Design and Analysis of Experiments

ommends a design methodology and strategy incorporating the use of statistical distributions and looks at the role played by supporting techniques such as failure modes and effects analysis (FMEA), fault tree analysis (FTA), and design reviews and audits. A. D. S. Carter clearly has much practical experience and knowledge concerning mechanical reliability, from both a design point of view and a field performance perspective. The strength of this book lies in its description of mechanical failure modes and its development of design guidelines based on tools such as the load/strength interference model, s-N curves, crack growth propagation models, and Miner’s rule. Standard reliability textbooks typically omit these subjects or treat them only cursorily [O’Connor (1991) did discuss many of these models, as did Rao (1992)]. Carter offers many practical insights into these subjects, derived both from the literature and case studies he was personally involved with. The weakest parts of the book occur when the author leaves the domain of mechanical engineering and ventures onto the turf of statistical modeling. His discussion of statistical distributions does not include basic reliability models such as the lognormal distribution or extreme value distributions. Though he advocates using Miner’s rule, he does not mention the Birnbaum-Saunders distribution, which can be derived from a probabilistic argument based on Miner’s rule (Mann, Schafer, and Singpurwalla 1974). No mention is made of deriving statistical distribution models using arguments arising from the nature of the failure mechanisms other than a misleading interpretation of the central limit theorem. Carter asserts that most of the time only a handful of physical phenomena are the root cause of the distributions we need to model and therefore there are not enough small additive terms to invoke a central limit argument and justify using a normal distribution model. This ignores the possibility that the few highlevel causative phenomena can, themselves, be broken down into many small additive physical processes. Carter has an empiricist’s mistrust of statistical models, especially with respect to tail effects. He offers many interesting arguments against extrapolation and seems comfortable only when it is possible to sample enough tail events to have a high (nonparametric) confidence of seeing a problem if it exists at a given probability level. He does finally conclude, however, that designing for reliability based on statistical models is at least as good as prior methods and turns out to be surprisingly accurate in the few instances in which he had sufficient data to validate results. Unfortunately, he makes a serious error when he advises designers to check their statistical models by using a chi-squared goodness-of-fit test with a 50% significance level value as the test criterion. They could save the effort involved and simply flip a coin and accept only on heads and have the same accuracy if, in fact, the model is correct. Carter also argues that commonly advocated methodologies such as FMEA and FTA offer little of value for the designer concerned with piecepart mechanical reliability, whereas design reviews and audits should be included in the design process. In summary, a designer reading Carter’s book will not learn much about reliability statistics, but a reliability engineer who already knows how to use statistical methods will gain some insight into the methods and practical problems of mechanical design.