake rotors that

were designed for more than two models.

Column IV reports results of tests including carry over design as an additional measure of design speci

ficity. Consistent with the results of column II, we

report significant effects for year-specific design and its interaction with models. However, the coefficient on carryover design and its interaction with num

ber of models is not significant. These results sug

gest that the benefits of design specificity are found

only in the year of brake rotor introduction and not in subsequent years. A model (not reported) combin

ing year-specific design and carryover design into a

single variable yielded insignificant results. We checked outlier diagnostics and found that the

results in Table 3 are robust to the influence of sin

gle data points. Further, we noted no problems with

multicollinearity, except for the interaction terms, for

which the variance inflation factor is quite high.8 Our data also exhibit uneven distribution of observations over brake rotors. We tested our results for robust ness to this distribution by controlling for brake clus ters as suggested by Allison (1995) and note that the

results are consistent with those reported in Table 3.

We reestimated our model using different subsets of the data to test the robustness of our results. These

model runs are reported in Table 4. We only report results for models using the year-specific design and

the cumulative volume variables.

Our first concern deals with a potential endoge nous association between quality and the number of

models on which a brake rotor is used. We have no

direct hypothesis about the number of models and

quality. However, if designers are given feedback on

the quality of a brake, a designer may choose to reuse a brake because of its observed quality as opposed to the number of models a new brake is designed for affecting quality by altering design specificity. Our

industry interviews yielded mixed opinions as to the existence and strength of this feedback loop. Also,

reliability data only becomes available a few years after a brake's introduction. Nevertheless, to alleviate

this potential concern, we eliminate instances where

quality feedback may have led to a reuse decision

by eliminating all observations where a brake was

not designed for the specific model or models.9 Col umn I of Table 4 reports the results of this analysis.

We observe results consistent with those in Table 3.

A second concern raised by discussions with industry

7 We also tried a specification including both cumulative volume

and time in use to capture experience effects. Our results were qual

itatively similar in this case.

8 We observe that in models that include the main effects of cumu

lative volume and number of models, but exclude the interaction

term, the signs of the main effects do not change from what is

reported in columns II and III.

9 By placing this constraint on the data, we not only reduce the

opportunity for endogenous effects, but also reduce the variance in

the number of models. Importantly, this reduction in the number

of models may occur in instances where the detrimental effects of

sharing may be most likely.





Table 4 Robustness Tests of Cox Proportional Hazard Models

I First time

usage

No early failures

No late failures

IV

North American

volume

V

Passenger cars

VI

Trucks

VII Eliminate rotors

with caliper failure

Horsepower 0.002 0.004**

Swept area per ton 0.007 0.006

Precipitation -0.003 -0.006*

ln(population density) 0.11** 0.11*** Vented 0.28 0.02 % Positive weight diff. 3.01 ** 0.64 % Negative weight diff. 1.41 0.52

Suggested retail price 0.0001*** 0.0001*

Early epoch -0.31 0.94*** Truck -0.20 -0.07

ln(cumulative volume) -0.25* -0.26***

Number of models -2.45** -1.73***

ln(cumulative volume) 0.16** 0.11** x number of models

Year-specific design -1.29*** -1.21***

Year-specific design 0.61*** 0.54***

x number of models

Chi-square statistic 181.66*** 183.77***

ff-squared (%) 26.54 24.14 N 589 665

0.005**

0.007

-0.007**

0.09**

-0.06

0.28

-0.00001

0.0001*?

0.80***

-0.09

-0.19**

-1.26***

0.08*

-1.07***

0.48**

166.65***

21.68

682

0.004*

0.007

-0.006**

0.09**

-0.07

0.76

0.55

0.0001*

0.61*

-0.57*

-0.41***

-2.99***

0.20***

-1.49***

0.69***

176.52***

23.34

664

0.002

0.02***

-0.009**

0.06

-0.88*

1.87

1.64

0.0001*

-0.07

-0.39**

-3.36***

0.22**

-1.67***

0.81***

158.59***

26.07

525

0.003

-0.002

-0.004

0.21**

-0.03

0.70

1.53

0.0001 1.19***

-1.05***

-7.23**

0.53**

-2.23***

1.20**

43.03

22.60

168

0.005*^

0.007

-0.006**

0.09**

-0.16

0.18

1.28

0.0001*

0.79***

-0.22

-0.23**

-1.48**

0.09*

-1.24***

0.54***

178.62***

23.49

667

, **, *

coefficient significant at the p < 0.01, 0.05, and 0.10 levels, respectively.

experts deals with a potential "lemon" effect, mean

ing that a certain number of parts fail at the out

set of an automobile's introduction. These failures

may not have any association with the factors in this

study. To examine the robustness of our results to

"lemon-" related failures, we eliminated observations

with failures that had occurred at less than 500,1,000, and 2,000 miles. The results of the 1,000-mile cutoff are qualitatively similar to the 500- and 2,000-mile results and are shown in column II of Table 4. Third,

we observe in Figure 1 that failures are reported on

brakes up to 134,000 miles. There exists the possi

bility that failures on high-mileage observations are

not failures on original equipment, but on replace ment brakes. We reran our models after truncating

the failures at different levels down to 100,000 miles.

The results of the regressions after eliminating all fail

ures with mileage over 100,000 miles is shown in col

umn III of Table 4. Fourth, we noted a limitation of the

data, which is that cumulative volumes are calculated

for North American auto sales only. Thus, volumes for

brakes shared globally will be understated, creating a

potential bias in the association between volume and

the hazard rate. We were unable to acquire precise volume estimates for brakes shared globally. How

ever, through interviews with company representa tives and automotive industry experts we were able to

identify several models where this effect was likely to

be most severe, and we reran the analysis eliminating these models. These results are shown in column IV

of Table 4. Fifth, our data contain both passenger cars

and trucks. It is possible that the magnitude of these

factors differs greatly across the types of vehicles. Col

umn V of Table 4 shows results for passenger cars

and column VI shows results for trucks. Sixth, there

exists the possibility that the failure of the rotor was

due to failure of other parts of the braking system. To mitigate this concern, we obtained detailed notes

on each reported failure. Using these notes, we iden

tified failures for which the rotor failure was men

tioned in conjunction with failure of another part of

the braking system. We estimate models after elimi

nating these observations in column VII of Table 4.

We note in Table 4 that the results of regressions esti

mated using subsets of our data consistently show

support for Hypotheses 1 and 2.

7. Discussion We find support for the two questions we address

in our research. Rotor reliability is higher when the

model using a rotor is among the set of models that

the rotor was designed for, than if this is not the case.

However, this specific-design effect is dissipated as

the number of models that the rotor was designed for increases. Further, greater experience with a brake

rotor is associated with higher reliability. However, the positive impact of cumulative experience on the

reliability of a brake rotor is moderated by the num

ber of models over which this experience is attained.

The inherent tension in these findings merits further

analysis and interpretation. To facilitate this process, we compare the ratios of relative hazards between dif

ferent design scenarios. The use of ratio comparison




with a Cox proportional hazards model isolates the

effects of variables of interest.

7.1. Scenario 1: Reuse of an Existing Rotor on a

Continuing Model

Consider a scenario where an automobile model (e.g.,

the Ford Escort) is being redesigned. To maximize

reliability, should the rotor be carried over from the

previous year's Escort model or should a new rotor

be designed for the new model version? Using the estimates in Table 3, column II and a general hazard

function, we calculate the ratio of hazard between a

newly designed brake rotor and a brake rotor that was used in the previous model year. Let V denote

the expected volume on the new brake, CV the cumu

lative volume of the reused brake rotor excluding the

volume from the new model, and N the number of models on which the existing rotor is in use (e.g., the

existing model might be used on the Escort and Lynx). After simplification the resulting ratio is as follows:10

hazard of newly designed rotor

hazard of reusing a rotor with a given cumulative volume

?-1.18+0.53-l-0.23-ln(V)-1.6-l+0.10-ln(V>l _

?-0.23-ln(V+CV)-1.6-N+0.10-N-ln(V+CV) '

Intuitively, we weigh the reliability gains from

product-specific design associated with a new rotor

against the reliability gains from larger production volume, and hence greater experience with the reused rotor. The case for new design will dominate the case

for reusing the existing rotor when the above ratio

is less than one. Figure 6 illustrates how this ratio

changes with V and CV. For purposes of discussion, the calculations in Figure 6 assume that N is equal to

two, which is the median number of models sharing a brake rotor in our data set. The x-axis shows rep

resentative values from our data set for anticipated

first-year volume V of a new brake rotor that is used on a single model. The curves are for the minimum, first quartile, median, third quartile, and maximum

values of cumulative volume for a rotor that is shared across two models in our data set. The figure illus trates that as the anticipated volume of the new brake rotor increases, the effect of specific design tends to

dominate the learning effects from cumulative vol ume of the reused rotor. This effect occurs because as

the volume V of the new rotor increases, the learning effects obtained from the new rotor, combined with

the benefit for specific design, more than compen sate for the learning effects lost when choosing not to

Figure 6 Ratio of Hazard of New Design to Hazard of Reused Design as a Function of Volume (V) of New Rotor, and Cumulative

Volume (CV) of Reused Rotor

c

S 1 2_

x (7,869 Min V, 1.21) I _+_ Min cv = 57k ?

'

\ ^~~ 1stQtlCV = 327K

S j\ ~-*~- Median CV = 577 K

S 4\ ~^~ 3rd Qtl CV = 961 K

Anticipated volume (V) of the new brake rotor

reuse the existing brake rotor. Across the entire range of cumulative volume (CV) for an existing rotor in our data set, if the new rotor volume is close to the

minimum value seen in our data set, reuse results in

a lower expected hazard. If the new rotor volume is

above the first quartile of volumes from our data set, the new design results in a lower expected hazard.

7.2. Scenario 2: Design for Multiple Models

Consider a scenario where a designer needs to design brake rotors for a series of models in some model

year?for example, while designing a new platform. The designer can capture the benefits of design speci

ficity by creating a unique brake rotor for each model or can capture the potential learning effects associated

with greater experience by using a universal design that serves all models. In this scenario, we assume

that the anticipated volume of each individual model

equals V. The resulting ratio is as follows:

hazard of newly designed rotor

hazard of universal design

?-1.18+0.53(l)-0.23-ln(V)-1.6(l)+0.104n(V>l ""

e-1.18+053(N)-0.23-]n(N-V-lMN)+0.10-(N)-]n(N-V)

'

Figure 7 shows values of this ratio for different val ues of V and N. Note that a set of uniquely designed rotors is more and more likely to dominate the uni

versal design as the anticipated volume per model (V) increases. With respect to the number of models, we

see an interesting effect. For volume per model, V

set at its minimum value in our data set, the ratio

of hazards of unique design to universal design first

increases and then decreases with the number of mod

els N. In this scenario, universal design dominates

10 For simplicity, we assume that the value of %-positive-weight

difference for the reused rotor is 7.72%, its mean value in our data

set. Also, we assume that the swept area per ton is the same for

the new and reused rotors. These assumptions do not change the

direction of our results.




Figure 7 Ratio of Hazard of Model-Specific Designs to Hazard of Universal Design as a Function of Volume per Model (V) and Number of Models Sharing the Rotor (A/)

O 50,000 100,000 150,000 200,000 250,000 300,000

Anticipated volume per model (V)

if there are two to eight models, but for nine or

more models, unique design dominates. This relation

is driven by the interaction between volume and the

number of models. Beyond a crossover volume per model V of 12,500 units, the hazard ratio is monoton

ically decreasing in number of models N. The inter

action among the variables is not straightforward, and the model enables a manager to avoid simplis tic heuristics such as "at low V, universal design is

increasingly better for reliability as N increases/'

7.3. Scenario 3: Reuse on a Continuing Model

with Uncertain Demand Volume

Consider a situation similar to scenario 1, but where

the demand for the continuing model is uncertain.

Suppose mean demand volume for the continuing model is 100,000 units, based on an equal chance of

two demand outcomes: 100,000 + D and 100,000 - D.

Volume variability is higher for larger D. In this setup we consider three scenarios, for low, medium, and

high volume variability. With high volume variability, for a swing in volume D that could be either posi tive or negative with equal probability, the reduction

in reliability of the new rotor relative to the existing rotor is a lot worse if a downswing in volume materi

alizes, than the increase in reliability of the new rotor

relative to the existing rotor if an upswing in volume

of the same magnitude materializes. Figure 8 shows

expected reliability ratios for the new to the existing rotor for different levels of variability in demand, as

well as the reliability ratio based on expected vol ume. If we look only at expected volume, then regard less of variability, the new rotor appears to provide

higher reliability than the existing rotor, for all val ues of cumulative volume of the existing rotor. How

ever, if we factor in variability in volume of the new

rotor, we find that it is better to go with reuse if the

volume variability is high enough and the cumula

tive volume of the existing option is high enough.

Figure 8

c ?) 75 1-10 <D "O Ui 1.05

1.00

3 0.95

0.90

O > 0.85

"? 0.80

B ?-75^

'?= 0.70

Ratio of Reliability of New to Existing Design as a Function of Variability in New Design Volume and Cumulative Volume of Existing Design

(3,576 K, 1.04)

s^" (576 K, 0.99)

K (56 K, 0.94)

~~o~~ Ratio using expected volume ?o? Expected ratio, low volume variability -a?Expected ratio, medium volume variability ?x-~ Expected ratio, high volume variability

500 1,000 1,500 2,000 2,500 3,000 3,500 4,000

Cumulative volume of existing design in thousands

Although intuitively it makes sense to go with a con

servative option (reuse) in the face of unpredictable demand, our model helps understand how unpre dictable demand has to be for it to make sense to go

with the conservative approach. Although we have

examined a simple demand distribution for illustra

tion, our model can be used in a similar way to navi

gate more complex distributions.

7.4. Scenario 4: Investment in Increasing

Design Modularity We expect the positive impact of unique design on

reliability to be greatest in the case of highly inte

gral architectures, where design fit is most important. A more modular architecture would facilitate compo nent sharing by lessening the importance of design fit. Suppose a firm decides to invest design effort

in modularizing its product's design. One benefit

from doing this would be a reduction in the pos itive impact of unique design on reliability, i.e., a

reduction in the magnitude of the coefficient of year

specific design. Suppose the magnitude of this coef

ficient is reduced by 50% (i.e., moving from ?1.18

to ?1.18*0.5) via moving

to a more modular archi

tecture. Figure 9 shows how the ratio of hazards for

designing uniquely versus reusing a rotor varies over

volume of the new design, for a more integral ver

sus a more modular architecture. For simplicity, the

cumulative volume of the reused rotor is set at its

median volume in our data set. We find that with

the more modular setup, reuse dominates designing anew over the entire range of volumes for the new

rotor, whereas in the current (more integral) setup, reuse dominates designing anew only if the new

rotor's volume is at or below the first quartile for a

new model's first-year volume in our data set. Thus,

our model helps us see the reliability impact of reuse




Figure 9 Ratio of Reliability of New to Existing Design as a Function of Integral vs. Modular Design

c:

d) .r' "O

8 2.0

o 0)

SB10

o (0

CO

* (Min V, 2.07) \

Vm (IstQtIV, 1.73)

Median CV = 577 K, integral Median CV = 577 K, modular

-??S^L^ (Max V, 1.33)

-1-1-1 0 100,000 200,000 300,000

Anticipated volume (V) of the new brake rotor

versus designing uniquely, for a given level of modu

larity. Together with this information, the design costs

saved via reuse can be weighed against the design costs associated with making the design more modu

lar, to decide how modular the design needs to be.

7.5. Scenario 5: Investment in Improving

Knowledge Transfer

The extent to which learning is transferred across fac

tories varies with organizational and structural factors

(Argote 1999). Similarly, such factors should impact

learning across models, within one factory or across

factories. How can a firm evaluate the benefits from

investing resources to increase cross-model learning? Our model provides one approach. If learning trans

fer improves, the coefficient of N ln(y) in our model

should be reduced in magnitude. Similar to scenario 4

above, we will find that reuse over multiple models

becomes more feasible with better learning transfer,

and, importantly, the model helps estimate how many models can share a

component.

The scenario analyses above illustrate different de

cision-making contexts for component sharing, and

identify the conditions where the unique design effects dominate and the conditions where the learn

ing effects dominate, within our data. The scenarios

were chosen because they are common decisions for a

designer, not because they represent a comprehensive list of design scenarios. Other scenarios are certainly

possible, and our approach provides a way to evalu

ate these scenarios.

8. Limitations and Conclusions The data are limited to one automotive company and are the product of the design processes at that

company. Generalization of the results will depend, in part, on the similarities among design processes across

companies. Further, our analysis focuses on a

single component, the brake rotor. Despite this, we

believe our methods and results may be generalized

in the following ways. First, brake rotors are mechani

cally similar to many other components in an automo

bile and components in other products. Second, the

methods and measures used to estimate the impact of component sharing on failure rate of brake rotors

are quite general and are applicable to components in

other assembled products. Increased experience enhances both learning by

doing in manufacturing as well as learning from

end-user feedback in the field, and both of these

mechanisms can result in better reliability. Although we are able to capture the overall effect of experience on reliability, we are unable to separate the effects

of these two mechanisms. We also recognize the fact

that we have not been able to collect all driver-specific control variables. Age and gender are examples of

variables for which hypotheses related to brake failure

might be formed. To the extent these variables are cor

related with our test variables, our study suffers from

omitted variable bias. Another variable that we did

not observe is design effort, which could be higher for

brakes intended for high-volume cars. We also did not

observe whether engineers planned ahead for future

vehicles in which a rotor would be used, which might result in purposeful sharing.

This study provides the first empirical evi

dence relating one dimension of quality?component

reliability?to component-sharing strategies. We find

support for the hypothesis that higher reliability is

associated with a component designed specifically for a model in a given year, but that this effect is

reduced when the component is designed for simul

taneous use on other models. A component that is

designed specifically for a model is likely to have the

best design fit in terms of meeting the specific design

requirements and constraints of that model, result

ing in higher reliability This fit aspect can be diluted

if a component is designed simultaneously for mul

tiple models, because different models are likely to

have different design requirements and constraints.

This finding suggests that the popular design strat

egy of developing multiple products off a common

platform with shared components can in some cases

compromise product quality We also observe that

improved reliability is associated with greater experi ence, but this effect decreases as the number of mod

els over which this experience is attained increases.

This dilution effect can occur due to incomplete trans

fer of knowledge gained via experience with one

model to other models that use the same compo nent, for example, because these different models

are made at different manufacturing locations, thus

offering less opportunity for knowledge exchange.

Comparison of the specific design effect and the expe rience effect suggests that the dominance of one effect

over another will depend on the sharing situation





being considered. These findings suggest that design ers and researchers should look beyond the inventory and cost savings associated with component-sharing strategies and also include the quality ramifications

of component sharing while formulating component

sharing strategies. Future research should incorpo rate these quality trade-offs in prescriptive models for

component sharing. Although the trade-offs we have

focused on are quite general, future empirical research

may identify nuances to these trade-offs in specific industrial settings.

Acknowledgments The authors are

grateful to executives, managers and engi neers at Ford and General Motors, several automotive

experts and race car enthusiasts, and the Department of

Transportation for providing them with information; and

to Noah Springer, Ryan Sundquist, Prasanna Velamuri,

and Baocheng Yang for research assistance. The authors

are grateful to Mary Margaret Frank, Richard Holubkov,

Nils Rudi, Christian Terwiesch, and seminar participants at

UCLA, Wharton, Harvard Business School, University of

Chicago, INFORMS, and the Wharton Technology Minicon ference for their valuable comments and, in particular, to

Steven Stern for his help with sampling related issues. This research was

supported in part by a grant from the Batten

Institute for Innovation and Entrepreneurship at the Uni

versity of Virginia.

Appendix Let X denote the vector of covariates?study variables

and control variables?with which the hazard of failure at

mileage t is assumed to vary. At any mileage t, we can

state the hazard of failure given X generally as h(t/X) =

A0(f)exp{?/3X}, where ? is a vector of coefficients. Let p(report/t, Xj) denote the probability that the owner

of a vehicle would file a report of a rotor failure if a failure were to occur at mileage t, and given

a vector of covari

ates Xl7 where Xl may partially overlap with X. The prob

ability of reporting if a failure were to occur is likely to

vary with the mileage at the time of failure, and also per

haps with some of the covariates in X. For example, if city drivers are more

likely to complain than country drivers,

then the population density of the area where the vehicle

was driven may impact the probability of reporting. Let

r(t/X, Xj) denote the hazard function for those individuals who both experienced

a rotor failure and chose to report it.

The hazard function that we can estimate from our data is

in fact r(f/X,X1). By conditioning on the occurrence of a

failure at time t, r{i/X,Xx) =

h(t/X)p(report/t,X1). Taking the derivative of the logarithm of r(t/X, X-?) with respect to

X, we have

^logr(f/X,X1) _ dlogh(t/X) dlogp(report/t,X1)dX1 dx

" sx +

?x? lx' Because an individual car driver likely does not know

the cumulative volume of the brake rotor used in his or

her car, the number of models on which that rotor was

used, or whether that rotor was designed specifically for

the car, it is reasonable to assume that none of the variables

of interest in our study

are in the vector X1. Therefore, the

second term in the right-hand side of the above equation does not impact

our study variables. In interpreting the Cox

regression coefficients for r(t/X, X^, the components of ? for our

study variables have the same interpretation

as they would in a Cox regression that estimates the unobserved

hazard h(t/X). Note that thinking in terms of the probability of report

ing if a failure were to occur at time t allows us to model

scenarios where a failure has not actually occurred by time

t. It also allows us to model scenarios where the vehicle was

taken off the road prior to time t due to some non-brake

related issue, precluding the possibility of a brake failure at time t. In this situation, if the reason the vehicle was taken

off the road has nothing to do with why the brakes might fail, then the components of ? for our

study variables would

continue to remain unbiased.

Brake rotors typically fail?i.e., require repair or

replace

ment?within the first few years of operation. Thus, except

for car models introduced in the last few years of our study,

most cars on the road during the period of our study would

have experienced their first rotor failure. Therefore, by con

ditioning on failure as above, we are

accounting for a large

part of the risk set.

References

Adler, P. 1990. Shared learning. Management Sei 36(8) 938-958.

Allison, P. D. 1995. Survival Analysis Using SAS: A Practical Guide.

SAS Institute, Cary, NC.

Anzoni, Y, H. A. Simon. 1979. The theory of learning by doing.

Psych. Rev. 86 124-140.

Argote, L. 1999. Organizational Teaming: Creating, Retaining and

transferring Knowledge. Kluwer Academic Publishers, Norwell, MA.

Baloff, N. 1971. The extension of the learning curve. Oper. Res.

Quart. 22 329-340.

Benkard, C. L. 2000. Learning and forgetting: The dynamics of air

craft production. Amer. Econom. Rev. 90(4) 1034-1054.

Carley, L. 2002. Big three brake symposium. Tech update. Brake and

Front End (November).

Cox, D. R. 1972. Regression models and life tables. /. Roy. Statist.

Soc.f Ser B. 34(2) 187-220.

Dasgupta, A., M. Pecht. 1991. Material failure mechanisms and

damage models. IEEE Trans. Reliability 40(5) 531-536.

Desai, P., S. Kekre, S. Radhakrishnan, K. Srinivasan. 2001. Product

differentiation and commonality in design: Balancing revenue

and cost drivers. Management Sei. 47(1) 37-51.

Dick, A. R. 1991. Learning by doing and dumping in the semicon

ductor industry. /. Eaw Econom. 34 662-669.

Fine, C. 1986. Quality improvement and learning in productive sys tems. Management Sei. 32(10) 1301-1315.

Fisher, M. L., K. Ramdas, K. T. Ulrich. 1999. Component sharing in the management of product variety: A study of automotive

braking systems. Management Sei. 45(5) 297-315.

Gupta S., V. Krishnan. 1999. A product family-based approach for

integrated component and supplier selection. Production Oper.

Management 8(2) 163-182.

Hatch, N. W., D. C. Mowery. 1998. Process innovation and learn

ing by doing in semiconductor manufacturing. Management Sei.

44(11) 1461-1477.




Heese, H. S., J. M. Swaminathan. 2006. Product line design with

component commonality and cost-reduction effort. Manufactur

ing Service Oper. Management 8(2) 206-219.

Helsen, K., D. C. Schmittlein. 1993. Analyzing duration times in

marketing: Evidence for the effectiveness of hazard rate mod

els. Marketing Sei. 12(4) 395-414.

Ittner, C. 1996. Exploratory evidence on the behavior of quality costs. Oper. Res. 44(1) 114-130.

Kececioglu, D. 1991. Reliability Engineering Handbook, Vol. 1. Prentice

Hall, Englewood Cliffs, NJ.

Kim, K., D. Chhajed. 2001. An experimental investigation of valua

tion change due to commonality in vertical product line exten

sion. /. Product Innovation Management 18(4) 219-230.

Krishnan, V., S. Gupta. 2001. Appropriateness and impact of

platform-based product development. Management Sei. 47(1) 52-68.

Lapr?, M. A., N. Tsikriktsis. 2006. Organizational learning curves

for customer dissatisfaction: Heterogeneity across airlines.

Management Sei. 52(3) 352-366.

Lapr?, M. A., L. N. Van Wassenhove. 2001. Creating and trans

ferring knowledge for productivity improvement in factories.

Management Sei. 47(10) 1311-1325.

Lieberman, M. 1984. The learning curve and pricing in the chemical

processing industries. RAND J. Econom. 15 213-228.

MacDuffie, J. P., K. Sethuraman, M. Fisher. 1996. Product variety and manufacturing performance: Evidence from the interna

tional automotive assembly plant study. Management Set 42(3) 350-369.

Macher, J. T. 2003. Vertical disintegration and process innova

tion in semiconductor manufacturing: Foundries vs. inte

grated producers. Working paper, Georgetown University,

Washington, D.C.

Mukherjee, A. S., M. A. Lapr?, L. N. Van Wassenhove. 1998. Knowl

edge driven quality improvement. Management Sei. 44(11) S35-S59.

Ramdas, K. 2003. Managing product variety: An integrative review

and research directions. Production Oper. Management 12(1) 79-101.

Ramdas, K., M. Sawhney. 2001. A cross-functional approach to

designing multiple line extensions for assembled products.


Ramdas, K., M. L. Fisher, K. T. Ulrich. 2003. Managing variety for assembled products: Modeling component systems sharing.

Manufacturing Service Oper. Management 5(2) 142-156.

Reagans, R., L. Argote, D. Brooks. 2005. Individual experience and

experience working together: Predicting learning rates from

knowing who knows what and knowing how to work together.


Rutenberg, D. P. 1971. Design commonality to reduce multi-item

inventory: Optimal depth of a product line. Oper. Res. 19(2) 491-509.

Schoonhoven, C. B. 1981. Problems with contingency theory: Test

ing assumptions hidden within the language of contingency

theory. Admin. Sei. Quart. 26(3) 349-377.

Swaminathan, J., S. Tayur. 1998. Managing broader product lines

through delayed differentiation using vanilla boxes. Manage ment Set. 44(12) S161-S172.

Thonemann, U. W., M. L. Brandeau. 2000. Optimal commonality in

component design. Oper. Res. 48(1) 1-19.

Ulrich, K. T. 1995. The role of product architecture in the manufac

turing firm. Res. Policy 24(3) 419^40.

Ulrich, K. T., D. J. Ellison. 1999. Holistic customer require ments and the design-select decision. Management Sei. 45(5) 641-658.

Wong, K. L. 1995. A new framework for part failure-rate prediction models. IEEE Trans. Reliability 44(1) 139-146.

Wright, T. 1936. Factors affecting the cost of airplanes. /. Aeronautical

Sei. 3(4) 122-128.

Yang, K., K. C. Kapur. 1997. Customer driven reliability: Integration of QFD and robust design. IEEE Annual Reliability Maintainabil

ity Sympos. Proc., Philadelphia, 339-344.

Yano, C. A., G. Dobson. 1998. Profit optimizing product line

design, selection and pricing with manufacturing cost consid

eration. T. H. Ho, C. S. Tang, eds. Product Variety Manage ment: Research Advances. Kluwer Academic Publishers, Boston/

Dordrecht/London, 145-176.



does component sharing help or hurt reliability? an ...faculty.london.edu/kramdas/ramdas and...

Documents