Estimate Stress-Strength Reliability Model Using Rayleigh and Half-Normal Distribution

Abstract

In the field of life testing, it is very important to study the reliability of any component under testing. One of the most important subjects is the “stress-strength reliability” term which always refers to the quantity $P\left(X>Y\right)$ in any statistical literature. It resamples a system with random strength (X) that is subjected to a random strength (Y) such that a system fails in case the stress exceeds the strength. In this study, we consider stress-strength reliability where the strength (X) follows Rayleigh-half-normal distribution and stress ( $Y_1,Y_2,Y_3$ , and $Y_4$ ) follows Rayleigh-half-normal distribution, exponential distribution, Rayleigh distribution, and half-normal distribution, respectively. This effort comprises determining the general formulations of the reliabilities of a system. Also, the maximum likelihood estimation approach and method of moment (MOM) will be utilized to estimate the parameters. Finally, reliability has been attained utilizing various values of stress and strength parameters.