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

Abstract

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. • The stress–strength model applied to the progressively Type-I interval censoring. • The finite mixture distributions are applied to describe the strength variables. • The reliability is estimated by EM algorithm and MH within Gibbs algorithm. • The homogeneity of the mixture distribution is tested by the D-test statistic.