71a. Understanding Exponential Smoothing-A Simple Way to Forecast Sales and Inventory and Feedback Control and Bounded Adjustment Charts
by George Box. (April 1991).
This article gives a simple account of exponential smoothing and the way it can be used in forecasting. The meaning of an exponentially weighted moving average (EWMA) is given and the role of the smoothing constant in balancing the need to average data against the need for immediacy in the forecast is discussed. A way of estimating the smoothing constant is presented. Publication(s): Quality Engineering, 1990-91, Vol. 3, No. 4, pp. 561-566.
71b. 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.
71c. 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.
72. A Method for the Identification of Defining Contrasts for 2k-p Designs
by Soren 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.
73. The Use of Statistics to Improve Manufacturing Systems
by Soren 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.
74. 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.
75. The Early Years of Designed Experiments In Industry: Case Study References and Some Historical Anecdotes
by Soren 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.
76. 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. 453-459.
77a. Blocking Generators for Small 2k-p Designs
by Soren Bisgaard. (January 1992).
Small 2k-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.
77b. A Note on the Definition of Resolution for Blocked 2k-p Designs
by Soren Bisgaard. (May 1992).
When 2k-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.
78a. What Can You Find Out From Eight Experimental Runs?
by George Box. (February 1992).
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. Publication(s): Quality Engineering, 1992, Vol. 4, No. 4, pp. 619-627.
78b. What Can You Find Out From Sixteen Experimental Runs?
by George Box. (February 1992).
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. Publication(s): Quality Engineering, 1992, Vol. 5, No. 11, pp. 167-178.
79. 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).
QIt 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.
80. 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 nonorthogonal 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.