A Tool for Evaluating Time-Varying-Stress Accelerated Life Test Plans with Log-Location-Scale Distributions

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2010-06-01
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Hong, Yili
Ma, Haiming
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Meeker, William
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Statistics
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Abstract

Accelerated life tests (ALTs) are often used to make timely assessments of the life time distribution of materials and components. The goal of many ALTs is estimation of a quantile of a log-location failure time distribution. Much of the previous work on planning accelerated life tests has focused on deriving testplanning methods under a specific log-location distribution. This paper presents a new approach for computing approximate large-sample variances of maximum likelihood estimators of a quantile of general log-location distribution with censoring and time-varying stress. The approach is based on a cumulative exposure model. Using sample data from a published paper describing optimum ramp-stress test plans, we show that our approach and the one used in the previous work give the same variance-covariance matrix of the quantile estimator from the two different approaches. Then, as an application of this approach, we extend the previous work to a new optimum ramp-stress test plan obtained by simultaneously adjusting the ramp rate and the lower start level of stress. We find that the new optimum test plan can have a smaller variance than that of the optimum ramp-stress test plan previously obtained by adjusting only the ramp rate. We also compare optimum ramp-stress test plans with the more commonly used constant-stress accelerated life test plans. We also conduct simulations to provide insight and to check the adequacy of the large-sample approximate results obtained by the approach.

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This preprint was published as Yili Hong, Haiming Ma, and W.Q. Meeker, "A Tool for Evaluating Time-Varying-Stress Accelerated Life Test Plans with Log-Location-Scale Distributions", IEEE Transactions on Reliability (2010): 620-627, doi: 10.1109/TR.2010.2083252.

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