Unbiased estimators for mean time to failure and percentiles in a Weibull regression model

Purpose - To present the bootstrap procedure to correct biases in maximum likelihood estimator of mean time to failure (MTTF) and percentiles in a Weibull regression model. Design/methodology/approach - A reliability model is described by a Weibull regression model with parameters being estimated by maximum likelihood method and they will be used estimate other quantities of interest as MTTF or percentiles. When a small sample is employed it is known that the estimates of these quantities are biased. A simulation study varying sample size, censored mechanisms, allocation mechanisms and levels of censored data are designed to quantify these biases. Findings - The bootstrap procedure corrects the biased maximum likelihood estimates of MTTF and percentiles. Practical implications - A minor sample may be required if the bootstrap procedure is required to produce estimator of the quantities as MTTF and percentiles. Originality/value - The employment of bootstrap procedure to quantify the biases since analytical expression of the biases are very difficult to calculate. And the minor samples are needed to obtain unbiased estimates for bootstrap corrected estimator.