Journal ArticleDOI
Determining Optimum Burn-In and Replacement Times Using Bayesian Decision Theory
TLDR
A multiparameter Bayesian analysis which requires multiple integration of the (multivariate) posterior of the parameters of the time-to-failure distribution to obtain the expected loss resulting from a particular choice of burn-in time and item replacement age is described.Abstract:
An important problem facing a manufacturer is the determination of the amount of time to burn-in items (in order to eliminate early failures) and the age at which to replace items (to avoid failures due to wearout) This problem becomes difficult to solve if the time-to-failure distribution of an item is unknown and must be estimated from test and operational data This paper describes a method of statistical data analysis which is readily applied to the solution of this decision problem under a realistic but general loss (or gain) function The method is a multiparameter Bayesian analysis which requires multiple integration of the (multivariate) posterior of the parameters of the time-to-failure distribution to obtain the expected loss (or gain) resulting from a particular choice of burn-in time and item replacement age This integration is performed by a Monte Carlo Procedure using importance sampling An example demonstrates the flexibility of this method of analysis The data are a mixture of ``point'' and truncated data, which often create difficulties when using conventional methods of decision analysis In addition, since the method permits up to ten parameters for the family of time-to-failure distributions, a ``bathtub'' hazard rate function is used to generate the data for the example The results are presented in the form of Bayesian confidence intervals for the true hazard rate function and a presentation of the expected loss as a function of burn-in time and age at replacementread more
Citations
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Journal ArticleDOI
Facing the headaches of early failures: A state-of-the-art review of burn-in decisions
TL;DR: This state-of-the-art review of studies of burn-in screenings applied to industrial products can serve as a guide in studying the burn- in problems.
Journal ArticleDOI
Optimal Burn-in Time to Minimize Cost for Products Sold Under Warranty
D. G. Nguyen,D. N. P. Murthy +1 more
TL;DR: This paper examines the optimal burn-In time to achieve a trade-off between the reduction in the warranty cost and the increase in the manufacturing cost (as burn-in can be viewed as a part of the manufacturing process).
Journal ArticleDOI
Design of Screening Procedures: A Review
Kwei Tang,Jen Tang +1 more
TL;DR: It has been well accepted that dependence on inspection to correct quality problems is ineffective and costly, and hence screening (100% inspection) should not be used as a long-term solution for quality problems.
Journal ArticleDOI
Minimizing Some Cost Functions Related to Both Burn-In and Field Use
TL;DR: Various additive cost functions are considered in this paper and it is shown that the optimal burn-in time b* minimizing the cost function is always before t1, i.e., b* > 0.
Journal ArticleDOI
Burn-In Models and Methods: A Review
TL;DR: This paper reviews the burn-in literature which considers different aspects of the problem, but lacks a structure that relates them to one another.
References
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Journal ArticleDOI
Average Renewal Loss Rates
M. V. Johns,R. G. Miller +1 more
TL;DR: In this article, it was shown that the expected value of the profit rate can be defined in four distinct and apparently equally plausible ways, and it is the purpose of this note to show that the various definitions are not necessarily equivalent and to determine the conditions under which they are equivalent.