Elementary Statistical Quality Control

This book presents recent applications of robust engineering methods, many involving computer-based simulations, to various engineering disciplines. These applications are illustrated by use of numerous case studies, which offer compelling arguments why robust engineering methods should now be an essential part of designing, developing, and testing new products and processes including software and information systems. Robust engineering minimizes the impact of uncontrollable noise factors on responses of interest to the customer under most usage conditions. The book is divided into three sections that contain chapters that discuss theory illustrated with case studies. The first four chapters comprise Section I, which focuses on simulation-based robust engineering. The authors emphasize that simulated experiments using the computer are more often replacing actual experiments because of time and resource constraints. Experiments for achieving robustness using simulation are done using a two step optimization strategy: determining levels of parameters that maximize robustness of responses of interest using signal-to-noise (S/N) metrics and then adjusting parameters to achieve responses at desired levels. Chapter 1 provides a brief introduction to the concepts of robust engineering, including the parameter diagram, orthogonal arrays, and static and dynamic S/N ratios. This chapter concludes with a brief discussion of robust engineering together with design for six sigma (DFSS) as a corporate strategy. Chapter 2 describes robust engineering with a simulation-based example using a theoretical equation that predicts output current from settings of various parameters (“control factors”) such as resistance and voltage. Using an L9 orthogonal array (OA), optimum levels of parameters that result in good output current stability on the basis of using nominal S/N ratios are found. These parameter levels are then used in the equation to determine the mean value of the output current. If this predicted mean value is on or close to target, which is the case in this example, then no further parameter adjustments are necessary. If the mean is not close to target, a parameter that shows a strong influence on sensitivity, but not on S/N ratios, is adjusted until the output mean is on or close to target. Chapter 3 elaborates on a simulation-based engineering strategy in research and development that uses the two-step design process discussed above. These concepts are illustrated with the design of a color ribbon shifting mechanism to guide four-color ribbons to their correct positions on printing heads, where the rotating angle (M) is the signal factor used to adjust target output values (ribbon guide sliding in millimeters). Whereas the signal factor can be changed to adjust the output to the desired target values, it may be necessary to calibrate the signal factor or to adjust control factors so the proportional constant β between signal and output is as close to 1.0 as possible. To evaluate tuning precision, an orthogonal decomposition of the variation of the response (involving linear, quadratic, and sometimes cubic terms) is done. Chapter 4 presents three simulation-based case studies: optimization of a discrete floating metal–oxide– semiconductor (MOS) gate driver, a direct injection diesel injector, and robust design of transistors. Section II, “Application of Robust Engineering Methods for Software Testing and Software Algorithm Optimization,” consists of two chapters. Chapter 5 discusses the use of OA’s to debug software where the response is binary: defect or no defect. This “nonparametric” technique works very well to detect the impacts of all two-way combinations of factors on the aforementioned binary response. This procedure can be extended to evaluate other types of products such as copy machines. Chapter 6 presents three case studies that involve software algorithm optimization. (1) Robust design of mobile wireless networks is described in which the network formation results are generated with MATLAB tools (tested and verified using Monte Carlo simulations). (2) Direct injection spark ignition gasoline engine development utilizing robust engineering is discussed. After optimization of hardware factors using an L18 OA, a threedimensional computation fluid dynamic simulation is applied to confirm the benefits of higher injector flow rates. (3) The third case study describes electronic warfare (EW) systems used to search for radar emitter types. The control factors consist of the EW system hardware and software configurations tested in a particular system configuration. Use of an L18 OA significantly reduces the time necessary to test system functionality when compared with conventional testing. Section III describes the design of information systems for pattern analysis and consists of two chapters. Chapter 7 describes the use of robust engineering methods to design information systems. A multivariate statistic, the Mahalanobis distance (MD), is used to detect pattern differences between groups of correlated variables (also termed multidimensional systems). As documented in Mason and Young (2002), this statistic is very similar to Hotelling’s T2 statistic. Examples of multidimensional systems, which the authors designate as information systems, include sensor systems, stock market prediction systems, and records of health data. When MD’s are combined with robust engineering techniques to assure accuracy, a Mahalanobis–Taguchi strategy (MTS) results. Four stages of MTS are described: construction of the measurement scale using uniform data (e.g., data from healthy patients, from companies exhibiting average growth, etc.), validation of this measurement scale using “abnormal” data (e.g., data from diseased patients, from companies that exhibit unusual growth patterns, etc.), identification of significant variables on the basis of S/N ratios obtained from OA experiments, and diagnosis of future data using only the significant variables. These different stages are illustrated with an example using clinical data. Gram–Schmidt’s orthogonalization process is described as a way to determine whether large MD’s calculated from correlated variables signify good or bad situations. Pattern analysis through this process is known as Mahalanobis–Taguchi Gram–Schmidt’s method. The last chapter further illustrates MTS with three case studies from the automotive and photographic industries. This book appears to have the average number of typos, misspellings, and other mistakes, which, however, could have been lowered by more careful proofreading. At the bottom of page 26, for example, two equations should read “Sm = (21.5 + 38.5)2/2 = 1800.00” and “Ve = (21.5 − 38.5)2/2 = 144.5.” Equation 3.8 on page 46 should read β1 = (m1y1 + m2y2 +· · ·+ m5y5)/(m1 + m2 + · · · + m5).” On the bottom of page 46 the phrase should read “To analyze the quadratic term, the following constants, K2 and K3 (not K1 and K2), are calculated. . . .” As the case studies throughout the book demonstrate, this book is a very valuable reference for engineers of various disciplines who are already experienced practitioners of robust engineering. They should be conversant with, if not experienced using, robust engineering methods discussed in texts such as Barker (1990), Fowlkes and Creveling (1995), and Phadke (1989). This book also contains a number of references that will enable the reader to explore various aspects of robust engineering in greater depth.