Truncated life testing under resubmitted sampling plans for Weibull distribution

In a truncated life testing, the test of each item is terminated at a predetermined time which is usually a coefficient of mean, median or other percentiles of lifetime. Life testing and acceptance sampling plans are two major fields of reliability theory and statistical quality control. In a reliability acceptance sampling (RAS) plan the quality characteristic of interest is lifetime. Thus, in designing RAS plans, two subjects of life testing and acceptance sampling plans should be taken into consideration. In this paper, one type of sampling plans, which is known as resubmitted sampling (RS) plans, is proposed for truncated life testing. The items are considered Weibull distributed with a known shape parameter. To obtain the operating characteristic (OC) curve of the RS plan, an equation is derived and to optimize the value of average sample number (ASN), three models are proposed: (I) minimizing ASN in acceptable quality level (AQL), (II) minimizing ASN in limiting quality level (LQL) and (III) minimizing ASN based on the both AQL and LQL. In optimizing the models, the constraints related to the consumer’s and producer’s risks are taken into consideration. Finally, numerical examples and sensitivity analyses are conducted. According to the results of comparison of RS and single sampling (SS) plans, it cannot be concluded that one scheme monotonically outperforms the other. Moreover, from the aspect of OC curve, the acceptance probability of a given lot under the RS plan is slightly larger than the corresponding value in the SS plans.