For the case where the lifetime at a constant stress level has a Weibull distribution, statistically optimal and practical accelerated life test plans are developed under the assumptions of intermittent inspection and Type Ⅰ censoring.
For a statistically optimal plan, the low stress level, the proportion of test units allocated, and the inspection times at each over stress level are determined such that the asymptotic variance of the maximum likelihood estimator of a certain quantile at the use condition is minimized. Although the practical plan adopts the same design criterion, it involves three rather than two overstress levels and easily calculated inspection schemes. Despite some loss in efficiency the practical plan has several advantages over the statistically optimal one. For instance, the practical plan can provide means for checking the validity of the assumptions made, may reduce the danger of extrapolation and is more convenient to determine and implement.
Computational experiments are conducted for various combinations of parameter values.
Computational results indicate that the number of inspections at a stress level need not be large for most practical plans to have comparable efficiency with statistically optimal plans, which is an encouraging result in terms of testing efforts ad cost. Among all the allocation plans considered for practical ALT plans, (5:3:2) plan is preferred unless the probability that an item until the censoring time at the use condition $(P_u)$ is close to the specified quantile, for which case (7:2:1) plan is recommended. When the shape parameter is large(i.e., when the failure rate is increasing), the equally-spaced inspection scheme can be used without any severe loss in efficiency. However, when the shape parameter is small (i.e., when the failure rate is decreasing) and $P_u$ and/or the number of inspections is small, equally-spaced inspection may not be an efficient way of inspecting test units, and therefore, equal probability inspection scheme may be used instead. Guidelines are also provided for selecting an appropriate pratical plan, including sample size determination and sensitivity analysis.
