Sampling Methodologies With Applications

deŽ ned. There are a few typographical errors; for example, in eq. (2.84), the partial derivative should be with respect to Xi. Chapter 3 provides a good exposure to the concept of loss functions associated with the deviation of the quality characteristic from a target value (Taguchi loss function). Expressions for the expected loss for three types of situations—nominal-is-best, smaller-the-better, and larger-the-better—are discussed. An excellent discussion of robust design that seeks to minimize the variance of an assembly characteristic that is a general function of component characteristics while also constraining the mean of the assembly characteristic to be held at the target value is provided. A nonlinear programming problem is formulated. This chapter contains a number of typographical errors. For instance, in eq. (3.25), shouldn’t the divisor “n” be “n1,” say, where n1 is the number of observations in the set A1? Similarly, in eq. (3.26), shouldn’t the divisor be “n2 ,” where n2 is the number of observations in the set A2? In Example 3.3, in the expression for k1 on p. 67, the numerator should be changed from “8” to “12.” Below eq. (3.45), the expression for gi4Œ5 should be “¡e4¢5=¡Xi”. On p. 77, in the expression for ‘ 2 , the term “g24Œ5‘ 21” should be “g24Œ5g14Œ5‘ 21 .” Chapter 4 presents a discussion of process capability. A good example illustrates the difference between short-term variability, which is the variability within subgroups and is the inherent process variability, and long-term variability, which is estimated by considering all observations obtained from the process. Common capability indices, including Cp , Cpk , Pp , Ppk , and Cpm, are presented. Because most of the discussion is based on the assumption of normality of the population distribution, an omission is the lack of coverage on either testing of normality or transformations of the characteristic [e.g., the Box–Cox (1964) transformation] to achieve normality. On p. 94, the “C” sign is missing between “P6Z < ƒ47” and “P6Z > 47.” Measurement error is the subject of Chapter 5. The chapter presents the concepts of gage repeatability and operator reproducibility, but has one major omission. Under reproducibility, only the variation between operators is stated. There is no mention of possible interaction between operators and parts, which may be one of the components contributing to reproducibility. Further, in the estimation of variance components of measurement error, the method presented (S X ƒ R method) cannot be used to estimate the interaction between operators and parts, if any. Hence a discussion of the analysis of variance procedure in this context, that may allow estimation of the interaction component, would be in order. Two other concepts, gage linearity and gage stability, also deserve a additional coverage. The rather unique Chapter 6 covers determination of the optimum value of the mean setting of a process under various objective functions. Chapter 7 is also distinctive, formulating the problem to determine the optimal process adjustments such that the process mean after a certain number (say, n) of adjustments is equal to the target value, and the variance of the process mean after such adjustments is minimized. Chapter 8 presents process control techniques. These include standard control charts for variables (S X and R, S X and s, X and MR) and for attributes (p, np, c, and u). A section is devoted to the design on control charts, with the decision variables sample size (n), the length of interval between successive samples (h), and probability of a type I error (). This chapter has some shortcomings. Discussing the revision of control limits, the author states that points out of control should be deleted and revised limits constructed. But in fact this procedure is not routine, and should be done only if assignable causes have been identiŽ ed and appropriate remedial actions taken. In the absence of remedial actions, deletion of points cannot be justiŽ ed. The chapter also needs some discussion on the various types of patterns (e.g., jump, trend, cycles, stratiŽ cations) in control charts and their possible associated special causes. Further, some exposure to the concepts of selection of rational subgroups would be beneŽ cial. Chapter 9 provides a limited discussion of the principles of experiment design. Models considered include single-factor experiments, random-effects models, two-factor experiments, nested factor designs, 2 factorial experiments, factorial experiments in incomplete blocks, fractional factorial designs, and Taguchi’s orthogonal arrays. The chapter lacks a discussion on the testing of assumptions for the purpose of model validation. In factorial experiments, testing of interactions effects must be considered Ž rst, before any main effects are tested. The point is not made that if interactions effects are signiŽ cant, it may not make sense to test for main effects. Also, there is a very limited discussion of contrasts, and, speciŽ cally, orthogonal contracts. Overall, I believe that the Statistical Quality Control will serve the needs of a one-semester graduate course in engineering. The course will become palatable if the instructor provides some supplementary information on the identiŽ ed areas.