Comparing Individual Reliability to Population Reliability for Aging Systems

Christine Anderson-cook
Christine M. Anderson-Cook has been a research scientist in the Statistical Sciences Group at Los Alamos National Laboratory since 2004. Her current research areas include design of experiments, response surface methodology, system reliability and multiple criteria optimization. Dr. Anderson-Cook holds a Ph.D in statistics from the University of Waterloo, Waterloo, Ontario, Canada, as well as an more


When analyzing single-use non-repairable systems that degrade over time, summaries of reliability as a function of age often are naturally formulated for individual systems to answer the question ��For a given system of a particular age, what is its reliability with its associated uncertainty?�� However, in other cases, the natural summary of interest is to predict the probability that an arbitrary system randomly selected from the population works. This second question is a function of both the probability of individual systems working at their given ages as well as the demographics of the population of interest. In this talk we discuss the relevance of both these questions for different applications, describe a method for predicting population reliability, and illustrate how the second summary can be efficiently obtained from individual reliability estimates for analyses based on Probit or Weibull models. We also will discuss how the methodology can be extended if reliability is modeled as a function of both age and usage. The discussion will be based on the following two papers: 1. Lu, L., Anderson-Cook, C.M. (2011) �Prediction of Reliability of an Arbitrary System from a Finite Population� Quality Engineering 23 71-83. 2. Lu, L., Anderson-Cook, C.M. (2011) �Using Age and Usage for Prediction of Reliability of an Arbitrary System from a Finite Population� Quality and Reliability Engineering International 27 179-190. And, both papers are available for download at

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