Reliability Estimation for Stress-Strength Model Based on Unit-Half-Normal Distribution

Many lifetime distribution models have successfully served as population models for risk analysis and reliability mechanisms. We propose a novel estimation procedure of stress-strength reliability in the case of two independent unit-half-normal distributions can fit asymmetrical data with either positive or negative skew, with different shape parameters. We obtain the maximum likelihood estimator of the reliability, its asymptotic distribution, and exact and asymptotic confidence intervals. In addition, confidence intervals of model parameters are constructed by using bootstrap techniques. We study the performance of the estimators based on Monte Carlo simulations, the mean squared error, average bias and length, and coverage probabilities. Finally, we apply the proposed reliability model in data analysis of burr measurements on the iron sheets.

Automated summary

This paper proposes a novel estimation procedure for stress-strength reliability, suitable for two independent unit-half-normal distributions with asymmetrical data and different shape parameters. The performance of the estimators is evaluated through Monte Carlo simulations and other metrics, and the proposed model is applied to data analysis of burr measurements on iron sheets.