Extracts: A Guide to Design of Experiments for Engineers and Scientists

This post summarizes the content of the book 'Design of Experiments for Engineers and Scientists' from Jiju Antony. The book delves into the crucial role of experiments in engineering, emphasizing the significance of statistical thinking and methods in conducting and interpreting experiments. It addresses common challenges such as the lack of statistical knowledge among engineers, undesirable selection of process variables, and non-technical issues like inadequate experimental planning. The book provides valuable insights into overcoming these barriers and highlights the importance of carefully planned experiments to achieve optimal results. The idea behind this post is to provide readers with the key takeaways from this guide, before they dive deeper into the topic.

1. Introduction to Industrial Experimentation

In an engineering environment, experiments are often conducted to explore, estimate or confirm.

Exploration: understanding the data from the process.
Estimation: determining the effects of process variables or factors on the output performance characteristic.
Confirmation: verifying the predicted results obtained from the experiment.

It is interesting to explore the relationship between the key input process variables (factors) and the output performance characteristics (quality characteristics).

The most common approach employed by engineers today is One-Variable-At-a-Time (OVAT), where we vary one variable at a time and keep all other variables in the experiment fixed. It has a few limitations:

Depends upon guesswork, luck, experience and intuition
Requires large quantities of resources to obtain limited amount of information about the process
Often unreliable, inefficient and time consuming
May yield false optimum conditions for the process

Statistical thinking and statistical methods play an important role in planning, conducting, analyzing and interpreting the data from engineering experiments. When several variables influence a certain characteristic of a product, the best strategy is to design an experiment so that valid, reliable and sound conclusions can be drawn effectively, efficiently and economically.

Not all variables affect the performance in the same manner. Some may have strong influences on the output performance, some may have medium influences and some may have no influence at all.

The objective of a carefully planned designed experiment is to understand which set of variables in a process affect the performance most and then determine the best levels for these variables to obtain satisfactory output functional performance in products.

2. Fundamentals of Design of Experiments

A process is the transformation of inputs into outputs. In performing a designed experiment, we will intentionally make changes to the input process or machine variables (or factors) in order to observe corresponding changes in the process output. In real-life situations, some of the process variables or factors can be controlled fairly easily and some of them are difficult or expensive to control during standard conditions.

Controllable variables (X) can be varied easily during an experiment and such variables have a key role to play in the process characterization. Uncontrollable variables (Z) are difficult to control during an experiment, thus it is important to determine the optimal settings of X's in order to minimize the effects of Z's.

2.1. Basic Principles of DOE

DOE refers to the process of planning, designing and analyzing the experiment so that valid and objective conclusions can be drawn effectively and efficiently.

In the context of DOE, one may come across two types of process variables or factors: qualitative and quantitative. For quantitative factors, one must decide on the range of settings and how they are to be measured and controlled during the experiment. Qualitative factors are discrete in nature.

A factor may take different levels, depending on the nature of the factor – quantitative or qualitative. A qualitative factor generally requires more levels when compared to a quantitative factor. Here the term ‘level’ refers to a specified value or setting of the factor being examined in the experiment.

In the DOE terminology, a trial or run is a certain combination of factor levels whose effect on the output (or performance characteristic) is of interest.

The three principles of experimental design, namely randomization, replication and blocking, can be utilized in industrial experiments to improve the efficiency of experimentation. These principles of experimental design are applied to reduce or even remove experimental bias.

2.1.1. Randomization

If you believe your system or process is stable, you do not then need to randomize the experimental trials. On the other hand, if you believe your process is unstable and without randomization, the results will be meaningless and misleading, thus you would need to think about randomization of experimental trials.

While designing industrial experiments, there are factors which may influence the process output performance because they are often expensive or difficult to control. Such factors can adversely affect the experimental
results and therefore must be either minimized or removed from the experiment.

Randomization is one of the methods experimenters often rely on to reduce the effect of experimental bias. The purpose of randomization is to remove all sources of extraneous variation which are not controllable in real-life settings.

2.1.2. Replication

In all industrial designed experiments, some variation is introduced because of the fact that the experimental units cannot be physically identical.

Replication means repetitions of an entire experiment or a portion of it, under more than one condition.

Replication has three important properties:

Allows for obtaining a more accurate estimate of the experimental error, which represents the differences that would be observed if the same experimental settings were applied several times to the same experimental units.
Permits to obtain a more precise estimate of the factor/interaction effect.
Replication can decrease the experimental error and thereby increase precision.

However, replication can result in a substantial increase in the time needed to conduct an experiment. Moreover, if the material is expensive, replication may lead to exorbitant material costs, thus the use of
replication in real life must be justified in terms of time and cost.

2.1.3. Blocking

Blocking is a method of eliminating the effects of extraneous variation due to noise factors and thereby improving the efficiency of experimental design.

The main objective is to eliminate unwanted sources of variability such as batch-to-batch, day-to-day, shift-to-shift, etc..

The idea is to arrange similar or homogenous experimental runs into blocks (or groups), corresponding to sets of relatively homogeneous experimental conditions. Variability between blocks must be eliminated from the experimental error, which leads to an increase in the precision of the experiment.

2.2. Degrees of Freedom

In the context of statistics, the term ‘degrees of freedom’ is the number of independent and fair comparisons that can be made in a set of data.

In the context of DOE, the number of degrees of freedom associated with a process variable is equal to one less than the number of levels for that factor:

$DoF = Levels - 1$

The number of degrees of freedom for the entire experiment is equal to one less than the total number of data points or observations.

The degrees of freedom for an interaction is equal to the product of the degrees of freedom associated with each factor involved in that particular interaction effect.

2.3. Confounding

The term ‘confounding’ refers to the combining influences of two or more factor effects in one measured effect.

One cannot estimate factor effects and their interaction effects independently. Effects which are confounded are called aliases, and a list of the confoundings which occur in an experimental design is called an alias structure or a confounding pattern.

2.3.1. Design Resolution

Design resolution is a summary characteristic of confounding patterns.

The degree to which the main effects are aliased with the interaction effects (two-factor or higher) is represented by the resolution of the corresponding design.

Design resolution identifies for a specific design the order of confounding of the main effects and their interactions. It is a key tool for determining what fractional factorial design will be the best choice for a given problem.

For designed experiments, designs of resolution III, IV and V are particularly important:

Resolution III designs: Designs in which no main effects are confounded with any other main effect, but main effects are confounded with two-factor interactions and two-factor interactions may be confounded with each other (i.e. three factors at 2-levels in four runs is a resolution III design).
Resolution IV designs: Designs in which no main effects are confounded with any other main effect or with any two-factor interaction effects, but two-factor interaction effects are confounded with each other (i.e. four factors at 2-levels in eight runs is a resolution IV design).
Resolution V designs: Designs in which main effects are not confounded with other main effects, two-factor interactions or three-factor interactions, but two-factor interactions are confounded with three-factor interactions (i.e. 5 factors at 2-levels in 16 runs is a resolution V design).

2.3.2. Measurement System Capability

The goal of a measurement system capability study is to understand and quantify the sources of variability present in the measurement system. Repeatability and Reproducibility (R&R) studies analyze the variation of measurements of a gauge and the variation of measurements by operators, respectively.

Repeatability refers to the variation in measurements obtained when an operator uses the same gauge several times for measuring the identical characteristic on the same part.

Reproducibility, on the other hand, refers to the variation in measurements when several operators use the same gauge for measuring the identical characteristic on the same part.

It is important to note that total variability in a process can be broken down into variability due to product (or parts variability) and variability due to measurement system.

A measurement system is considered to be capable and adequate if it satisfies the criterion:

where P/T is the Precision-to-Tolerance ratio, given by:

where USL = Upper Specification Limit and LSL = Lower Specification Limit of a quality characteristic.

2.4. Selection of Quality Characteristics for Industrial Experiments

To identify a good quality characteristic, it is suggested to start with the engineering or economic goal. Having determined this goal, identify the fundamental mechanisms and the physical laws affecting this goal. Finally, choose the quality characteristics to increase the understanding of these mechanisms and physical laws.

3. Understanding Key Interactions in Processes

In order to determine whether two process parameters are interacting or not, one can use a simple but powerful graphical tool called interaction graphs. If the lines in the interaction plot are parallel, there is no interaction between the process parameters. On the other hand, if the lines are non-parallel, an interaction exists between the factors and the greater the degree of departure from being parallel, the stronger the interaction effect.

3.1. Synergistic Interaction vs. Antagonistic Interaction

The effects of process parameters can be either fixed or random.

Fixed process parameter effects occur when the process parameter levels included in the experiment are controllable and specifically chosen because they are the only ones for which inferences are desired.

Random process parameter effects are associated with those parameters whose levels are randomly chosen from a large population of possible levels.

4. A Systematic Methodology for Design of Experiments

4.1. A Practical Methodology for DOE

The methodology of DOE is fundamentally divided into four phases. These are:

Planning Phase
Designing Phase
Conducting Phase
Analyzing Phase

4.1.1. Planning Phase

The planning phase is made up of several steps. Many engineers pay special attention on the statistical details of DOE and very little attention to the non-statistical details. However, experimental studies may fail not only as
a result of lack of technical knowledge of the process under study or wrong use of statistical techniques but also due to lack of planning.

Problem Recognition and Formulation

A clear and succinct statement of the problem can create a better understanding of what needs to be done. The statement should contain an objective that is specific, measurable and which can yield practical value. Objectives can be either short term or long term. Some manufacturing problems that can be addressed using an experimental approach include:

Development of new products; improvement of existing processes or products
Improvement of the process/product performance relative to the needs and demands of customers
Reduction of existing process spread, which leads to poor capability

Selection of Response or Quality Characteristic

The selection of a suitable response for the experiment is critical to the success of any industrially designed experiment. The response can be variable or attribute in nature. Variable responses such as length, thickness,
diameter, viscosity, strength, etc. generally provide more information than attribute responses such as good/bad, pass/fail or yes/no. Moreover, variable characteristics or responses require fewer samples than attributes to achieve the same level of statistical significance.

Selection of Process Variables or Design Parameters

Some possible ways to identify potential process variables are the use of engineering knowledge of the process, historical data, cause-and-effect analysis and brainstorming. If important factors are left out of the experiment, then the results of the experiment are not accurate or useful for any improvement actions. It is a good practice to conduct a screening experiment in the first phase of any experimental investigation to identify the most important design parameters or process variables.

Classification of Process Variables

Having identified the process variables, the next step is to classify them into controllable and uncontrollable variables. Control variables are those which can be controlled by a process engineer/production engineer in a production environment. Uncontrollable variables (or noise variables) are those which are difficult or
expensive to control in actual production environments. These variables may have an immense impact on the
process variability and therefore must be dealt with for enhanced understanding of our process. The effect of such nuisance variables can be minimized by the effective application of DOE principles such as blocking, randomization and replication.

Determining the Levels of Process Variables

A level is the value that a process variable holds in an experiment. The number of levels depends on the nature of the process variable to be studied for the experiment and whether or not the chosen process variable is qualitative or quantitative. For quantitative process variables, two levels are generally required in the early stages of experimentation. However, for qualitative variables, more than two levels may be required.

List All the Interactions of Interest

In order to effectively interpret the results of the experiment, it is highly desirable to have a good understanding of the interaction between two process variables. In the context of DOE, we generally study two-order interactions. The number of two-order interactions within an experiment can be easily obtained by using the equation:

where n is the number of factors.

4.1.2. Designing Phase

In this phase, one may select the most appropriate design for the experiment. During the design stage, it is quite important to consider the confounding structure and resolution of the design. It is good practice to have the design matrix ready for the team prior to executing the experiment. The design matrix generally reveals all the settings of factors at different levels and the order of running a particular experiment. The principles of randomization, replication and blocking should be carefully taken into account prior to conducting the real experiment.

4.1.3. Conducting Phase

This is the phase in which the planned experiment is carried out and the results are evaluated.

4.1.4. Analyzing Phase

Having performed the experiment, the next phase is to analyze and interpret the results so that valid and sound conclusions can be derived. In DOE, the following are the possible objectives to be achieved from this phase:

Determine the design parameters or process variables that affect the mean process
performance
Determine the design parameters or process variables that influence performance variability
Determine the design parameter levels that yield the optimum performance
Determine whether further improvement is possible

4.2. Analytical Tools of DOE

4.2.1. Main Effects Plot

A main effects plot is a plot of the mean response values at each level of a design parameter or process variable.

This plot can be used to compare the relative strength of the effects of various factors:

The sign of a main effect indicate the direction of the effect (i.e. whether the average response increases or decreases)
The magnitude of a main effect tells us the strength of the effect

The effect of a process or factor can be mathematically calculated by taking the difference between the average response at the high and low level setting of the factor.

4.2.2. Interactions Plots

An interactions plot shows the mean response of two factors at all possible combinations of their settings.

If the lines are parallel, this indicates that there is no interaction between the factors. Non-parallel lines are an indication of the presence of interaction between the factors.

4.2.3. Cube Plots

Cube plots display the average response values at all combinations of process or design parameter settings.

One can easily determine the best and worst combinations of factor levels for achieving the desired optimum response and a cube plot is helpful to also determine the path of steepest ascent or descent for optimization problems.

4.2.4. Pareto Plot or Factor Effects

The Pareto plot allows one to detect the factor and interaction effects that are most important to the process or design optimization study one has to deal with.

It displays the absolute values of the effects, and draws a reference line on the chart. Any effect that extends past this reference line is potentially important.

It is always a good practice to check the findings from a Pareto chart with the Normal Probability Plot (NPP) of the estimates of the effects.

4.2.5. NPP of Factor Effects

For NPPs, the main and interaction effects of factors or process (or design) parameters should be plotted against cumulative probability (%).

Inactive main and interaction effects tend to fall roughly along a straight line, whereas active effects that are statistically significant tend to appear as extreme points falling off each end of the straight line. The results are absolutely identical to that of a Pareto Plot of factor/interaction effects.

4.2.6. NPP of Residuals

One of the key assumptions for the statistical analysis of data from industrial experiments is that the data come from a normal distribution. The appearance of a moderate departure from normality does not necessarily imply a serious violation of the assumptions. Gross deviations from normality are potentially serious and require further analysis.

In order to check the data for normality, it is best to construct an NPP of the residuals. NPPs are useful for evaluating the normality of a data set, even when there is a fairly small number of observations. Here the term residual corresponds to the mean difference between the observed value, obtained from the experiment, and the predicted or fitted value.

If the residuals fall approximately along a straight line, they are then normally distributed. In contrast, if the residuals do not fall fairly close to a straight line, they are then not normally distributed and hence the data do not come from a normal population.

4.2.7. Response Surface Plots and Regression Models

Response surface plots such as contour and surface plots are useful for establishing desirable response values and operating conditions.

In a contour plot, the response surface is viewed as a two-dimensional plane where all points that have the same response are connected to produce contour lines of constant responses.

A surface plot generally displays a three-dimensional view that may provide a clearer picture of the response.

If the regression model (i.e. first-order model) contains only the main effects and no interaction effect, the fitted response surface will be a plane (i.e. contour lines will be straight).

If the model contains interaction effects, the contour lines will be curved and not straight. The contours produced by a second-order model will be elliptical in nature.

4.3. Model Building for Predicting Response Function

In order to develop a regression model based on the significant effects (either main or interaction), the first step is to determine the regression coefficients. For factors at 2-levels, the regression coefficients are obtained by dividing the estimates of effects by 2. A regression model for factors at 2-levels is usually of the form:

where β₁, β2 are the regression coefficients and β0 is the average response in a factorial experiment. The term ‘ε’ is the random error component which is approximately normal and independently distributed with mean zero and constant variance σ2. The regression coefficient β12 corresponds to the interaction between the process parameters x1 and x2.

The response values obtained from this equation are called predicted values and the actual response values obtained from the experiment are called observed values. Residuals can be obtained by taking the difference of observed and predicted values.

Once the statistical analysis is performed on the experimental data, it is important to verify the results by means of confirmatory experiments or trials.

4.4. Confidence Interval for the Mean Response

The statistical confidence interval (CI) (at 99% confidence limit) for the mean response can be computed using the equation:

where
y = mean response obtained from confirmation trials or runs
SD = standard deviation of response obtained from confirmation trials
n = number of samples (or confirmation runs).

If the results from the confirmatory trials or runs are within the CI, then improvement action on the process is recommended. If the results from the confirmation trials or runs fall outside the statistical CI, possible causes must be identified.

5. Screening Designs

In many process development and manufacturing applications, the number of potential factors is large. Screening is used to reduce the number of factors by identifying the key ones that affect the product quality or process performance. Screening designs provide an effective way to consider a large number of factors in a minimum number of experimental runs or trials (i.e. with minimum resources and budget).

The purpose of screening designs is to identify and separate out those factors that demand further investigation.

Plackett-Burman designs (P-B designs) are one type of these screening designs, and they are suitable for studying up to k = (N-1)/(L-1) factors, where L is the number of levels and k is the number of factors.

One of the interesting properties of P–B designs is that all main effects are estimated with the same precision. This implies that one does not have to anticipate which factors are most likely to be important when setting up the study.

For screening designs, experimenters are generally not interested in investigating the nature of interactions among the factors. The aim is rather to study as many factors as possible in a minimum number of trials and to identify those that need to be studied in further rounds of experimentation in which interactions can be more thoroughly assessed.

5.1. Geometric and Non-geometric P-B designs

Geometric P-B designs are those in which N is a power of two. Geometric designs are identical to fractional factorial designs in which one may be able to study the interactions between factors.

Non-geometric P–B designs are designs which are multiples of four but are not powers of two. These designs do not have complete confounding of effects. For non-geometric P–B designs, each main effect is partially confounded with all interactions that do not contain the main effect.

If the process is suspected to be highly interactive, it would be better to use a geometric design as opposed to a non-geometric design. In contrast, if interactions are of no concern to the experimenter, it is advisable to use a non-geometric design.

The obvious advantage of P–B designs is the limited number of runs to evaluate large number of factors. The obvious disadvantage of P–B designs is tied to the assumption required to evaluate up to k = (N − 1) factors in N runs.

Geometric P–B designs are resolution III designs and therefore these designs can be folded over to achieve a resolution IV design.

6. Full Factorial Designs

It is widely accepted that the most commonly used experimental designs in manufacturing companies are full and fractional factorial designs at 2-levels and 3-levels. A factorial design can be either full or fractional factorial. A full factorial designed experiment consists of all possible combinations of levels for all factors. The total number of experiments for studying k factors at 2-levels is 2^k. The 2^k full factorial design is particularly useful in the early stages of experimental work, especially when the number of process parameters is less than or equal to 4.

One of the assumptions we make for factors at 2-levels is that the response is approximately linear over the range of the factor settings chosen.

6.1. Example of a 2² Full Factorial Design

Simple nickel plating process with two plating process parameters: plating time and plating solution temperature. . Each process parameter is studied at 2-levels. The response of interest is plating thik The response of interest is plating thickness. Each experimental condition was replicated five times so that a reasonable estimate of error variance (or experimental error) could be obtained.

6.1.1. Objective 1: Determination of Main/Interaction Effects That Influence Mean Plating Thickness

In order to determine the effect of process parameters A and B and its interaction AB, we need to construct a coded design matrix with mean plating thickness values. The column AB is obtained by simply multiplying the coded values in columns A and B. Interaction AB yields a combined effect of two factors, A and B.

6.1.2 Objective 2: Determination of Main/Interaction Effects That Influence Variability in Plating Thickness

In order to determine the effect of A, B and interaction AB on process variability, we need to construct a coded design matrix with response as variability in plating thickness.

6.1.3 Objective 3: How to Achieve a Target Plating Thickness of 120 Units?

In order to achieve a target plating thickness of 120 units, we need to initially develop a simple regression model (or mathematical model) which connects the response of interest (i.e., plating thickness) and the significant process parameters. In order to develop a regression model, we need to construct a table of effects and regression coefficients. Regression coefficients for factors at 2-levels are just half the estimate of effect.

The regression model for the plating thickness can be therefore written as:

Using the above predicted model, we need to determine the settings of parameters which give a target thickness of 120 units.

Therefore, to achieve a target plate thickness of 120 units, we need to set the plating time for 9.85 s at a temperature of 32°C. We need to perform confirmation experiments or runs to verify the results of our analysis. If the results of the confirmation experiments or runs (i.e., each observation from the trials) fall within the interval of y ± 3 (s.e.), then the results are satisfactory. Here s.e. refers to standard error and is obtained by s/√n, where SD is the sample standard deviation and n is sample size.

The analysis of a 2^k factorial design assumes that the observations are normally and independently distributed. The best way to check the normality assumption is by constructing an NPP of residuals. If the residuals fall approximately along a straight line, we can conclude that the data come from a normal population.

6.2. Example of a 2³Full Factorial Design

Now we consider an experiment with three factors at 2-levels. The response of interest for the experiment was yield of a chemical process. Each trial condition was replicated three times in order to obtain an accurate estimate of experimental error (or error variance).

6.2.1. Objective 1: To Identify the Significant Main/Interaction Effects That Affect the Process Yield

In order to identify the significant main/interaction effects, it was decided to construct an experimental layout, which shows all the combinations of process parameters at their respective levels. The Pareto graph shows that main effects T (temperature) and R (reaction time), and interaction between pressure (P) and reaction time (R), are significant at 5% significance level. It is quite interesting to note that pressure (P) on its own has no significant impact on the process yield. It is important to analyze the interaction between P and R for determining the best settings for optimizing the chemical process yield.

6.2.2 Objective 2: To Identify the Significant Main/Interaction Effects That Affect the Variability in Process Yield

In order to identify the significant main/interaction effects that affect process variability, we need to construct a coded design matrix with ln(SD) as the response of interest. Due to zero degrees of freedom for the error term, we need to rely on a procedure called ‘pooling’ of insignificant effects. Pooling is a process of obtaining a more accurate estimate of error variance.

6.3.3 Objective 3: What Is the Optimal Process Condition?

In order to determine the optimal condition for the process, we need to analyze both response mean and variability. The above settings can be easily obtained by analyzing the mean process yield and mean ln(SD) values at both low- and high-level settings of T, P and R. For normality assumption of data, it is best to construct an NPP of residuals.

7. Fractional Factorial Designs

Very often experimenters do not have adequate time, resources or budget to carry out FFEs. If the experimenters can reasonably assume that certain higher-order interactions (third order and higher) are not important, then information on the main effects and two-order interactions can be obtained by running only a fraction of the FFE.

A fractional factorial design is a type of orthogonal array design which allows experimenters to study main effects and desired interaction effects in a minimum number of trials or experimental runs.

These fractional factorial designs are the most widely and commonly used types of design in industry. These designs are generally represented in the form 2^(k-p), where k is the number of factors and 1/2^p represents
the fraction of the full factorial 2^k.

7.1. Construction of Half-Fractional Factorial Designs

The construction of half-fractions of a FFE is simple and straightforward. Consider a simple experiment with three factors. Based on our assumption about three-factor (or third-order) and higher-order interactions
being negligible, one could use the ABC interaction column to generate settings for the fourth factor D.

For the above design, the resolution is IV (as main effects are confounded with three-factor interactions and two-factor interactions are confounded with other two-factor interactions). In real-life situations, certain two-factor interactions may be confounded with other two-factor interactions, and hence we cannot determine which of the two-factor interactions are important to that process.

Under such circumstances we may use ‘fold-over designs’. Fold-over designs are used to reduce confounding when one or more effects cannot be estimated independently or separately. In other words, the effects are said to be aliased. However, fold-over designs are used in resolution III designs to break the links between main effects and two-factor interaction effects.

8. Design of Experiments and its Applications in the Service Industry

Services are characterized as being different from products along a number of dimensions that have implications for the quality of service provided to customers. Manufacturing companies make products that are tangible, whereas services have an associated intangible component. Services are produced and consumed simultaneously, whereas manufactured goods are produced prior to consumption. Services cannot be stored, inventoried or inspected prior to delivery as manufactured goods are.

One of the difficulties in applying DOE in service an transactional businesses is that it is often difficult or impossible to physically experiment with the system under study. The usual approach in these situations is to build a computer model of the process and then apply designed experiments to the model. If the model is built
properly and validated, then results from the experiment conducted on the model can be transferred to the actual process. There are two types of computer models used in improvement activities:

Discrete event models
Deterministic models

Usually transaction-based and driven by random components that are modelled by probability distributions. Because discrete-event simulations are driven internally by random forces, they produce an output response that is a random variable.

Some practical problems that arise when experimenting on computer simulations include sample size determination, the issue of multiple responses and the problem of nonlinearity.

9. Design of Experiments and its Role Within Six Sigma

Six Sigma provides a scientific and statistical basis for quality assessment for all processes through measurement of quality levels. Six Sigma methodology integrates the most powerful and well-established quality and problem-solving tools and techniques in a disciplined and systematic manner.

The DMAIC methodology is the driving force behind Six Sigma process improvement projects. This methodology is used only for improving existing processes. Six Sigma focuses on the application of DMAIC (Define–Measure–Analyze–Improve–Control) methodology in the form of continuous or even breakthrough improvement projects compared to many other initiatives we have witnessed in the past.

9.1. Define Phase

In the Define Phase, we need to identify the process where the problem lies; this is followed by a proper definition of the problem. In this phase, it is important to justify the use of Six Sigma methodology. In the Define Phase, one may have to develop the project charter, which is a living document throughout the life of the project. The project charter should include:

The Problem Statement: the purpose of the problem statement is to clearly describe the problem at hand and to provide important details of the problem's impact on the organization.
The Goal Statement: this element defines the results expected from the project. This should include the targets to be achieved, savings expected from the project, etc.
Project Scope: every project should have some boundaries and these must be clearly understood at the outset of the project.
Cost of Poor Quality: this indicates how much the problem has costed the organization over a period of 1 year and assists the team to understand the impact of the problem in financial terms.
Risk Assessment: there is always a risk associated with the execution of any project and hence it is absolutely critical to evaluate the potential for these and to develop strategies to mitigate such risks.

9.2. Measure Phase

In the Measure Phase, it is important to baseline key performance measures associated with the problem. The objective of this phase is to garner as much information as possible from the current process. The important tasks in the Measure Phase are the creation of a detailed process map, collection of baseline data and summarizing the collected data. The process map provides a visual representation of the process under investigation. It can also provide additional awareness of process inefficiencies such as cycle times and bottlenecks or identify non-value-added process requirements.

9.3. Analyze Phase

In the Analyze Phase, the team sets out to identify the root cause or causes of the problem being studied. DMAI requires the root cause to be validated by data. This validation can be done through statistical tools such as hypotheses testing, correlation analysis, regression analysis, ANOVA, etc. The Analyze Phase of the Six Sigma methodology focuses on why errors, defects or excessive variation occur, which often result from one or more of the following:

failure to understand the capability of a process to meet specifications
poor instrument calibration and testing
inadequate control on environmental factors such as temperature, noise, humidity, pressure, etc.
lack of control of materials and equipment used in a process
lack of training
lack of knowledge about how a process works, etc.

10. Conclusion

"Design of Experiments for Engineers and Scientists" offers a wealth of information on conducting effective experiments in research and development. From the significance of statistical methods to the challenges and solutions in experimental planning, this book provides key insights that could help engineers and scientists structuring their workplan. I personally recommend to the readers to delve deeper into the book to gain a comprehensive understanding of the principles and strategies for successful experimentation, as this summary only aims to report the key takeaways to get started on the topic.

Acknowledgements

This post summarizes the content provided in the book “Design of Experiments for Engineers and Scientists” by Jjju Antony, published by Elsevier. Any image reported in this summary is reported from the original book.

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Extracts: A Guide to Design of Experiments for Engineers and Scientists