**10. Conclusions**

In this paper, inference for multi-reliability using unit alpha power exponential distributions for stress–strength variables based on the progressive first failure is considered. The conventional methods such as maximum likelihood and Bayesian methods for point estimation of the parameter model and R are obtained. The Fisher information and confidence intervals such as asymptotic, boot-p, and boot-t methods are also examined. Various optimal criteria have been found. Monte Carlo simulations and real-world application examples are used to evaluate and compare the performance of the various proposed estimators.

**Author Contributions:** Investigation, R.A., E.M.A., A.A.M., C.P., and H.R.; methodology, R.A., C.P., and H.R.; software, R.A. and E.M.A.; validation, R.A., A.A.M., E.M.A., C.P., and H.R.; writing, R.A., E.M.A., and H.R.; funding acquisition, R.A. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by Princess Nourah bint Abdulrahman University Researchers Supporting Project number (PNURSP2022R50), Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The data used to support the findings of this study are included within the article.

**Acknowledgments:** The authors extend their appreciation to Princess Nourah bint Abdulrahman University Researchers Supporting Project number (PNURSP2022R50), Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia.

**Conflicts of Interest:** The authors declare no conflict of interest.
