Bayes estimation of defective proportion for single shot device testing data with information on masking and manufacturing defects

The present work addresses the problem of estimating the defective proportion of Single-Shot-Devices under the Bayesian paradigm while taking failure cause information into account. In addition, the maximum likelihood estimation is also presented. The logit transformation is suggested to use for defective proportion parameter for better stability of the numerical maximum likelihood estimate. The same transformation is used for the posterior distribution. Since the posterior distribution becomes complex, we propose the use of Metropolis-Hastings method to draw the posterior samples and present posterior sample based inferences. Bayes estimation under several symmetric and asymmetric loss functions is presented in this work. Predictive posterior density of future failures is also derived. The prior distributions of the model parameters are assumed to follow specific functional forms. A comprehensive simulation study is conducted to examine the performance of the estimates in relation to sample size and model parameters. Our study demonstrates that integrating combined information on masking and defective proportions is crucial for parameter estimation. To demonstrate the practical application of our proposed methodology, we apply it to skin cancer data using the linear failure rate model as survival distribution.