EXACT SAMPLE SIZE DETERMINATION IN A WEIBULL TEST PLAN WHEN THERE IS TIME CENSORING

摘要

Engineers who conduct reliability tests need to choose the sample size when designing a test plan. The model parameters and quantiles are the typical quantities of interest. The large-sample procedure relies on the property that the distribution of the Mike quantities is close to the standard normal in large samples. In this paper, we use a new procedure based on both simulation and asymptotic theory to determine the sample size for a test plan. Unlike the complete data case, the Mike quantities are not pivotal quantities in general when data are time censored. However we show that the distribution of the Mike quantities only depend on the expected proportion failing and obtain the distributions by simulation for both complete and time censoring case when data follow Weibull distribution. We find that the large-sample procedure usually underestimates the sample size even when it is said to be 200 or more. The sample size given by the proposed procedure insures the requested nominal accuracy and confidence of the estimation when the test plan results in complete or time censored data. Some useful figures displaying the required sample size for the new procedure are also presented.