The Center for Quality and Productivity Improvement

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Feedback Control by Manual Adjustment
by George Box, (April 1991).
While we should always make a dedicated endeavor to bring a process into a state of control by fixing causes of variation, there sometimes remains a tendency for the process to wander from the target. In such a case, some method of feedback adjustment may be needed. This article discusses an easily used manual feedback adjustment chart which is equivalent to integral control used by the control engineer. Publication(s): Quality Engineering, 1991-92, Vol.4, No.1, pp.143-151.

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Bounded Adjustment Charts
by George Box, (April 1991).
The feedback adjustment charts discussed in the previous article are valuable when the cost of adjustment is essentially zero. However, when process adjustment is associated with a specific cost (for example, of stopping a machine and changing a tool), it is more economical to use a scheme that requires less frequent adjustment. For this purpose, bounded adjustment charts using an exponentially weighted average of past data may be used. A simple interpolation chart is presented for updating the forecast and indicating when and how large an adjustment is needed. A table is given allowing a scheme to be chosen by balancing a longer average interval between adjustments against the resulting increase in the standard deviation about the target value. Publication(s): Quality Engineering, 1991-92, Vol.4, No.2, pp.331-338.
UW72
A Method for the Identification of Defining Contrasts for 2^k-p Designs
by Søren Bisgaard, (July 1991).
The defining relation for a two-level fractional factorial design uniquely characterizes a design; from it the design can be studied, all the aliases can be found, the resolution determined, and the design if necessary reproduced. Finding a set of generators which is the key to finding the defining relation for a given two-level fractional factorial design is, however, usually a tedious job. In this article an algebraic method is presented that simplifies this job. Publication(s): Journal of Quality Technology, January 1993, Vol.25, No.1, pp.28-35.
UW73
UW73
The Use of Statistics to Improve Manufacturing Systems
by Søren Bisgaard, (October 1991).
This article presents a general overview of statistical methods applied to solving manufacturing problems. We also provide a specific example of a statistically designed experiment used to study factors affecting robot accuracy. The robot experiment illustrates how manufacturing engineers can improve quality and productivity, and reduce costs by applying relatively simple statistical tools on the shop floor. Publication(s): appeared as "Statistical Tools for Manufacturing" in Manufacturing Review, Vol.6, No.3, pp.192-200.
UW74
UW74
Quality Improvement – The New Industrial Revolution
by George Box, (October 1991).
Beginning from Bacon’s famous aphorism that "Knowledge Itself is Power", the underlying philosophy of modern quality improvement is seen as the mobilization of presently available sources of knowledge and knowledge gathering. These resources, often untapped include the following: (i) that the whole workforce possesses useful knowledge and creativity; (ii) that every system by its operation produces information on how it can be improved; (iii) that simple procedures can be learned for better monitoring and adjustment of processes; (iv) that elementary principles of experimental design can increase the efficiency many times over of experimentation for process improvement, development, and research. Publication(s): International Statistical Review, Vol.61, No.1, pp.3-19.
UW75
The Early Years of Designed Experiments in Industry:
Case Study References and Some Historical Anecdotes
by Søren Bisgaard, (November 1991).
Case studies are important because they provide illustrations of the industrial use of designed experiments. However, they are usually hard to come by; nevertheless unknown to many, there are quite a few case studies already published in the literature. Most of them are unfortunately scattered in many different technical and scientific journals, and are not readily available unless one knows where to look. In this article we provide a list of approximately 130 references to case study articles published over the past six decades. We also provide a causerie of historical anecdotes from early initiatives in the use of designed experiments in industry. Publication(s): Quality Engineering, 1992, Vol.4, No.4, pp.547-562.
UW76
UW76
Teaching Engineers Experimental Design with a Paper Helicopter
by George Box, November 1991).
How a paper "helicopter" made in a minute or so from a 8 1/2" x 11" sheet of paper can be used to teach principles of experimental design including- conditions for validity of experimentation, randomization, blocking, the use of factorial and fractional factorial designs, and the management of experimentation. Publication(s): Quality Engineering, 1992, Vol.4, No.3, pp. 453459.
UW77
Blocking Generators for Small 2^k-p Designs
by Søren Bisgaard, (January 1992).
Small 2^k-p designs are increasingly being used in industry for processes and product experimentation. Blocking of these designs can often significantly increase their efficiency, but does not seem to be its full potential in industry. To facilitate the practical use of blocking, a comprehensive table providing information about blocking generators for all the possible eight and sixteen runs, two-level fractional factorial designs has been developed. Examples of blocking and application of the table are also provided. Publication(s): Journal of Quality Technology, October 1994, Vol.26, No.4, pp.288-296.

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A Note on the Definition of Resolution for Blocked 2^k-p Designs
by Søren Bisgaard, (May 1992).
When 2^k-p designs are blocked, the application of the standard definition of resolution requires careful consideration. The problem is that the degrees of freedom associated with a set of blocking contrasts are essentially all "first order effects." Hence contrasts that superficially may appear as higher order interaction effects in reality are first order effects. Experimenters might therefore inadvertently confound these first order effects with important effects among the primary factors. In this note we discuss this subtle problem and provide an additional rule to the usual definition of resolution that helps provide a conservative but more realistic estimate of the resolution of a blocked design. We also show that this amendment to the definition is useful when several two-level contrasts are combined to yield factors with more than two levels. A few illustrative examples are provided. Publication(s): Technometrics, August 1994, Vol.36, No.3, pp. 308-311.
UW78
UW78
What Can You Find Out From Eight Experimental Runs?
by George Box, (February 1992).
Publication(s): Quality Engineering, 1992, Vol.4, No.4, pp.619-627.

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What Can You Find Out From Sixteen Experimental Runs?
by George Box, (February 1992).
Publication(s): Quality Engineering, 1992, Vol.5, No. 11, pp.167-178.
Different ways to use n = 8 and n = 16 experimental runs are described to generate two-level factorial and fractional factorial designs for studying up to n - 1 factors. The roles of "aliases" and of design "resolution" are discussed and the rationales for the employment of designs with different degrees of fractionation are presented.
UW79
Taguchi’s Parameter Design: A Panel Discussion
edited by Vijayan N. Nair
with discussants B. Abraham, G. Box, R. Kacker, T. Lorenzen, J. Lucas, J. MacKay, R. Myers, J. Nelder, M. Phadke, J. Sacks, A. Shoemaker, S. Taguchi, K. Tsui, G. Vining, W. Welch, and J. Wu (March 1992).
It is more than a decade since Genichi Taguchi’s ideas on quality improvement were introduced in the U.S. His parameter design approach for reducing variation in products and processes has generated a great deal of interest and debate among both quality practitioners and statisticians. This panel discussion provides a forum for a technical discussion of these diverse views. The topics discussed include the importance of variation reduction, the use of noise factors, the role of interactions, selection of quality characteristics, signal-to-noise (SN) ratios, experimental strategy, dynamic systems, and applications. The discussion also provides an up-to- date overview of recent research on alternative methods of design and analysis. Publication(s): Technometrics, May 1992, Vol.34, No.2, pp.127-161.
UW80
Finding the Active Factors in Fractionated Screening Experiments
by R. Daniel Meyer and George Box, (April 1992).
Highly fractionated factorial designs and other orthogonal arrays are powerful tools for identifying important, or active, factors, and improving quality. We show, however, that interactions, and important factors involved in those interactions, may go unidentified when conventional methods of analysis are used with these designs. This is particularly true of Plackett and Burman designs with number of runs not a power of two. A Bayesian method is developed in which the marginal posterior probability that a factor is active is computed, and allows for the possibility of interactions. The method can be applied to both orthogonal and non-orthogonal designs, as well as other troublesome situations, such as when data are missing, extra data are available, or factor settings for certain runs have deviated from those originally designed. The value of the new technique is demonstrated with three examples in which potential interactions and factors involved in those interactions are uncovered. Publication(s): Journal of Quality Technology, Vol.25, No.2, pp.94-105.
UW81
UW81
A New Design for Quality Paradigm
by Mikkel Mørup (April 1992).
Product development and design has a tremendous influence on the final product quality and the cost of quality. This paper presents a critical look at the position of Design for Quality in western industry and academia. It is suggested that Design for Quality should be enhanced in the context of design methodology in order to better fit the way that products are actually designed. Finally, the paper presents new concepts, models and a structured procedure for Design for Quality that have evolved by looking at quality from the viewpoint of design methodology. Publication(s): Journal of Engineering Design, 1992, Vol.3, No. l. pp.63-80.
UW82
A Comparative Analysis of the Performance of Taguchi’s Linear Graphs
by Søren Bisgaard, (June 1992).
In this article we use conventional concepts of aliasing and confounding to analyze several two-level fractional factorial designs constructed with the use of Taguchi's linear graph technique. We also compare these designs with more conventional alternatives and show that the conventional design are often better in terms of resolution, and are robust to assumptions that are likely to be violated in practice. We also comment on the practice of making strong prior assumptions based on engineering knowledge about which two-factor interactions are active and which are inert. We conclude that the value of linear graphs is limited, that the designs obtained are non-robust, and that better and simpler conventional alternatives already exist. Publication(s): To appear in the Journal of the Royal Statistical Society.
UW83
UW83
Sequential Experimentation and Sequential Assembly of Designs
by George Box, (June 1992).
Because of the many uncertainties in choosing an appropriate experimental design, it is best to avoid "all encompassing" experiments which must necessarily be planned when least is known about the system. Instead, where possible, it is best to run smaller sets of experiments in sequence. Examples are given of how a strategy of "sequential assembly" of design can be used. Publication(s): Quality Engineering, 1993, Vol.5, No.2,
pp.321-330.
UW84
UW84
How to Get Lucky
by George Box, (June, 1992).
Some principles for success in quality improvement projects discuss, in particular, how to encourage the discovery of useful phenomena not initially being sought. A graphical version of the analysis of variance which can help to show up the unexpected is illustrated with two examples. Publication(s): Quality Engineering, 1993, Vol.5, No.3, pp.517-524.
UW85
Comparison of Two Approaches for Feedback Control
by Alberto Luceño, (July 1992).
Two forms of feedback regulation that have been used for process adjustment in Automatic Process Control are considered. In the first, recommended originally by Box and Jenkins (1963) and by Box, Jenkins and MacGregor (1974), action is taken when the absolute difference between an exponentially weighted moving average (EWMA) of the past data z_n+1 and the target value T first crosses a threshold value L*. In the second, recommended by Taguchi (1981), the action is triggered when the absolute difference between the last observation z_n and the target value T exceeds a given constant l. However, it is shown here that the actual cost of regularly applying the policy based on z_n may be considerably more expensive than that based on z_n+1. For example, in practice h is frequently in the range from about 0.6 to about 0.9 and it is shown here that an increase in the mean square deviation of 64% can occur with h =0.8. Publication(s): Communications in Statistics, January 1993, Vol.22, No.1, pp.241-255.
UW86
An Iterative Non-Graphical Approach to Accommodate Interactions for Two-Level Fractional Factorials
by Søren Bisgaard and Howard Fuller, (July 1992).
Taguchi and Wu (1985) introduced the method of linear graphs to accommodate pre-specified interaction effects in orthogonal arrays. Kacker and Tsui (1990) developed a method called interaction graphs and Wu and Chen (1992) proposed another graph-aided method that optimizes resolution by minimizing aberration subject to the requirement that all the specified main effects and interactions are estimable. We present a simple approach based on iterative substitution, easily implemented with commercially available word processing software, which guarantees a maximum resolution solution to the accommodation problem. Publication(s): Quality Engineering, 1994, Vol.7, No.1, pp.71-87.
UW87
Experimental Optimization of Computer Models
by Søren Bisgaard, Bruce Ankenman and Tim Osswald, (July 1992).
Reducing the time and cost of product and process development is a key concern of today's competitive industrial firms. Although engineers often have available complex computer models of the product or process being developed, the use of these simulation models is often limited to ad hoc, one-factor-at-a-time exploration. In this article, a compression molding example is used to demonstrate a sequential strategy for optimizing complex computer simulation models based on response surface methodology. It is explained how the use of this approach can reduce the time and cost of prototype building and testing and thus aid in reducing the development time and cost. Publication(s): Manufacturing Review, 1994, Vol.7, No.4, pp.332-345.
UW88
UW88
What Can You Find Out From 12 Experimental Runs?
by George Box and Søren Bisgaard, (August 1992).
Report 78 has shown how 8 and 16 run two-level factorial designs could be used to study a number of factors. In particular they could be used to generate fractional factorial designs whose projective properties made them excellent screening designs for finding a few vital factors having major effects on a system. These fractional designs are particular examples of orthogonal arrays developed by Plackett and Burman which are available when N is a multiple of 4. In particular these authors derived such a design to study 11 factors in 12 runs. It turns out that this design has the remarkable property that it yields a full 23 factorial plus an additional optimal half replicate for any of the 165 choices of 3 factors out of the 11 factors tested. Publication(s): Quality Engineering, 1993, Vol.5, No.4, pp.663-668.
UW89
Charts for Optimal Feedback Control with Recursive Sampling and Adjustment
by George Box and Alberto Luceño, (September 1992).
A cost model proposed by Box and Jenkins (1963) and later generalized by Box and Kramer (1992) for obtaining minimum cost for feedback control of processes is considered. Unfortunately, it is sometimes difficult to assign values to the costs of making an adjustment, of taking a sample and of being off target as is required by their approach. An alternative that avoids the direct assignment of values to these costs is discussed in this paper and charts are provided to aid in choosing a reasonable scheme. For different values of the action limit and the non-stationarity measure, it is possible to compute an envelope of optimal schemes from which a choice may be made by judging the disadvantage of an increased mean square deviation against the advantage of having to take samples less frequently and/or increasing the average adjustment interval. Publication(s): Appeared as "Selection of Sampling Interval and Action Limit for Discrete Feedback Adjustment" in Technometrics, Vol.36, No.4, pp. 369-3 78.
UW90
The Design and Analysis of 2^k-p % 2^q-r Inner and Outer Array Experiments
by Søren Bisgaard, (September 1992).
Inner and outer array designs are useful for the development of robust products. In this article we will provide a discussion of their design and analysis from a classic factorial and fractional factorial design standpoint. In particular we will focus on inner and the outer arrays composed of two4evel fractional factorials. Confounding, split plotting, split plot confounding, and economics will be discussed and we will show how savings in terms of runs or increased information sometimes can be achieved.
UW91
Sample Size Estimates for Two-level Factorial Experiments with Binary Response
by Søren Bisgaard and Howard Fuller, (September 1992).
When the number of defectives (non conforming products) is used as the response in two-level factorial and fractional factorial experiments it is important to have an estimate of the necessary sample size needed for detecting a specific change. In this article we provide a set of easy-to-use tables for standard 8, 16 and 32 run two-level factorial experiments that provide rough guidelines for the necessary sample sizes for different average quality levels and different shifts. Examples of the use of the tables are also provided. Publication(s): to appear in the Journal of Quality Technology.
UW92
UW92
Process Adjustment and Quality Control
by George Box, (November 1992).
To be competitive in the international marketplace modern manufacturers need to pay keen attention to quality monitoring and control. In this paper I discuss process quality monitoring, control and adjustment of a modern statistical time series analysis point of view. In particular, I show how several past approaches can be unified. Publication(s): Total Quality Management, Vol.4, No. 2. pp.215-227.
UW93
UW93
Confounded Dispersion Effects in Robust Design Experiments with Noise Factors
by David M. Steinberg and Dizza Bursztyn, (December 1992).
Robust design experiments can be a very useful tool for improving quality. They enable engineers to reduce the variance of important quality characteristics by identifying design factors with dispersion effects and guiding the choice of nominal levels of those factors. Robust design experiments are especially effective when it is possible to build some variation directly into the experiment by including noise factors-factors that are impossible or too expensive to control during actual production or use. When noise factors are included, it is important to model their effects explicitly in the subsequent analysis. We present two examples in which failure to do so leads to incorrect conclusions about dispersion effects. Publication(s): to appear in Journal of Quality Technology.
UW94
UW94
Graphical Aids to Measurement System Analysis
by John Hallinan and Søren Bisgaard (February 1993). Report In Progress
UW95
UW95
Spreadsheets for Analysis of Two-Level Factorials
by Søren Bisgaard (March 1993).
Analysis of two-level factorial and fractional factorial experiments can be performed very simply in a standard spreadsheet environment on a personal computer. This article shows a simple way to program Yates’ Algorithm for effects and the Reverse Yates’ Algorithm for predicting values and residuals. Publication(s): Quality Engineering, 1993, Vol.6, No.1, pp. 149-1 57.

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Iterative Analysis of Data from Two-level Factorials
by Søren Bisgaard (March 1993).
Thorough analysis of data from two-level factorial and fractional factorials can help engineers gain further
insight into the technical system under investigation. This article provides an example of how data can be analyzed iteratively to reveal the underlying structure of the data. An example by Taguchi is used to illustrate the iterative use of estimation residual analysis and transformations to model this data from an experiment on viscosity. Publication(s): Quality Engineering, 1993, Vol.6, No.2, pp.319-360.
UW96
The Design and Analysis of 2^k-p % S Prototype Experiments
by Søren Bisgaard and David Steinberg (March 1993).
Prototype testing and experimentation play a key role in the design of new products. These experiments enable engineers to assess the feasibility of the design. It is common practice to build a single prototype product and then test it at specified operating conditions. We argue that it will often be more fruitful to make several variants of a prototype according to a fractional factorial design. The information obtained can be of great value in comparing design options and improving product performance and quality. In such experiments the response of interest is often not a single number but a performance curve over the test conditions. In this article we develop a general method for the design and analysis of prototype experiments that combines orthogonal polynomials with two-level fractional factorials. The method we propose is simple to use and has wide applicability in the design of new products. We illustrate our ideas by applying them to an experiment reported by Taguchi (1986) on the carbon monoxide (CO) exhaust of eight motors made up according to a 2^7-4 design and tested at three operating conditions.
UW97
UW97
Bringing Total Quality Improvement into the College Classroom
by W. Lee Hansen (March 1993).
This paper describes a recent effort to infuse the Total Quality Improvement (TQI) approach, popularized by Deming and others, into an upper-division, junior-senior economics course at the University of Wisconsin – Madison. The process of infusing TQI into instruction has received relatively little attention. Most efforts to bring TQI into higher education focus on improving administrative operations and establishing courses and programs for students to learn how to apply TQI in their future jobs. The challenge is in using TQI to help students realize their potential for learning in traditional courses.
UW98
UW98
A Review of Scientific Method for Setting Manufacturing Tolerances
by Paul R. Weiss (April 1993).
Several traditional and newer techniques for setting manufacturing tolerances are discussed. The traditional methods include worst case, statistical case, and proportional and constant factor scaling. Newer methods, such as Optimization and Monte Carlo Simulation are described more briefly. The Estimated Mean Shift model is included as a method for setting tolerances more realistically, while at the same time improving the communication between design and manufacturing departments. Additionally, some techniques are described for setting initial tolerances when little or no data or tables are available. Three tolerancing examples are included.
UW99
Experimental Design for Tolerancing Assembled Products
by Søren Bisgaard (May 1993).
This article provides an outline of theory and methods for the experimental determination of tolerance limits for mating components of assembled products. The emphasis is on novel combinatorial problems pre- and post-fractionation of certain products of two-level factorial designs. The cost of experimentation is discussed and used as a guide to allocating experimental runs. Several alternative design examples are provided. The article concludes with a comprehensive example of the experimental determination of tolerances for the components of a throttle handle for a small motor. Publication(s): to appear in Technometrics.
UW100
William G. Hunter: An Innovator and Catalyst for Quality Improvement
by George Box (June 1993).
This is the text of a talk given at the Speakers’ Dinner at the Sixth Annual William G. Hunter Conference on Quality in Madison, Wisconsin, on June 2, 1993. In it, George Box recalls Bill Hunter’s pivotal role in the birth of the quality movement in the city of Madison. Without Hunter’s catalytic contributions, Madison would not have its current leadership position in the improvement of quality in government, industry, and education.
UW101
UW101
Is Your Robust Design Product Robust?
by George Box and Conrad Fung (June 1993).
Robustifying a product is the process of defining its specifications to minimize the product’s sensitivity to variation. This article reviews two approaches to the problem of minimizing transmitted variation propagated from the product's components. The authors point out that no matter what approach is used, the solution can be extremely sensitive to certain assumptions which must be checked out. Sometimes tacit assumptions that seem innocuous turn out to be perilous. Thus we need to consider the robustness to assumptions of the robust design procedure itself. Publication(s): Quality Engineering, 1994, Vol.6, No.3, pp. 503-5 14.
UW102
UW102
Role of Statistics in Quality Control
by George Box (June 1993).
The role of Statistics in Quality Systems depends on certain philosophical issues which the author believes have been inadequately addressed. Three such issues are the role of statistics in the process of discovery, the extrapolation of results from the particular to the general, and the management climate in which quality improvement needs to be conducted. Statistical methods appropriate to discovery are discussed as distinct from those appropriate only to the testing of an already discovered solution. The manner in which the tentative solution has been arrived at is shown to determine with what assurance the experimental conclusions can be extrapolated to the practical application in mind. Whether or not statistical methods and training can have any impact depends on the system of management. A vector representation of management strategies is discussed. This can help to realign policies so that members of an organization can work together for its benefit. Publication(s): appeared as "Statistics and Quality Improvement" in the Journal of the Royal Statistical Society, Series A, 1994, 157, Part 2, pp.209-229.
UW103
Analytic Parameter Design
by Søren Bisgaard and Bruce Ankenman (June 1993).
Parameter design, a method introduced by Taguchi for robustifying products to uncontrollable variation in components or the environment, has often for its solution relied on computer experiments using inner and outer array methods. In this article we use a simple electrical circuit to formulate the parameter design problem as a constrained optimization problem and use analytic methods of non-linear programming to solve it. Such an approach is now relatively simple with the proliferation of symbolic manipulation software to perform differentiation and other analytic operations. Our discussion is illustrated with graphics to further elucidate the basic structure of the parameter design problem. We also show that the solutions to the parameter design problem and the tolerance design problem, the phase where a design’s tolerances are determined, cannot be separated. Our use of Lagrange multipliers also allows us to perform a sensitivity analysis. Publication(s): Quality Engineering, 1995, Vol.8, No.1, pp.75-91.
UW104
UW104
Compensation and Employment Security
by Spencer Graves (June 1993).
Research by economists supports a couple of Japanese management practices that seem to have been under-emphasized in many Total Quality implementation efforts in the US – lifetime employment and linking pay to the accomplishments of the team. This paper illustrates the value of these policies with a few examples from consulting experience, then describes research by economists that suggests that the effects noted in the examples are commonplace and not isolated incidents. The focus is primarily on the link between management policies and productivity and profitability; this should make the conclusions largely independent of an understanding of the role of quality in organizational performance.
UW105
UW105
Total Quality Management and D*A*T Model
by Joe Van Matre (June 1993).
Total Quality Management (TQM) is the current embodiment of the quality movement that began at AT&T in the early 1930’s. Although initiated by Americans such as Walter Shewhart, W. Edwards Deming and Joseph Juran, it has been the Japanese who brought the quality movement to international attention. Japanese success in the global marketplace led their competitors to adopt similar strategies. In the United States, firms leading the way in TQM during the 1980’s were primarily manufacturers such as Motorola, Ford and Xerox. Their experiences coupled with the success of "Japanese management" employing American labor in Ohio (Honda), Kentucky (Toyota), Tennessee Nissan), and California (Sony), further increased the credibility of TQM as a major managerial development. Now many firms, service as well as manufacturing, are experimenting with and adopting the new philosophy. This paper reviews the essential elements of TQM (i.e., attitudes, tools and data) and proposes a conceptually simple but effective framework, the D*A*T model (Van Matre 1992), which focuses on those core elements and their interrelationships. Examples from the health care industry are used to show the role of TQM implementation in service industries. Publication(s): Journal of American Health Information Management Association, 1992, Vol.63, No.11.
UW106
Projection in 12-run Plackett and Burman
by John Tyssedal (June 1993).
In this article we prove the form of the projections in the 12-run Plackett and Burman design. We do this by exploiting the close relationship between Hadamard matrices, orthogonal two-level arrays and a special type of balanced incomplete block designs. Projections into 2-5 dimensions are treated.
UW107
Noise Factors, Dispersion Effects and Robust Design
by David Steinberg and Dizza Burnstyn (July 1993).
There has been great interest recently in the use of designed experiments to improve quality by reducing the variation of industrial products. A major stimulus has been Taguchi’s robust design schema in which experiments are used to detect dispersion effects (that is, factors that affect process variation). We study here one of Taguchi’s novel ideas, the use of noise factors to represent varying conditions in the manufacturing or use environment. We show that the use of noise factors can dramatically increase power for detecting dispersion effects, provided their effects are explicitly modeled in the subsequent analysis.
UW108
UW108
Changing Management Policy to Improve Quality and Productivity
by George E.P. Box (August 1993).
It is generally accepted that the effectiveness of a quality improvement program often depends on changing the management culture in which it operates. Contemplated changes of policy affect different parts of an organization in different ways. A geometric representation of viewpoint on policy is introduced which makes it possible to compensate difficulties in making changes and finding effective ways to overcome them. Publication(s): Quality Engineering, 1994, Vol.6, No.4, pp.719-724.
UW109
UW109
UW109
Total Life Models – An Important Tool in Design of Quality
by Mikkel Mørup (December 1993).
Product quality is far more than "fitness for use" and robustness in the manufacturing process. This paper discusses the phenomena of product quality in the entire product life. It presents a total life model which serves several purposes, such as expanding the design teams' understanding of quality and adding structure to total life scenarios in the specification phase.
UW110
UW110
Quality and the Bottom Line
by Suren Bisgaard (December 1994).
Over the long term, Total Quality Management techniques must be validated economically or they will lose the support of management. In this article, a fictitious example is used to demonstrate how quality improvement tools can be applied to accounting data. These tools allow managers to make informed decisions about where quality improvement efforts will be most effective and show the resulting improvement in the bottom line. Publication(s): Quality Engineering, 1994-95, Vol.7, No.1, pp.223-235.
UW111
Discrete Proportional-Integral Control with Constrained Adjustment
by George Box and Alberto Luceño (February 1994).
It is well known that discrete feedback control schemes chosen to produce minimum mean square error at the output can require excessive manipulation of the compensating variable. Also very large reductions in the manipulation variance can be obtained at the expense of minor increases in the output variance by using constrained schemes. Unfortunately, however, both the form and the derivation of such schemes are somewhat complicated. The purpose of this article is to show that suitable "tuned" proportional-integral (PI) schemes in which the required adjustment is merely a linear combination of the two last observed errors can do almost as well as the more complicated optimal constrained schemes. If desired, these PI schemes can be applied manually using a feedback adjustment chart which is no more difficult to use than a Shewhart chart. Several examples are given and tables are provided that allow the calculation of the optimal constrained proportional-integral scheme and the resulting adjustment variance and output variance. Methods of tuning such controllers using Evolutionary Operation and experimental design are briefly discussed.
UW112
Orthogonal Design of Life Testing with Replacement: Exponential Parametric Regression Model
by Ilya Gertsbakh (March 1994).
This paper describes how to plan an ‘optimal’ life testing experiment when the lifetime is assumed to have an Exponential distribution. We further assume that the mean lifetime is equal to exp(b ₁x₁ +… +b _kx_k) where the covariates x, form an orthogonal Hadamard-type matrix which depends on testing conditions, and b ₁ are the unknown parameters. n₀ devices are put on test. The period of testing, t₀, is divided into k stages of length t_i, i=1,…,k, and on each of these stages all devices operate under a fixed testing regime. (The number of different testing regimes, k ,equals to the number of parameters to be estimated). Each device which fails is immediately
restored and continues to operate. A closed maximum likelihood solution is given for estimates of b ₁ which exists if and only if at least one failure has been observed on each of the testing stages. Also the approximate optimal duration of the i-th testing stage, t_i*, which would provide the minimum of S AsVar [b _i] is derived. It is shown that the near-optimal testing policy is obtained when t_i* is proportional to the square root of the mean lifetime for the corresponding testing regime.
Finally, the expression for the Fisher information matrix is derived and the optimality criterion (which is the trace of its inverse) is expressed as a function of model parameters b _i the duration of testing stages t_i, and the number of devices operating on each of the testing stages.
UW113
Standard Errors of the Eigenvalues of Second Order Response Surface Models
by Søren Bisgaard and Bruce Ankenman (March 1994).
When second order response surface models involve more than three factors, confidence intervals for the eigenvalues of the second order coefficient matrix play an important role in the interpretation of their geometric shape. In this article, we propose a new method for estimating the standard errors, and thus confidence intervals of these eigenvalues. The method is simple in both concept and execution and involves the refitting of a full quadratic model to the data using the rotated coordinate system obtained from canonical analysis. The standard errors of the pure quadratic terms from this refitting are used to approximate the standard errors of the eigenvalues. Since it uses the canonical form as a basis, the method is geometrically intuitive and thus is easily taught. Our approach is intended to provide practitioners with quick estimates of the standard errors of the eigenvalues. In our justification of the method, we show that it is equivalent to using the delta method as proposed for this problem by Carter, Chinchilli and Campbell (1990).
UW114
The Impact of Measurement Error and Cost on Tolerancing a Single Dimension
by Søren Bisgaard and Spencer Graves (April 1994). Report In Progress
UW115
UW115
Common Principles of Quality Management and Development Economics
by Spencer Graves (May 1994). Report In Progress
UW116
Projective Properties of Certain Orthogonal Arrays
by George Box and John Tyssedal (May 1994).
The projective properties of two-level orthogonal array designs are important in factor screening. General results are given which, particular, allow the designs derived by Plackett and Burman to be categorized in terms of these properties. The following results are given: 1) every saturated fractional factorial design is of projectivity P=2; 2) a design obtained by doubling is always of projectivity P=2; 3) any saturated two-level design obtained from a orthogonal array constructed by cyclic generation is either a factorial orthogonal array with P=2 or else has projectivity P=3; and 4) any saturated two-level design obtained from an orthogonal array containing n=4m runs, with m odd, is of projectivity P=3.
UW117
Tolerance Analysis Considering Manufacturing Variability and the Cost of Deviating from the Nominal
by Spencer Graves (May 1994).
A number of different formulae for tolerance analysis and synthesis have appeared over the years. This article discusses the interrelationships between alternative formulae, showing how each is best for a specific set of assumptions regarding the cost of deviating from the nominal and the distributions of dimensions of parts. To
increase the use of appropriate statistical tolerancing, a procedure is outlined for converting process capability studies into a simple formula tailored to a given manufacturing organization.
UW118
Normalizing Transformations for Shewhart-Type Control Schemes
by Haim Shore (May 1994).
Traditional Shewhart-type process control schemes and process capability analyses assume that the process distribution (or distributions of statistics derived thereof) are approximately normally distributed. When this assumption fails to materialize, normalizing transformations are sometimes needed. However, many of the currently used transformations are difficult to apply and at times require expertise that the common practitioner does not possess. In this paper, a new set of normalizing transformations are suggested that are simple to carry out, may be generally applied (since they are distribution-free) and are associated with a non-iterative standard procedure that is easy to program. Implications for current practices regarding Shewhart-type control schemes and for capability analyses are discussed.
UW119
UW119
Analysis of Factorial Experiments with Defects or Defectives as the Response
by Søren Bisgaard and Howard Fuller (June 1994).
The performance of a production process is often characterized by the number of defects in its products or the number of defective products. Typically, reduction of the number of defects or defectives is paramount to improving the quality of such a process. A powerful tool used for identifying variables that influence the process level of defects or defectives is experimental design. However, when using counts of defects or defectives as the experimental response the assumption of constant variance made with almost all standard analyses is violated. A common method for dealing with this problem is to transform the data before the analysis so that the assumption of constant variance is more likely. In this paper, we present various transformations that can be used to approximately stabilize the variance of counts of defects and the variance of proportion of defectives. We also re-analyze examples of each case where transformation of the experimental data followed by a simple analysis of the data led to significantly different conclusions. Publication(s): Quality Engineering, 1994-95, vol.7, No.2, pp.429443.
UW120
UW120
Assuring Product Success with ISO 9001?
by Gunhild Dalen (July 1994).
Several research projects have been conducted, and several reports and books have been written with the hope of finding the factors important for successful new product development. This article compares the portions of ISO9001 related to new product development with relevant research results. The conclusion is that ISO9001 is mainly concerned with the formal written documentation of the development process, the adherence to these documents, documentation of the result, and qualification of personnel and resources available to the project. But 1809001 does not include all the elements necessary for assuring a successful product development, such as customer contact, teamwork, consistent project team, authority of the team leader, or design for manufacturability.
UW121
The Importance of Data Transformations in Designed Experiments for Life Testing
by George Box and Conrad Fung (July 1994).
Data transformation can sometimes yield big improvements in model simplicity, variance homogeneity, and precision of estimation, especially in the analysis of designed experiments for life testing. This article shows several simple ways to choose an appropriate transformation. Lambda plots are introduced as a useful graphical way to understand how transformation can affect model simplicity. The methods are illustrated with several real examples, including a life test where some of the test items survived the experiment, resulting in "censored" data that needed to be imputed. Publication(s): Quality Engineering, 1995, vol.7, No.3, pp.625-638.
UW122 Follow-up Designs to Resolve Confounding in Fractional Factorials
by R. Daniel Meyer, David M. Steinberg and George E. P. Box (November 1994).
Fractional factorial and Plackett-Burman designs are often effective in practice due to factor sparsity. That is, just a few of the many factors studied will have major effects. In those active factors, these designs usually have higher resolution. We have previously developed a Bayesian method based on the idea of model discrimination that uncovers the active factors. Sometimes, the results of a fractional experiment are ambiguous due to confounding among the possible effects and more than one model may be consistent with the data. Within the Bayesian construct, we have developed a method for designing a follow-up experiment to resolve this ambiguity. The idea is to choose runs that allow maximum discrimination among the plausible models. This method is more general than methods which algebraically decouple aliased interactions, and more appropriate than optimal design methods which require specification of a single model. The method is illustrated through examples of fractional experiments.
UW123
Total Quality: Its Origins and Its Future by George Box (January 1995).
This article discusses how an efficient organization is characterized by its knowledge and learning capability. It examines the learning ability of the human animal, the logic of continuous, never-ending improvement, the catalysis of learning by scientific method, and Grosseteste’s Inductive-Deductive iteration related to the Shewhart Cycle. Total Quality is seen as the democratization and comprehensive diffusion of Scientific Method and involves extrapolating knowledge from experiment to reality which is the essence of the idea of robustness. Finally, barriers to progress are discussed and the question of how these can be tackled is considered.
UW124
UW124
A Case Study of the Use of Experimental Design and Multivariate Analysis in Product Improvement
by Marit Ellekjaer, M.A Ilseng and T Naes, (January 1995).
The overall purpose of this study is to identify an effective strategy for improving the sensory quality of a product. A study on processed cheese was used to develop and illustrate our ideas. A screening experiment, with seven processing and ingredients variables, was performed in order to identify the processing variables with the greatest effect on sensory quality. A fractional factorial design with resolution Iv was used to keep the number of experimental runs to a minimum. ANOVA and normal plots were used to evaluate the effects of the different factors on the sensory variables one by one. The same factors were identified as being important when the scores from a principal component analysis (PCA) of the sensory variables were analyzed. PCA was found to be of value in identifying samples that had improved properties compared to today’s product in addition to having a low intensity of undesirable properties.
UW125
Quality Quandaries - Analysis of Factorial Experiments with Ordered Categories as the Response
by Søren Bisgaard and Howard T. Fuller, (January 1995).
One of the more difficult aspects of setting up a quality improvement experiment is how to define an appropriate scale for the response. Often we must simply classify the outcomes into ordered categories such as how "discolored" how "clean," how "smooth," or how "good" an object is. A simple and useful approach to the analysis of such data recommended by several prominent statisticians is to attach a score to each of the categories and proceed with standard least squares techniques applied directly to the assigned score. In this article we present an illustration of the use of this technique to a two-level fractional factorial experiment involving the identification of the bad part in an assembled product originally due to Taguchi and Wu (1985). We also show how a very simple sensitivity analysis relative to the scale can be performed. Publication(s): Quality Engineering, 1995, Vol. 8, No.1, pp.199-207.
UW126
Variable Selection or Variable Assessment?
by R. D. Meyer and R. G. Wilkinson, (February 1995).
Variable-selection regression methods are oriented towards selecting a single model as the vehicle for further inferences. The appropriate inference about variables not included is unclear – the conclusion that they have no effect may be misleading. In many situations, the objective of the statistical method should be to assess the relative importance of every variable. The term variable assessment we think is more descriptive of this objective. We develop a method for variable assessment that makes use of Bayesian model-selection methodology. The marginal posterior probability that a variable is needed in the model is a measure of its importance. Using the Gibbs sampler for computation greatly reduces CPU requirements and also allows us to extend the model to one that allows for outliers. A simulation demonstrates that the method has good statistical properties.
UW127
Quality Quandaries - Reducing Variation with Two-Level Factorial Experiments
by Søren Bisgaard and Howard T. Fuller, (May 1995).
In many quality improvement projects the objective is to reduce variation. A powerful approach is to use factorial experiments with the log of the sample variance as the response. This paper demonstrates with an example how to reduce variation using this approach.
UW128
On Robust Design in the Conceptual Design Phase – A Qualitative Approach
by Peder Andersson, (July 1995).
One of the most important contributions to quality engineering over the last decades is the concept of robust design and its accomplishment through the use of various experimental methods. However, the prerequisite parameter design in terms of a robust solution principle are seldom discussed and methods that aid robust design in the conceptual design phase are, to our knowledge, few. This article forwards the suggestion to use the principles behind the error transmission formula as a semi-analytic method for evaluation of robustness of concept solutions, prior to entering Taguchi’s parameter design stage.
UW129
UW129
Analysis of Unreplicated Split-Plot Experiments with Multiple Responses
by Marit Risberg Ellekjær, Howard T. Fuller and Kirsti Ladstein, (July 1995).
The purpose of this study is to demonstrate an effective strategy for unreplicated split-plot experiments with multiple responses. Through principal component analysis (PCA) the response variables are reduced to only those that describe different phenomena among the experimental samples. These selected response variables are then analyzed individually using ANOVA and Normal probability plots to identify the factors with the greatest influence on the quality and cost of the product. This approach makes it possible to take both the preferred quality characteristics and the production costs into account when studying a process or product. A case study from a fish food manufacturing company is used to illustrate our ideas.
UW130
Redesigning the Introductory Statistics Course
by Ronald D. Snee and Roger Hoerl, (July 1995). Report In Progress.
UW131
Quality Quandaries – Split-Plot Experiments
by George Box, (August 1995).
Industrial experiments are frequently by necessity run in a "split-plot" mode. The structure and analysis of such experiments is explained and illustrated. It is shown how split-plot experiments can increase experimental efficiency. Publication(s): Quality Engineering, 1995-96, Vol. 8, No. 3, pp. 515-520.
UW132
Quality Quandaries – Two-Level Factorials Run as Split-Plot Experiments
by Søren Bisgaard, Howard T. Fuller and Ernesto Barrios, (October 1995).
Many industrial experiments are often executed more economically in split-plot mode when hard to change factors are varied less frequently than others. This, however, needs to be considered when analyzing the data. An example illustrates a sample approach. Publication(s): Quality Engineering, to appear.
UW133
X Charts With Variable Sample Sizes and Sampling Intervals
by Antonio F.B. Costa, (September 1995).
Recent theoretical studies have shown that the X chart with variable sampling intervals (VSI) and the X chart with variable sample sizes (VSS) are quicker than the traditional X chart for detecting shifts in a process. This article considers the X chart with variable sample sizes and sampling intervals (VSSI). It is assumed that the amount of time the process remains in control has an exponential distribution. The properties of the VSSI X chart are obtained using Markov chains. The VSSI X chart is shown to be quicker than the VSI or VSS X charts in detecting moderate shifts in the process.
 
UW134
A Total Quality Improvement Approach to Student Learning
by W. Lee Hansen (October 1995). Report In Progress
UW135
Projective Properties of the Sixteen Run Two-Level Orthogonal Arrays
by George Box and John Tyssedal (December 1995). Report In Progress
UW136
Quality Quandaries – Two-Level Factorials Run as Split-Plot Experiments
by Søren Bisgaard, Howard T. Fuller and Ernesto Barrios, (October 1995).
Many industrial experiments are often executed more economically in split-plot mode when hard to change factors are varied less frequently than others. This, however, needs to be considered when analyzing the data. An example illustrates a sample approach. Publication(s): Quality Engineering, to appear.
UW137
Importance of Graphics in Problem Solving and Detective Work
by Søren Bisgaard (October 1996). Report In Progress
UW138
Discrimination and Criticism of Single-Response Models
by Warren Stewart, George Box and Thomas Benson, (February 1996).
Formulas are developed for assessing the probability and adequacy of rival models fitted to a common data set. Cases of full, partial and minimal variance information are treated. The use of the formula is demonstrated with three examples, including a modeling study of a heterogeneous catalytic reaction.
UW139
Series Models for Forecasting Wastewater Treatment Plant Performance
by P.M. Berthouex and George Box, (February 1996).
This paper describes a time series modeling procedure that can be useful for calculating predictions, with confidence intervals, of effluent quality one to five days ahead, and it explains how these predictions can serve as an early warning of process upsets that will sometimes enable an operator to take preventive action. The time series model has the form of an exponentially weighted moving average (EWMA). The interpretation of the model is that the response of the system can be predicted by deviations from the EWMA smoothed values of the predictor variables.
UW140
UW140
Nonstatistical Skills That Can Help Statisticians Become More Effective
by Ronald D. Snee (March 1996).
The T new economic era we live in has resulted in a variety of new work situations for statisticians. Many are asked to be a member of a team that involves several different functions of the organization. Statisticians are also asked to work with groups in non-technical areas. These groups tend to have less experience with data-based problem solving methods but, nonetheless, are working on problems critical to the success of the organization. Many statisticians have the opportunity to work with mid-and upper-level managers. All of these opportunities that require new skills and methods that can help statisticians become more effective are discussed. It is also shown how these new skills have much in common with statistical thinking.
UW141
Conditional Inference Chart
by Søren Bisgaard (March 1996). Report In Progress
UW142
Joint X and R Charts with Variable Sample Sizes and Sampling Intervals
by Antonio F.B. Costa (March 1996).
Recent studies have shown that the X chart with variable sampling intervals (VSI) and/or with variable sample sizes (VSS) detects process shifts faster that the traditional X chart This article extends these. studies for processes that are monitored by both, the X and the R charts. A Markov chain model is used to determine the properties of thc joint X and R charts with variable sample sizes and sampling intervals (VSSI) scheme improves the joint X and R control chart performance (in terms of the speed with which process mean and/or variance shifts are detected).
UW143
The Anatomy and Robustness or Discrete Proportional -Integral Adjustment and
Its Application to Statistical Process Control
by George Box and Alberto Luceño (April 1996).
This paper explains the nature and importance of Proportional -Integral control and shows how it may be adapted to Statistical Process Control. The relation of this type of control to exponential smoothing, minimum mean squared error control, and optimal constrained schemes is discussed. Robustness properties which simplify considerably the practical application of this type of control are demonstrated.
UW144
Team Work and Design of Experiments
by Joseph G. Van Matre and Neil Diamond (June 1996).
UW145
X Charts With Variable Parameters
by Antonio P. B. Costa (June 1996).
The idea of varying the X chart parameters has been explored extensively in recent years. Basically, the X value establishes if the control should be relaxed or not. When X falls near the target the control is relaxed because one will wait more to take the next sample and/or the next sample will be smaller than usual. When X falls far from the target but not in the action region the control is tightened because one will wait less to take the next sample and/or the next sample will be larger than usual. In this paper, we extend this study to consider the action limits variable too. The idea is to draw the action limits wider than usual when the control is relaxed and narrower than usual when the control is tightened. This new feature makes the X chart comparable with the CUSUM and EWMA schemes in terms of the speed they detect small shifts in process mean.
UW146
Scientific Statistics, Teaching, Learning and the Computer
by George Box (June 1996).
It is argued that the domination of Statistics by Mathematics rather than by Science has greatly reduced the value and the status of the subject. The mathematical "theorem - proof paradigm" has supplanted the "iterative learning paradigm" of scientific method. This misunderstanding has affected university teaching, research, the granting of tenure to faculty and the distributions of grants by funding agencies. Possible ways in which some of these problems might he overcome and the role that computers can play in this reformation are discussed.
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