Estimation of Stress-Strength Reliability for Exponentiated Inverted Weibull Distribution Based on Lower Record Values
Amal S. Hassan
Institute of Statistical Studies and Research, Cairo University, Egypt.
Hiba Z. Muhammed
Institute of Statistical Studies and Research, Cairo University, Egypt.
Mohammed S. Saad *
Institute of Statistical Studies and Research, Cairo University, Egypt.
*Author to whom correspondence should be addressed.
Abstract
The estimation of stress-strength reliability function based on record values has attracted the attention of authors because of its important role in industrial tests, where in some situations not all observations are considered in the study but only observations which are more extreme than the current observations, which represent record values, are the subject of the study. This paper deals with the estimation of R = P [Y < X ] , when X and are two independently exponentiated inverted Weibull distributed random variables based on lower record values. Non-Bayesian estimator using maximum likelihood method and Bayesian estimators using squared error and LINEX loss functions are derived. The exact confidence interval of the reliability is also derived. For illustrative purposes, analysis of a simulated data set has been performed to compare the different estimators and to investigate the coverage probabilities of confidence intervals.
Keywords: Exponentiated inverted Weibull distribution, stress- strength reliability, lower record values.