BITS PilaniPilani | Dubai | Goa | Hyderabad

QM ZG536DESIGN OF

EXPERIMENTSShaibal Kr. Sen

Session 01

BITS PilaniPilani | Dubai | Goa | Hyderabad

DESIGN of EXPERIMENTS (DOE) INTRODUCTION

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1. Introduction

2. Preparation

3. Components of Experimental Design

4. Purpose of Experimentation

5. Experimental Design Guidelines

6. Experimental Design Process

7. Test of Means – One Factor Experiment

8. Multifactor Experiment

9. Advanced Topic – Taguchi Methods

BITS Pilani, Deemed to be University under Section 3 of UGC Act, 1956

1. Introduction

The term experiment is defined as the systematic procedure carried out under controlled conditions in order to discover an unknown effect, to test or establish a hypothesis, or to illustrate a known effect. When analyzing a process, experiments are often used to evaluate which process inputs have a significant impact on the process output, and what the target level of those inputs should be to achieve a desired result (output). Experiments can be designed in many different ways to collect this information. Design of Experiments (DOE) is also referred to as Designed Experiments or Experimental Design - all of the terms have the same meaning.

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Experimental design can be used to reduce design costs by

speeding up the design process, reducing late engineering

design changes, and reducing product material and labor

complexity. Designed Experiments are also powerful tools to

achieve manufacturing cost savings by minimizing process

variation and reducing rework, scrap, and the need for inspection.

2. Preparation

General knowledge of statistics (Histogram, Statistical Process

Control, and Regression and Correlation Analysis modules) is

required, prior to working with this module.

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3. Components of Experimental Design

Consider the following diagram of a cake-baking process (Figure 1).

There are three aspects of the process that are analyzed by a

designed experiment:

Factors, or inputs to the process. Factors can be classified as

either controllable or uncontrollable variables. In this case, the

controllable factors are the ingredients for the cake and the oven

that the cake is baked in. The controllable variables will be

referred to throughout the material as factors. Note that the

ingredients list was shortened for this example - there could be

many other ingredients that have a significant bearing on the end

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result (oil, water, flavoring, etc). Likewise, there could be other

types of factors, such as the mixing method or tools, the sequence

of mixing, or even the people involved. People are generally

considered a Noise Factor - an uncontrollable factor that causes

variability under normal operating conditions, but we can control

it during the experiment applying certain techniques. Potential

factors can be categorized using the Fishbone Chart (Cause &

Effect Diagram).

Levels, or settings of each factor in the study. Examples include

the oven temperature setting and the particular amounts of sugar,

flour, and eggs chosen for evaluation.

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Response, or output of the experiment. In the case of cake-

baking, the taste, consistency, and appearance of the cake are

measurable outcomes potentially influenced by the factors and

their respective levels. Experimenters often desire to avoid

optimizing the process for one response at the expense of another.

For this reason, important outcomes are measured and analyzed

to determine the factors and their settings that will provide the

best overall outcome for the critical-to-quality characteristics –

both measurable variables and assessable attributes.

BITS Pilani, Deemed to be University under Section 3 of UGC Act, 1956

Figure 1

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4. Purpose of Experimentation

Designed experiments have many potential uses in improving

processes and products, including:

Comparing Alternatives. In the case of our cake-baking

example, we might want to compare the results from two

different types of flour. If it turned out that the flour from

different vendors was not significant, we could select the lowest-

cost vendor. If flour were significant, then we would select the

best flour. The experiment(s) should allow us to make an

informed decision that evaluates both quality and cost.

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Identifying the Significant Inputs (Factors) Affecting an Output

(Response) - separating the vital few from the trivial many.

We might ask a question: “What are the significant factors

beyond flour, eggs, sugar and baking?”

Achieving an Optimal Process Output (Response). "What are

the necessary factors, and what are the levels of those factors, to

achieve the exact taste and consistency of Mom's chocolate cake?

Reducing Variability. "Can the recipe be changed so it is more

likely to always come out the same?"

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Minimizing, Maximizing, or Targeting an Output (Response).

"How can the cake be made as moist as possible without

disintegrating?"

Improving process or product "Robustness" - fitness for use

under varying conditions. "Can the factors and their levels

(recipe) be modified so the cake will come out nearly the same no

matter what type of oven is used?"

Balancing Tradeoffs when there are multiple Critical to Quality

Characteristics (CTQCs) that require optimization. "How do you

produce the best tasting cake with the simplest recipe (least

number of ingredients) and shortest baking time?"

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5. Experiment Design Guidelines

The Design of an experiment addresses the questions outlined

above by stipulating the following:

The factors to be tested.

The levels of those factors.

The structure and layout of experimental runs, or conditions.

A well-designed experiment is as simple as possible - obtaining

the required information in a cost effective and reproducible

manner.

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Like Statistical Process Control, reliable experiment results are

predicated upon two conditions: a capable measurement system,

and a stable process. If the measurement system contributes

excessive error, the experiment results will be muddied.

Likewise, you can use the Statistical Process Control module to

help you evaluate the statistical stability of the process being

evaluated. Variation impacting the response must be limited to

common cause random error - not special cause variation from

specific events.

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When designing an experiment, pay particular heed to four

potential traps that can create experimental difficulties:

i). In addition to measurement error (explained above), other sources of error, or unexplained variation, can obscure the results. Note that the term "error" is not a synonym with "mistakes". Error refers to all unexplained variation that is either within an experiment run or between experiment runs and associated with level settings changing. Properly designed experiments can identify and quantify the sources of error.

ii). Uncontrollable factors that induce variation under normal operating conditions are referred to as "Noise Factors". These factors, such as multiple machines, multiple shifts, raw

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materials, humidity, etc., can be built into the experiment so that their variation doesn't get lumped into the unexplained, or experiment error. A key strength of Designed Experiments is the ability to determine factors and settings that minimize the effects of the uncontrollable factors.

iii). Correlation can often be confused with causation. Two factors that vary together may be highly correlated without one causing the other - they may both be caused by a third factor. Consider the example of a porcelain enameling operation that makes bathtubs. The manager notices that there are intermittent problems with "orange peel" - an unacceptable roughness in the enamel surface. The manager also notices that the orange peel is worse on days with a low production rate.

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A plot of orange peel vs. production volume below (Figure 2) illustrates the correlation:

Figure 2

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If the data are analyzed without knowledge of the operation, a false conclusion could be reached that low production rates cause orange peel. In fact, both low production rates and orange peel are caused by excessive absenteeism - when regular spray booth operators are replaced by employees with less skill. This example highlights the importance of factoring in operational knowledge when designing an experiment. Brainstorming exercises and Fishbone Cause & Effect Diagrams are both excellent techniques to capture this operational knowledge during the design phase of the experiment. The key is to involve the people who live with the process on a daily basis.

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iv). The combined effects or interactions between factors demand careful thought prior to conducting the experiment. For example, consider an experiment to grow plants with two inputs: water and fertilizer. Increased amounts of water are found to increase growth, but there is a point where additional water leads to root-rot and has a detrimental impact. Likewise, additional fertilizer has a beneficial impact up to the point that too much fertilizer burns the roots. Compounding this complexity of the main effects, there are also interactive effects - too much water can negate the benefits of fertilizer by washing it away. Factors may generate non-linear effects that are not additive, but these can only be studied with more complex experiments that involve more than 2 level settings.

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Two levels is defined as linear (two points define a line), three levels are defined as quadratic (three points define a curve), four levels are defined as cubic, and so on.

6. Experiment Design Process

The flow chart below (Figure 3) illustrates the experiment design process:

Figure 3

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Figure 3

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7. Test of Means - One Factor Experiment One of the most common types of experiments is the

comparison of two process methods, or two methods of treatment. There are several ways to analyze such an experiment depending upon the information available from the population as well as the sample. One of the most straight-forward methods to evaluate a new process method is to plot the results on an SPC (Statistical Process Control) chart that also includes historical data from the baseline process, with established control limits.

Then apply the standard rules to evaluate out-of-control conditions to see if the process has been shifted. You may need to collect several sub-groups worth of data in order to make a

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determination, although a single sub-group could fall outside of the existing control limits.

An alternative to the control chart approach is to use the F-test (F-ratio) to compare the means of alternate treatments. This is done automatically by the ANOVA (Analysis of Variance) function of statistical software, but we will illustrate the calculation using the following example: A commuter wanted to find a quicker route home from work. There were two alternatives to bypass traffic bottlenecks. The commuter timed the trip home over a month and a half, recording ten data points for each alternative.

Take care to make sure your experimental runs are randomized - i.e., run in random order. Randomization is necessary to

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avoid the impact of lurking variables (a lurking variable is a characteristic of each 'individual' that is either unrecorded or unused in the analysis, but that distorts the apparent

relationship between two variables, X and Y). Consider the example of measuring the time to drive home: if a major highway project is started at the end of the sample period increases commute time, then the highway project could bias the results if a given treatment (route) is sampled during that time period.

Scheduling the experimental runs is necessary to ensure independence of observations. You can randomize your runs using pennies - write the reference number for each run on a penny with a pencil, then draw the pennies from a container and record the order.

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The data are shown below along with the mean for each route (treatment), and the variance for each route:

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As shown on the table above, both new routes home (B & C) appear to be quicker than the existing route A. To determine whether the difference in treatment means is due to random chance or a statistically significant different process, an ANOVA F-test is performed.

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8. Multi-Factor Experiments Multi-factor experiments are designed to evaluate multiple

factors set at multiple levels. One approach is called a Full Factorial experiment, in which each factor is tested at each level in every possible combination with the other factors and their levels. Full factorial experiments that study all paired interactions can be economic and practical if there are few factors and only 2 or 3 levels per factor. The advantage is that all paired interactions can be studied. However, the number of runs goes up exponentially as additional factors are added. Experiments with many factors can quickly become unwieldy and costly to execute, as shown by the chart below:

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BITS Pilani, Deemed to be University under Section 3 of UGC Act, 1956

When selecting the factor levels for an experiment, it is critical to capture the natural variation of the process. Levels that are close to the process mean may hide the significance of factor over its likely range of values. For factors that are measured on a variable scale, try to select levels at plus/minus three standard deviations from the mean value.

9. Advanced Topic - Taguchi Methods Dr. Genichi Taguchi is a Japanese statistician and Deming

prize winner who pioneered techniques to improve quality through Robust Design of products and production processes. Dr. Taguchi developed fractional factorial experimental designs that use a very limited number of experimental runs.

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It is useful to understand Taguchi's Loss Function, which is the foundation of his quality improvement philosophy.

Traditional thinking is that any part or product within specification is equally fit for use. In that case, loss (cost) from poor quality occurs only outside the specification (Figure 5). However, Taguchi makes the point that a part marginally within the specification is really little better than a part marginally outside the specification.

As such, Taguchi describes a continuous Loss Function that increases as a part deviates from the target, or nominal value (Figure 6).

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The Loss Function stipulates that society's loss due to poorly performing products is proportional to the square of the deviation of the performance characteristic from its target value.

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Taguchi adds this cost to society (consumers) of poor quality to the production cost of the product to arrive at the total loss (cost). Taguchi uses designed experiments to produce product and process designs that are more robust - less sensitive to part / process variation.