Repetitive Sampling Plans for Life Tests Based on Percentiles of the Half-Normal Distribution with Applications to Software Reliability and Device Lifetime Data

Muhammad Naveed; Muhammad Iltaf; Muhammad Azam; Nasrullah Khan; Muhammad Saeed; Muhammad Zahid Akbar

doi:10.64060/JASR.v1i3.5

Authors

Muhammad Naveed Department of Statistics, Govt Graduate College for boys Gulberg, Lahore, Pakistan Author https://orcid.org/0000-0003-1074-5965
Muhammad Iltaf Department of Statistics, National College of Business Administration and Economics, Lahore, Pakistan Author https://orcid.org/0009-0000-6391-406X
Muhammad Azam Department of Statistics and Computer Science, University of Veterinary and Animal Sciences, Lahore, Pakistan Author https://orcid.org/0000-0001-9123-837X
Nasrullah Khan College of Statistical Science, University of the Punjab, Lahore, Pakistan Author https://orcid.org/0000-0003-0232-3260
Muhammad Saeed Department of Statistics, Punjab Group of Colleges, Lahore, Pakistan Author https://orcid.org/0009-0007-6123-5304
Muhammad Zahid Akbar Department of Mathematics, Kips College Johar Town, Lahore, Pakistan Author https://orcid.org/0009-0007-9308-5945

DOI:

https://doi.org/10.64060/JASR.v1i3.5

Keywords:

Percentile Lifetime, Truncated Life Test, Repetitive Sampling, Average Sample Number

Abstract

Acceptance Sampling Plans (ASPs) are indispensable statistical tools in quality control for making decisions regarding the acceptance or rejection of product lots. While traditional plans often rely on the mean lifetime, percentile-based criteria offer a more robust measure, particularly for capturing tail behavior in lifetime distributions. This paper introduces a novel repetitive sampling plan (RSP) for life tests based on percentiles of the Half-Normal Distribution (HND). The plan is designed to verify that a specified quantile of the product lifetime exceeds a predefined standard. The design parameters, namely the sample size, acceptance number, and rejection number, are obtained through an optimization model that minimizes the Average Sample Number (ASN) while ensuring that both the producer’s risk and the consumer’s risk constraints are satisfied. Comprehensive tables are presented for various practical scenarios, examining the effects of the percentile ratio, termination time multiplier, and life percentile on the performance of plan. A comparative analysis demonstrates that the proposed RSP consistently requires a smaller ASN than the comparable single sampling plan, confirming its superior efficiency in reducing inspection effort and cost. The practical utility of the methodology is illustrated through a real-life example using software reliability data, showcasing its straightforward implementation and significant advantages for quality assurance in industrial settings.

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