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Technometrics Highlights
Reliability, Robustness, and Design of
Experiments Featured in Latest Issue
O
ne of the quandaries in reliability an important step forward on this problem in their
experiments is that failures are article, “Tolerance Intervals with Improved Coverage
needed to estimate reliability. Yet Probabilities for Binomial and Poisson Variables.”
few, if any, failures may occur in studies of They propose procedures to compute the exact mini-
high-rh eliability components and systems mum and average coverage probabilities of tolerance
and pra oducts. Two major directions have intervals for Poisson and binomial variables. These
been advb anced to address this problem: procedures are illustrated with examples and real data
accelerated failura e experiments, in which a applications. Based on these procedures, improved tol-
high-strh ess environment is used to induce erance intervals are proposed that can ensure the true
higher failurh e rates, and degradation analy- minimum or average coverage probabilities are close to
sis, in which cumulativs e damage to the sys- the nominal levels.
tem is modeled and used to prt edict the The breakdown point is an important measure of
failurfa e time. robustness, related to the fraction of outliers that can
Ying Shi, Luis Escobar, and William be tolerated by an estimator. Computing the break-
Meeker consider how to plan experiments down point is useful in tuning some robust regression
that combine these strategies in their arh ticle, estimators, but can be a computationally demand-
“Accelerated Destructive Degradation Test Planning.” ing task. Jung Jin Cho, Yong Chen, and Yu Ding
They focus on settings in which testing is destruc- address this problem in their article, “Calculating the
tive, so only one degradation measurement can be Breakdown Point of Sparse Linear Models.” They
made on each unit. Their test plans specify settings present an algorithm for calculating the maximum
of an accelerating factor (e.g., temperature), evalua- breakdown point for sparse linear models, a special
tion times, and the allocations of test units to these type of structured linear model whose design matrix
acceleration/time combinations. The paper describes has many zero entries. The algorithm decomposes
methods to find good plans for an important class of a sparse design matrix into smaller submatrices, on
destructive degradation models. First, plans are derived which the computation is performed, and thus leads
that minimize the large sample approximate variance to substantial savings in computation. An assembly
of the maximum likelihood estimator of a specified process and several numerical examples are used to
quantile of the failure-time distribution. Then, more illustrate the application of the algorithm and its
robust and useful compromise plans are proposed. computational benefit.
The methods are illustrated with an application for an The remaining articles in this issue explore a
adhesive bond. variety of issues in the design and analysis of experi-
Warranty data are an important source of infor- ments. Carla Vivacqua and Søren Bisgaard present
mation on the reliability of many consumer prod- ideas on post-fractionated strip-block designs. They
ucts. Motivated by claims data on motor vehicles, present novel arrangements for strip-block designs
J. F. Lawless, M. J. Crowder, and K. A. Lee wrote that can reduce experimental effort and theoretical
“Analysis of Reliability and Warranty Claims in properties of strip-block designs that employ post-
Products with Age and Usage Scales.” They present fractionation. They show how to appropriately ana-
models that may be used to assess the dependence on lyze the data from these experiments, illustrating the
age or usage history in heterogeneous populations of ideas with an experiment on an industrial process.
products and show how to estimate model param- As a tool to aid the selection of appropriate plans,
eters based on different types of field data. The set- they provide catalogs of post-fractionated strip-block
ting of the events in question is complicated because designs with 16 and 32 trials.
the data are sparse and incomplete. North American Timothy Robinson, Christine Anderson-Cook,
automobile warranty data are used to illustrate the and Michael Hamada present methods for Bayesian
methodology used. analysis of split-plot experiments with non-normal
Tolerance intervals predict likely future values responses for evaluating nonstandard performance
and are useful for assessing product performance criteria. Many industrial experiments generate
and reliability. Although there has been considerable non-normal response variables and include factors
work devoted to tolerance intervals for continuous with levels that are difficult or costly to change,
distributions, little has been devoted to discrete dis- resulting in a split-plot randomization structure.
tributions. Hsiuying Wang and Fugee Tsung make Valid statistical inferences must account for the
20 AMSTAT NEWS FEBRUARY 2009
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