Research Article Decision-Making for the Lifetime Performance Index Basim S. O. Alsaedi , 1 M. M. Abd El-Raouf , 2 E. H. Hafez , 3 Zahra Almaspoor , 4 Osama Abdulaziz Alamri, 1 Kamel Atallah Alanazi, 5 and Saima Khan Khosa 6 1 Department of Statistics, Faculty of Science, University of Tabuk, Tabuk, Saudi Arabia 2 Basic and Applied Science Institute, Arab Academy for Science, Technology and Maritime Transport (AASTMT), Alexandia, Egypt 3 Department of Mathematics, Faculty of Science, Helwan University, Cairo, Egypt 4 Department of Statistics, Yazd University, P. O. Box 89175-741, Yazd, Iran 5 University of Jeddah, Faculty of Science and Arts (Al Kamil), Department of Mathematics, Jeddah, Saudi Arabia 6 Department of Statistics, Bahauddin Zakariya University, Multan, Pakistan Correspondence should be addressed to Zahra Almaspoor; z.almaspoor@stu.yazd.ac.ir Received 29 May 2021; Accepted 2 July 2021; Published 13 July 2021 Academic Editor: Ahmed Mostafa Khalil Copyright © 2021 Basim S. O. Alsaedi 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. e purpose of this research is to develop a maximum likelihood estimator (MLE) for lifetime performance index C L for the parameter of mixture Rayleigh-Half Normal distribution (RHN) under progressively type-II right-censored samples under the constraint of knowing the lower specification limit (L). Additionally, we suggest an asymptotic normal distribution for the MLE for C L in order to construct a mechanism for evaluating products’ lifespan efficiency. We have specified all the steps to carry out the test. Additionally, not only does hypothesis testing successfully assess the lifetime performance of items, but it also functions as a supplier selection criterion for the consumer. Finally, we have added two real data examples as illustration examples. ese two applications are provided to demonstrate how the results can be applied. 1. Introduction Process capability analysis is an efficient method for de- termining a production process’s performance and pro- spective capabilities. In manufacturing sectors, process capability indices (PCIs) are used to determine if the quality of the product meets specified standards. PCIs have garnered considerable interest in the statistical literature during the last three decades. e key motivation for analyzing the process capacity producing PCI is to evaluate the process’s performance and potential capabilities. Process capability analysis aids in the following ways: continuously monitoring process quality using PCI to en- sure produced goods adhere to requirements, giving in- formation on product development to manufacturers and specialists, and establishing a foundation for lowering item failures. e PCIs are classified into three categories: the first is used to quantify the target-the-better quality feature, the second is used to quantify the larger-the-better quality characteristic, and the third is used to quantify the smaller- the-better quality characteristic. For more information and extra details, see [1]. Due to a variety of variables such as time limits or other constraints on money, material resources, or data collection, the researcher may be unable to track the lifespan of all commodities or things in a test. As a result, it is possible that censored samples will be encountered during operation. Proper filtering happens when just the lifetime’s lower limit is known. When only the lifetime cutoff is set, proper filtering occurs. One type of right censorship is referred to as “type-II censorship.” is type of censorship may occur when a certain number of failures occur during the lifespan experiment. Progressive type-II censorship occurred when our at- tention shifted from monitoring n goods to monitoring until the m th failure occurs, and then, the test is ended. As the i th item fails, r i of the items that still functional are cut off from Hindawi Computational Intelligence and Neuroscience Volume 2021, Article ID 3005067, 7 pages https://doi.org/10.1155/2021/3005067