Research Article InferencesforStress-StrengthReliabilityModelinthePresenceof PartiallyAcceleratedLifeTesttoItsStrengthVariable RashadM.El-Sagheer , 1 AhlamH.Tolba , 2 TaghreedM.Jawa , 3 andNeveenSayed-Ahmed 3 1 Mathematics Department, Faculty of Science, Al-Azhar University, Naser City 11884, Cairo, Egypt 2 Mathematics Department, Faculty of Science, Mansoura University, Mansoura 35516, Egypt 3 Department of Mathematics and Statistics, College of Science, P.O. Box 11099, Taif University, Taif 21944, Saudi Arabia Correspondence should be addressed to Neveen Sayed-Ahmed; nevensayd@yahoo.com Received 21 January 2022; Accepted 14 February 2022; Published 18 March 2022 Academic Editor: Mario Versaci Copyright © 2022 Rashad M. EL-Sagheer et al. is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. We focus on estimating the stress-strength reliability model when the strength variable is subjected to the step-stress partially accelerated life test. Based on the assumption that both stress and strength random variables follow Weibull distribution with a common first shape parameter, the inferences for this reliability system are constructed. e maximum likelihood, two parametric bootstraps, and Bayes estimates are obtained. Moreover, approximate confidence intervals, asymptotic variance-covariance matrix, and highest posterior density credible intervals are derived. A simulation study and application to real-life data are conducted to compare the proposed estimation methods developed here and also check the accuracy of the results. 1.Introduction Stress-strength models have attracted many statisticians for many years due to their applicability in different and diverse areas such as engineering, economics, and quality control, and, in the last years, there have been numerous applications to medical and engineering problems. In the last ten years, many authors have been interested in studying the application of the simple stress-strength reliability model, which is more handled theoretically and at the same time is more simple and applicable to im- plement in practice. is model of reliability contains a strength variable X and a stress variable Y, which is ex- posed to it. Such a system will properly function when X exceeds Y; namely, R � P(X > Y) denotes the reliability system. Many estimation studies of reliability system are considered by several statistician researchers under both complete and censored samples from different models, for example, exponential distribution under progressive type- II censoring by Saraço˘ glu et al. [1], Weibull distribution under complete samples by Kundu and Gupta [2], Kumaraswamy distribution under upper record values by Nadar and Kızılaslan [3], Kumaraswamy distribution under progressive type-II censoring by Nadar et al. [4], Lomax distribution under record values by Mahmoud et al. [5], Burr X distribution under complete samples by Surles and Padgett [6], inverse Lindley distribution under com- plete samples by Sharma et al. [7], exponential and Weibull by Kumar and Siju [8], Weibull-Gamma distribution under progressively type-II censored samples by Mahmoud et al. [9], general exponential form distribution under complete samples by Mokhlis et al. [10], Rayleigh distribution under complete samples by Afshin [11], modified Weibull model under progressively type-II censored samples by Soliman et al. [12], Lindley distribution using progressively first- failure censoring by Kumar et al. [13], generalized inverted exponential distribution under progressively first-failure censoring by Krishna et al. [14], Kumaraswamy expo- nential distribution under progressively type-II censored samples by El-Sagheer and Mansour [15], Burr XII dis- tribution under progressively first-failure censored sam- ples by Saini et al. [16], and generalized Maxwell failure distribution under progressive first-failure censoring by Saini et al. [17]. Hindawi Computational Intelligence and Neuroscience Volume 2022, Article ID 4710536, 13 pages https://doi.org/10.1155/2022/4710536