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

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  ( > ) in any statistical literature. It resamples a system with random strength () that is subjected to a random strength () such that a system fails in case the stress exceeds the strength. In this study, we consider stress-strength reliability where the strength () follows Rayleigh-half-normal distribution and stress ( , , , and ) 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.