Planning of step-stress accelerated degradation test

Estimating the long term performance of highly reliable products has been a difficult problem as accelerated life testing (ALT), which involves testing at highly elevated stresses, often results in too few failures for drawing useful inferences. To overcome this problem, accelerated degradation testing (ADT) has been proposed as a means to predict performance for highly reliable products. It requires one to identify a performance measure that would exhibit degradation and to monitor it over time. Product reliability can then be inferred from the degradation paths without the need of observing actual failures. Although physical failures are not needed in ADT, one usually defines failure as the first time when the degradation process exceeds a pre-specified threshold, so that the degradation path can be correlated to product reliability. As a result, reliability information of a product is embedded in degradation paths of units tested under ADT. In this paper, we look into planning of an ADT in which the test stress is increased in steps from lower stress to higher stress during the test, so that specimens are gradually conditioned to the stressed environment thus avoiding over-stressing. Our objective is to minimize the cost of testing, which is a function of sample size, test duration and number of inspections, as well as obtaining a reliability estimate of a requisite level of precision. Data from degradation paths are used to characterize the appropriate stochastic model underlying the product degradation process. We then derive the maximum likelihood estimators and the mean life at the use stress and its asymptotic variance. This variance is then used as a constraint, in a test plan which minimizes the testing cost. The optimal test plan gives the optimal sample size, number of inspections at each intermediate stress level and number of total inspections.