Ordinary, Bayes, empirical Bayes, and non-parametric reliability analysis for the modified Gumbel failure model Original Research Article

The Gumbel, or double exponential, probability distribution function is modified in order to characterize the failure times of a given system. The maximum likelihood (ML), minimum variance unbiased (MVU), Bayes, empirical Bayes, and non-parametric kernel density estimates of the reliability, failure rate, and cumulative failure rate functions are being studied. We also study target time subject to a specified reliability. Numerical computations are given to illustrate the usefulness of our study.