Consider a reliability model described by a Weibull regression, whose parameters are estimated by the maximum likelihood method. These parameters are used to estimate other quantities of interest such as MTTF (mean time to failure) and quantiles, which in turn play an important role in a reliability analysis. This paper proposes improvements in MTTF and quantile estimators, whose maximum likelihood estimates (MLEs) are biased, particularly in cases involving small sample sizes. A Bootstrap procedure is presented to correct such biases. The proposed procedure is evaluated based on simulations in which the sample size, censoring mechanisms, and percentiles of censored data are varied. These simulations allow one to quantify the bias, since the analytical expression is highly complex. The proposed procedure is illustrated through an example.
bias correction; Bootstrap; MTTF; quantiles; weibull regression model
