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Abstract:
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In developing an optimal accelerated degradation test (ADT) plan in a reliability analysis, most existing studies pre-specify the form of their test plans (e.g., a constant-stress, parallel-stress, or ramp test plan) and then determine the optimal values of the plan design parameters. Few provide clear justifications for using these types of plans, other than their ease of implementation. In this paper, we assume the product's degradation signal follows a time-transformed Wiener process and intermediate degradation data during the test are available. The objective function for obtaining an optimal ADT is the estimated asymptotic variance of the maximum likelihood estimator for the pth quantile of the lifetime distribution, subject to a budget constraint and time-censoring. We prove that, for any given optimal test plan with a continuous stress function, there exists a step-stress plan that is also optimal or nearly optimal. The explicit Fisher information used in the objective function is too complicated to obtain so we consider an approximation and, with some simple assumptions, obtain the (approximate) optimal step-stress plan with just a few steps. An example of LED is given.
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