## 3 Interval Estimation
### Bootstrap Confidence Interval
Then, the ACI based on the MLE is derived, where the delta method is used. The percentile BootCI is also constructed. Additionally, the Bayes estimates, BCIs, and HPDCIs are obtained using the MCMC method. The stochastic simulations are performed using the R software. According to the results, the Bayes estimates under the gamma priors using the precautionary loss function exhibit the smallest MADs and MSEs among all the point estimates. Among all the interval estimates, the BCIs have the shortest lengths and the HPDCIs have the highest coverage probabilities. Finally, the applicability of the method is illustrated using real data. Our study focuses solely on the estimation of the MSSR based on the Chen distribution using a common second shape parameter. In the future, we will explore the case of unequal shape parameters. Additionally, the multicomponent stress-strength system we study contains only one stress component and we do not consider scenarios involving multiple stress components. In the future, we will explore a more complex system and further extend the model to cases where there is more than one stress component. Furthermore, we assume that the strength random variables are independently and identically distributed, which may not accurately reflect certain real-world situations. Therefore, the study of multicomponent stress-strength systems with non-identical strength variables will be considered in the future. Investigation, C.H. ; Supervision, W.G. All authors have read and agreed to the published version of the manuscript. [PERSON]'s work was partially supported by The Development Project of China Railway (No. N202J017) and the Fund of China Academy of Railway Sciences Corporation Limited (No. 2022 YJ161). Not applicable. The data presented in this study are openly available in [9]. The authors declare no conflict of interest. ## Abbreviations \begin{tabular}{l l} MSSR & Multicomponent stress-strength reliability \\ MLE & Maximum likelihood estimate \\ ACI & Asymptotic confidence interval \\ BootCI & Bootstrap confidence interval \\ BCI & Bayesian credible interval \\ HPDCI & Highest posterior density credible interval \\ MCMC & Markov Chain Monte Carlo \\ GELF & Generalized entropy loss function \\ C.S & Censoring scheme \\ F1 & Squared error loss function \\ F2 & Entropy loss function \\ F3 & Precautionary loss function \\ MAD & Mean absolute deviation \\ MSE & Mean squared error \\ AL & Average length \\ CP & Coverage probability \\ PDF & Probability density function \\ \end{tabular} 

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