Generalized Stress-Strength Reliability Estimation Under Censoring Schemes

Generalized framework for data generation, Maximum Likelihood Estimation, and Bayesian estimation of stress-strength reliability R = P(Y < X) for arbitrary continuous distributions under censoring schemes based on Chapter 9 of 'Balakrishnan', 'Cramer', and 'Kundu' (2023) . Users provide probability density functions, cumulative distribution functions, survival functions, support bounds, parameter ranges, and sample sizes. Implements data generation under Type-I, Type-II, progressive Type-II, Type-I hybrid, Type-II hybrid, generalized hybrid, progressive hybrid, joint, block random, middle, and truncation censoring schemes, accompanied by diagnostic histograms, dot plots, and autocorrelation plots. Maximum Likelihood Estimation supports optimization routines including 'Newton-Raphson', 'Broyden'-'Fletcher'-'Goldfarb'-'Shanno' ('BFGS'), 'BFGS' in R ('BFGSR'), 'Berndt'-'Hall'-'Hall'-'Hausman' ('BHHH'), Simulated Annealing ('SANN'), Conjugate Gradients ('CG'), and 'Nelder'-'Mead' ('NM'), returning summaries ('AIC', 'coef', 'logLik', 'nIter', 'stdEr', summary, 'vcov'). Bayesian estimation of stress-strength reliability R = P(Y < X) is performed via Gibbs sampling, Metropolis-Hastings algorithm, Importance Sampling, and 'Lindley' approximation (1980). Methods and censoring schemes are described in 'Balakrishnan', 'Cramer', and 'Kundu' (2023, ISBN:978-0-12-398387-9), 'Lindley' (1980) , 'Geweke' (1989) , 'Metropolis' (1953) , 'Hastings' (1970) , 'Geman' and 'Geman' (1984) , 'Kundu' and 'Gupta' (2005) , 'Kundu' and 'Gupta' (2006) , 'Berndt', 'Hall', 'Hall', and 'Hausman' (1974) , 'Fletcher' (1987, ISBN:978-0-471-91547-8), and 'Nelder' and 'Mead' (1965) .