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Classical and Bayesian inferences of stress-strength reliability model based on record data
Communications for Statistical Applications and Methods 2024;31:497-519
Published online September 30, 2024
© 2024 Korean Statistical Society.

Sara Moheb1,a, Amal S. Hassanb, L.S. Diabcd

aDepartment of Mathematical Statistics, Egypt;
bDepartment of Mathematical Statistics, Faculty of Graduate Studies for Statistical Research, Egypt;
cDepartment of Mathematical Statistics, Al-Azhar University, Egypt;
dDepartment of Mathematics and Statistics, Faculty of Science, Imam Mohammad Ibn Saud, Saudi Arabia
Correspondence to: 1 Department of Basic Science, Canadian International College, Khalid Ibn El Waleed, Cairo, 4731261, Egypt. E-mail: sara_moheb@science.helwan.edu.eg
Received January 1, 2024; Revised June 1, 2024; Accepted June 27, 2024.
 Abstract
In reliability analysis, the probability P(Y < X) is significant because it denotes availability and dependability in a stress-strength model where Y and X are the stress and strength variables, respectively. In reliability theory, the inverse Lomax distribution is a well-established lifetime model, and the literature is developing inference techniques for its reliability attributes. In this article, we are interested in estimating the stress-strength reliability R = P(Y < X), where X and Y have an unknown common scale parameter and follow the inverse Lomax distribution. Using Bayesian and non-Bayesian approaches, we discuss this issue when both stress and strength are expressed in terms of lower record values. The parametric bootstrapping techniques of R are taken into consideration. The stress-strength reliability estimator is investigated using uniform and gamma priors with several loss functions. Based on the proposed loss functions, the reliability R is estimated using Bayesian analyses with Gibbs and Metropolis-Hasting samplers. Monte Carlo simulation studies and real-data-based examples are also performed to analyze the behavior of the proposed estimators. We analyze electrical insulating fluids, particularly those used in transformers, for data sets using the stress-strength model. In conclusion, as expected, the study’s results showed that the mean squared error values decreased as the record number increased. In most cases, Bayesian estimates under the precautionary loss function are more suitable in terms of simulation conclusions than other specified loss functions.
Keywords : inverse Lomax distribution, lower record values, Bayesian estimation, bootstrap confidence intervals, Markov Chain Monte Carlo