Reliability estimation of stress-strength model using finite mixture distributions under progressively interval censoring

This paper considers the reliability estimation of the stress-strength model based on progressively Type-I interval censored data, where the random stress variable follows a Lindley distribution and the random strength variable follows a finite mixture of exponential distributions. The maximum likelihood estimation and 95% confidence interval estimation of the stress-strength reliability are deduced by using EM algorithm and Bootstrap sampling, respectively. The Bayesian estimation and 95% highest posterior density credible interval of the stress-strength reliability under squared error loss function are obtained by using the Metropolis-Hastings within Gibbs algorithm. To test the homogeneity of the finite mixture distributions, the D-test statistic is introduced. Then, we use the D-test statistic to test the homogeneity of a real data, compare the finite mixture exponential distributions with a single exponential distribution by using the Akaike information criterion (AIC) values, and analyze this data using the proposed methodology. Finally, Monte Carlo simulations are performed for illustrative purpose.