Analysis of Sequential Quality Improvement Plans to Obtain Confidence Bounds

Article Type

Research Article

Publication Title

Journal of Statistical Theory and Practice


Sequential quality improvement plans create a series of product versions with improving reliability by addressing the failure modes of the previous versions. They represent a widely used reliability improvement strategy. Reliability metrics for the current product version needs to be estimated from the failure times of the previous versions. Confidence bounds of the reliability metrics are of more importance to decision makers than point estimates as they allow for an evaluation of a margin of reliability in the product. The availability of exactly one failure time for each product version poses a challenge for obtaining this confidence bound. In this article, we consider a model in which the time to failure distributions belong to a family of distributions indexed by a real valued parameter, whose ordering determines the stochastic ordering of the distributions. We do not make any assumptions about the nature of improvement in reliability, allow for no improvement in reliability for some consecutive versions and relax the requirement of independence of the failure times. We propose a novel statistic, based upon the maximum of the observed failure times, which is proved to be a confidence bound for the parameter of interest with a specified minimum coverage probability. Since the proposed method makes very few assumptions about the nature of the reliability improvement and does not use asymptotic theory, it may be ideal for analysis of time to failure data for catastrophic failures where one would expect few failures. If required, we propose a method for ensuring the monotonicity of the confidence bounds. The methods developed are applied to datasets relating to software debugging and a new dataset derived from an automated error logger. The analysis reveals some surprising insights.



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