BAYESIAN ANALYSIS OF DATA WITH ONLY ONE FAILURE

摘要

The bearings of a certain type have their lives following a Weibull distribution. In a life test with 20 sets of bearings, only one set failed within the specified time, and none of the remainder failed even after the time of test has been extended. With a set of testing data like that in Table 1, it is required to estimate the reliability at the mission time. In this paper, we first use hierarchical Bayesian method to determine the prior distribution and the Bayesian estimates of various probabilities of failures, p_i's, then use the method of least squares to estimate the parameters of the Weibull distribution and the reliability. Actual computation shows that the estimates so obtained are rather robust. And the results have been adopted for practical use.