On some sequential life tests

Abstract

B. Epstein and M. Sobel proposed sequential life tests in the exponential case [1], in which a statistic V(t), called "total life", is observed continuously in time t and decision is made at an instant when V(t) does cross the preassigned limits. In the nonreplacement case of tha t test, the probability that a decision can be made af ter all ~ items on test have failed is smaller than one. Therefore the average test time can not remain to be finite so long as ~, the number of test items simultaneously placed on test, is finite. Thus they recommended the sequential test, in which n must be determined so large tha t the probability not to reach any decision is negligible small and some decision rules must be defined in advance to provide for such indeterminable cases. However, it seems to be expensive and troublesome that a sufficiently large number of items are placed on test simultaneously, because test equipments must be so large according to the number of test items. In this paper, the test procedures applicable to the wider class of distributions including the exponential case will be proposed, in which a suitable number of test items are placed on test repeatedly untiU it reaches a decision. The operating characteristic function, the average failure (sample) number and the average test time will be obtained in comparison with the usual sequential test without a continuous time parameter.