Optimal repetitive reliability inspection of manufactured lots for lifetime models using prior information

Repetitive group inspection of production lots is considered to develop the failure censored plan with minimal expected sampling effort using prior information. Optimal reliability test plans are derived for the family of log-location-scale lifetime distributions, whereas a limited beta distribution is assumed to model the proportion nonconforming, p. A highly efficient and quick step-by-step algorithm is proposed to solve the underlying mixed nonlinear programming problem. Conventional repetitive group plans are often very effective in reducing the average sample number with respect to other inspection schemes, but sample sizes may increase under certain conditions such as high censoring. The inclusion of previous knowledge from past empirical results contributes to drastically reduce the amount of sampling required in life testing. Moreover, the use of expected sampling risks significantly improves the assessment of the actual producer and consumer sampling risks. Several tables and figures are presented to analyse the effect of the available prior evidence about p. The results show that the proposed lot inspection scheme clearly outperforms the standard repetitive group plans obtained under the traditional approach based on conventional risks. Finally, an application to the manufacture of integrated circuits is included for illustrative purposes.