Stress-Strength Reliability and Randomly Censored Model of Two-Parameter Power Function Distribution

The power function distribution is a flexible waiting time model that may provide better fit for some failure data. This paper presents the Bayes estimates of two-parameter power function distribution under progressive censoring. Different progressive censoring schemes have been used for the analysis. The Bayes estimates are obtained, using conjugate priors, under five loss functions including square error, precautionary, weighted, LINEX, and DeGroot loss function. The Gibbs sampling algorithm and Tierney and Kadane's Approximation are used for the Bayes estimates of model parameters, reliability function, and stress-strength reliability. The comparison of the Bayes estimates is considered through the root mean squared errors. One real-life dataset is analyzed to illustrate the applications of proposed estimates. The results from the simulation study and real data analysis suggest that the Bayes estimation was more efficient for the progressive censoring schemes with all the withdrawals at the time of first failure.