Statistical Inferences of the Rest Lifetimes of Ball Bearings&amp;#039; Residual Lifetimes Based on Rayleigh Residual Type II Censored Data

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

doi:10.3844/jmssp.2016.182.191

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.

Highlights

In the last few decades, the prediction problem of future lifetimes, based on a sequence of known lifetimes, had a great reputation among other important sciences
We introduce an example of some ball bearings lifetimes, where we will ignore the lifetimes which are less than other known t which is considered by experts to be the lifetime that a single ball bearing will survive with its artificial error
We have studied the problem of estimation and prediction for the two-parameter Rayleigh distribution under residual type-II censored data

Summary

Introduction

In the last few decades, the prediction problem of future lifetimes, based on a sequence of known lifetimes, had a great reputation among other important sciences. We may ignore some known lifetimes called as non effective, this term (non effective lifetimes) is used to denote lifetimes that are less than some predetermined time t This predetermined time t may be determined as a lifetime that some chipset will survive for a small lifetime even though it has some artificial error. We introduce an example of some ball bearings lifetimes, where we will ignore the lifetimes which are less than other known t which is considered by experts to be the lifetime that a single ball bearing will survive with its artificial error. Based on the remaining lifetimes of non defective ball bearings, we will use the methodology that is introduced below to predict the future lifetimes of still surviving ball bearings. The origin and other aspects of this distribution can be found in Siddiqui (1962) and Miller and Sackrowttz (1967)

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Conclusion