Journal of Mathematics and Statistics

Statistical Inferences of the Rest Lifetimes of Ball Bearings' Residual Lifetimes Based on Rayleigh Residual Type II Censored Data

Ghassan K. Abufoudeh, Omar M. Bdair and Raed R. Abu Awwad

DOI : 10.3844/jmssp.2016.182.191

Journal of Mathematics and Statistics

Volume 12, Issue 3

Pages 182-191

Abstract

In this study, we consider statistical inference problems for the residual life data that come from the Rayleigh model based on type II censored data. Maximum likelihood and Bayesian approaches are used to estimate the scale and location parameters for the Rayleigh model, the Gibbs sampling procedure is used to draw Markov Chain Monte Carlo (MCMC) samples and MCMC samples have been used to compute the Bayes estimates and to construct symmetric credible intervals. Furthermore, we estimate the posterior predictive density of the future ordered data and then obtain the corresponding predictors. The Gibbs and Metropolis samplers are used to predict the life lengths of the missing lifetimes in multiple stages of the residual type II censored sample. Numerical comparisons for a real life data involving the ball bearings’ lifetimes and the artificial data are conducted to assess the performance of the parameters' estimators and the predictors of future ordered data using some specialized computer programs.

Copyright

© 2016 Ghassan K. Abufoudeh, Omar M. Bdair and Raed R. Abu Awwad. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.