On Estimation of Reliability Functions using Record values from Proportional Hazard Rate Model

Ananya Malhotra,Ajit Chaturvedi

doi:10.17713/ajs.v48i3.831

Abstract

Two measures of reliability functions, namely R(t)=P(X>t) and P=P(X<Y) have been studied based on record values from proportional hazard rate model (PHR) model. For estimation of P, we generalize the results of Basirat et al. (2016) when X and Y belong to different family of distributions from PHR model. Uniformly minimum variance unbiased estimator (UMVUE), maximum likelihood estimator (MLE) and Bayes estimator (BS) are obtained for the powers of the parameter and reliability functions. Simulation studies and a real data example have been presented for illustrative purposes. Asymptotic and exact confidence intervals of the parameters and reliability functions are constructed. Testing procedures are also developed for various hypotheses.

Highlights

The most popularly used parameter in life testing analysis and reliability engineering is the reliability function
Basirat, Baratpour, and Ahmadi (2016) estimated P based on record values from proportional hazard rate model (PHR) model and obtained its maximum likelihood estimator (MLE), Uniformly minimum variance unbiased estimator (UMVUE) and Bayes estimator
The Bayes estimator of P (X < Y ) when X and Y belong to the same family of distributions of PHR model, is n + ν1 + 1 n + m + ν1 + ν2 + 2

Summary

Introduction

The most popularly used parameter in life testing analysis and reliability engineering is the reliability function. One may refer to the work of Baklizi (2008a) who compared the likelihood and Bayesian estimation of stress-strength parameter using lower records from generalized exponential model. The hottest day ever, the longest winning streak in professional basketball, the lowest stock market figure, are a case in point Such type of data can be analyzed as record values from a sequence of independent and identically distributed random variables. Basirat, Baratpour, and Ahmadi (2016) estimated P based on record values from PHR model and obtained its MLE, UMVUE and Bayes estimator. Their estimation procedures assumed that X and Y belong to the same family of distribution but have different shape parameters. The paper ends with a brief discussion on our results

The proportional hazard rate model and record values

Bayesian estimators

Confidence intervals

Hypotheses testing

Real data example

Numerical computations and simulations

10. Discussion