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Reliability estimation in a Weibull lifetime distribution with zero-failure field data



The estimation of product reliability has attracted worldwide attention during the past several decades. The estimation procedure usually begins with parameter estimation based on test data. When there is no failure occurring in tests, traditional approaches like Maximum Likelihood Estimation (MLE) cannot be applied to estimate parameters. When product lifetime follows a Weibull distribution, to cope with this problem, we propose the modified MLE (MMLE) for estimating the parameters, based on the zero-failure data. In this paper, we also consider the prior reliability estimate from a similar product and make use of it by incorporating it with the MMLE to construct the shrinkage preliminary test estimator (SPTE). We present the calculation method of the shrinkage factor in the SPTE, by referring to the comparison of critical quality characteristics related to product reliability, between the current batch of products and the similar (or earlier version) batch of products. Restrictions for the shrinkage factor to ensure the performance of SPTE are also discussed. The example demonstrates that the proposed SPTE of the product reliability is an effective methodology to estimate the product reliability and improve the estimation performance of the MMLE, when only zero-failure data are available. Copyright © 2010 John Wiley & Sons, Ltd.