Lio, YuhlongChen, Ding-Geng (Din)Tsai, Tzong-RuWang, Liang2024-08-142024-08-142024-03Lio, Y.; Chen, D.-G.; Tsai, T.-R.; Wang, L. The Reliability Inference for Multicomponent Stress–Strength Model under the Burr X Distribution. AppliedMath 2024, 4, 394–426. https://doi.org/10.3390/appliedmath4010021.2673-9909 (online)10.3390/appliedmath4010021http://hdl.handle.net/2263/97640DATA AVAILABILITY STATEMENT: Complete monthly water capacity data for the Shasta Reservoir from 1981 to 1985 are given in Appendix G. Section 6 includes the observed complete strength and stress data sets.The reliability of the multicomponent stress–strength system was investigated under the two-parameter Burr X distribution model. Based on the structure of the system, the type II censored sample of strength and random sample of stress were obtained for the study. The maximum likelihood estimators were established by utilizing the type II censored Burr X distributed strength and complete random stress data sets collected from the multicomponent system. Two related approximate confidence intervals were achieved by utilizing the delta method under the asymptotic normal distribution theory and parametric bootstrap procedure. Meanwhile, point and confidence interval estimators based on alternative generalized pivotal quantities were derived. Furthermore, a likelihood ratio test to infer the equality of both scalar parameters is provided. Finally, a practical example is provided for illustration.en© 2024 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).Multicomponent stress–strength modelBurr X distributionGeneralized pivotal estimationAsymptotic theoryMaximum likelihood estimator (MLE)SDG-04: Quality educationSDG-09: Industry, innovation and infrastructureArticle