Statistical inference and prediction for the Weibull process with incomplete observations

In this article, statistical inference and prediction analyses for the Weibull process with incomplete observations via classical approach are studied. Specifically, observations in the early developmental phase of a testing program cannot be observed. We derive the closed-form expressions for the maximum likelihood estimates of the parameters in both the failure- and time-truncated Weibull processes. Confidence interval and hypothesis testing for the parameters of interest are considered. In addition, predictive inferences on future failures and the goodness-of-fit test of the model are developed. Two real examples from an engine system development study and a Boeing air-conditioning system development study are presented to illustrate the proposed methodologies.