extended warranty models

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1

A Study on Extended

Warranty Models

Prof. Dr. Alagar Rangan

Vahid.H KhiabaniDepartment of Industrial Engineering

Eastern Mediterranean UniversityNorth Cyprus


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Outline

Introduction

Extended Warranty Model

Extended Warranty Model based on TotalSales Volume

Extended Warranty Model based on TotalSales Volume and Customer Satisfaction

Conclusions

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Introduction

A warranty is a contractual obligation thatassures the buyer that the product will

perform its intended function at aspecified level under the stated conditionsfor a specified period of time. If it fails to

do so, the manufacturer will repair/replacethe product at no cost or at a reducedcost to the buyer as the case may bedepending on the warranty terms.

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Introduction

The manufacturer uses warranty as a toolof advertisement in competition to other

products.

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5A schematic diagram of various warranty policies


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Introduction

Presently a large number of products arebeing sold in the market with long term orextended warranty policies. This is mainly

due to fierce competition in the marketshare and customer demand. An extendedwarranty is the extension of the base

warranty and is an obligation on the partof the manufacturer for further service tothe consumer beyond the free

replacement period W. 6


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Introduction

On average 27% of the new car buyerspurchased extended warranty.

Sears Roebuck reported a revenuegeneration of nearly US $1 billion from thesale of extended warranties.

The annual sale of extended warranties inUK alone is more than US $1 billion.

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Literature Review

Blishke and Murthy (1994), Anisur andChattopadhyay (2006), and Thomas and Rao (1999)

Nguyen and Murthy (1984 and 1986)

Mamer (1982)

Sahin and Polatoglu (1996)

Amit Monga and Ming J.Zuo (1998)

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Literature Review

Mitra and Patnakar (1997)

Lutz and Padmanabhan (1998)

Hollis (1999)

Yeh Lam and Peggo Kwok Wai Lam (2001)

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The Model

A repairable product is purchased at timet=0 which is subject to failures. The times

between successive failures areindependently and identically distributedwith distribution function F (). Failures

are classified as type I and type II failureswith probabilities q and p respectively.

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The Model

Type I failures are minor in nature andcan be minimally repaired (Barlow and

Proschan, 1965) restoring the product toits original condition just prior to failure. Ifa product is minimally repaired at time t,

then its failure rate after minimal repair isgiven by

11

(t)F

f(t)r(t)


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The Model

Also it is well-known that if productfailures are maintained by minimal repairs

only, then the failures are governed by anon-homogeneous Poisson process withintensity function r (t). A type II failure is

major and necessitates productreplacement.

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13

The Model

Major Repair

Minimal Repair

0

0

t+xt

t t+x

0

:Minor failure

:Major failure


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The Model

The customer at the time of the purchasebuys the product along with FRW with an

option for an extended warranty policy atthe expiry of FRW for an additional cost.The manufacturer while agreeing to

replace items on failure of any type duringthe FRW period W offers the followingextended warranty policies:

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Policy 1 (Tm)

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0 w

1Y


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Policy 2 (Tk)

16

0 w

2Y

12

,min YTY k

0 w kth

2Y


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Policy 3 (T)

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0 w

3Y

0 w W+T

3Y


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Cost Analysis

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Cost Analysis

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Numerical Illustration

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The reason for writing LAP in the aboveform is to separate the cost parameters

under the control of the manufacturer andthe parameters associated with productlifetime.

For the specific choice of the costparameters not shown here in our case,the long run average profits under

different policies are given by: 21


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Optimization Based on Total

Sales Volume We wish to determine the optimal product

price and warranty periods based on the

total sales volume. The motivation forchoosing such an objective is that salesvolume is directly affected by these

variables.

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Sales Volume

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Sales Volume The manufacturers total long run average

profit under the assumed demand function

is seen to be

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Sales Volume

29

In our analysis the extended warrantyperiod is fixed once the model parameters

are known. Thus, we treat , the extendedwarranty period for policy i, as fixed andmerge it with the amplitude factor so that

the total long run average profit is


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Sales Volume

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Policy 1

Policy 3Policy 2


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EXT Warranty based on T.S.V

and Customer Satisfaction Each dissatisfied customer can impact future

sales in several ways and this has serious cost

implications for the manufacturer. Though customer satisfaction with a purchased

product is influenced by several reasonsincluding product price and after sale service,

the main factor that attracts (detracts) acustomer to return to buy the product again isits performance over the warranty and extendedwarranty periods.

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and Customer Satisfaction Existing warranty models in the literature

mainly focus on minimizing total warranty

cost to optimize for warranty period andmaintenance strategies; however they failto take into consideration the penalty cost

of customers non return in computingtheir objective functions as such a penaltyseems to play a major rule. Lasser et al.(1998), Jack and Murthy (2004)

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and Customer Satisfaction We assume that the customer satisfaction

of the product depends on the number of

major failures during the warranty andextended warranty periods. It is tacitlyassumed that the customers satisfaction

is not influenced by minor failures.

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and Customer SatisfactionIf W is the FRW and T is the extendedwarranty period, the customer satisfaction

depends on N2(W+T), the number majorfailures in W+T. We assume that theconditional probability function of customerreturn given N2(W+T) = k is specified as

follows:

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and Customer Satisfaction

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Other forms for the customerdissatisfaction depending on the product

could be chosen. For instance when thecustomer is highly sensitive to failures ofthe product, one can choose to be:


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and Customer Satisfaction Let be the probability of exactly k

major failures during the warranty and

extended warranty period for ourextended warranty model. Then theprobability Pr of the customer making a

repurchase of the product is given by:

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and Customer Satisfaction

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Let Cp be the penalty cost to themanufacturer for a dissatisfied customer

not returning to repurchase the product,then the manufacturers total profitfunction given in previous section can be

rewritten as:


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Policy 2

Policy 1

Policy 3


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Conclusion

The present work develops a newextended warranty model with different

options for the consumer. Several extensions and generalizations are

possible from here on, and in the

following we will spell out a few of them:

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Different types of failures

p and q functions of the time

General repair

Alternate forms of demand function

Optimal burn in period

Preventive maintenances

Other factors that influence the product sales

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References Amit Monga. and Ming J.Zuo. Optimal system design considering maintenance

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References Hollis, A. Extended warranties, adverse selection and after markets, The

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References

Lassar, W.M. Folkes, V.S. Grewal, D. and Costley, C. Consumer affective

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Research Logistics Quarterly, 29(2), pp. 345-356, 1982. Matis, T.I. Jayaraman, R. and Rangan, A. Optimal price and pro-rata decisions

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Stadje, W. and Zuckerman, D. Optimal Strategies for some repair-replacement Models, Advances in Applied Probability, 22, pp. 641-656,1990.

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extended warranty models

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