Stress-Strength Modelling for a New Modified Lindley Distribution Under Progressively Censored Data

In this chapter, the analysis of the stress-strength reliability of the type \(\Lambda = P\left( {X < Z} \right)\) is considered with progressive Type-II censored data when two independent random variables \(X\) (stress) and \(Z\) (strength) follow a modified form of Lindley distribution. The average amount of time a component can withstand stress is derived under this setup in the form of the mean remaining strength. In a classical example, the maximum likelihood and maximum product spacings estimators for the stress-strength parameter are examined. In addition to classical methods, the Bayes estimator of \(\Lambda\) is derived by taking independent gamma priors with a squared error loss function. In this non-classical approach, the estimation of \(\Lambda\) is carried out using a prevalent Markov chain Monte Carlo approach. An investigation using Monte Carlo simulations is accompanied so that the performance of the suggested estimators may be compared. Based on an analysis of a real-world dataset, it has been shown how the proposed stress-strength model may be used in actual practice.