Sequential inspection sampling plan based on Burr-Ⅻ amputated life testing with numerical illustrations and industrial applications

Mohammad Abiad; Md. Mahabubur Rahman; Oluwafemi Samson Balogun; Yusra A. Tashkandy; Mahmoud E. Bakr; M. Yusuf; Anoop Kumar; Haitham M. Yousof; Basma Ahmed; Mohammad Abiad; Md. Mahabubur Rahman; Oluwafemi Samson Balogun; Yusra A. Tashkandy; Mahmoud E. Bakr; M. Yusuf; Anoop Kumar; Haitham M. Yousof; Basma Ahmed

doi:10.3934/math.2025669

AIMS Mathematics

2025, Volume 10, Issue 6: 14917-14942. doi: 10.3934/math.2025669

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Research article

Sequential inspection sampling plan based on Burr-Ⅻ amputated life testing with numerical illustrations and industrial applications

1.
College of Business Administration, American University of the Middle East, Kuwait; mohammad.abiad@aum.edu.kw
2.
Department of Statistics, Islamic University, Kushtia-7003, Bangladesh; sagor@stat.iu.ac.bd
3.
Department of Computing, Faculty of Science, Forestry and Technology, University of Eastern Finland, FI-70211 Kuopio, Finland; Samsb@uef.fi
4.
Department of Statistics and Operations Research, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia; ytashkandi@ksu.edu.sa
5.
Department of Statistics and Operations Research, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia; mmibrahim@ksu.edu.sa
6.
Department of Mathematics, Helwan university, Faculty of Science, Egypt; mohammed.yousof@yahoo.com
7.
Department of Statistics, Faculty of Basic Science, Central University of Haryana, Mahendergarh, India, 123031; anoop.asy@gmail.com
8.
Department of Statistics, Mathematics and Insurance, Benha University, Egypt
9.
Department of Information System, Higher Institute for Specific Studies, Giza, Egypt; dr.basma13@gmail.com

Received: 25 October 2024 Revised: 30 May 2025 Accepted: 05 June 2025 Published: 30 June 2025
MSC : 62N05; 62P30; 62L10; 62L10

It is often desired for practical reasons to cease a life test at a predetermined period $ {{𝓽}}_{0} $. In this study, we provide sequential inspection sampling plan (SISP) for amputated life tests underlying the Burr Ⅻ (BTXII) distribution. We considered the $ \rho ^{{\rm{th}}}$ percentile lifetime of a product as the quality parameter. The sequential sampling plan is a dynamic and efficient technique to quality control and statistical decision-making. Unlike fixed sample plans, which require a predetermined number of samples before deciding, sequential plan enables ongoing analysis as a batch is examined. This flexible plan enables decisions- such as rejecting, accepting or continuing the sampling process - to be made after each sample, which is cumulative data for the number of nonconforming items. Acceptance, rejection limit lines, and optimal sample size at levels of manufacturer and customer errors were analyzed. A technique is provided for calculating the operation characteristic (OC) function and average sample number (ASN) in the suggested SISP. The effectiveness of the SISP was compared to the single, double, and repeating sampling strategies. In comparison to the single, double, and repetitive acceptance sampling plans (RASPs) the proposed sequential sampling acceptance strategy requires fewer sample resources on average for amputated life testing. The suggested method's uses are demonstrated with illustrated instances. In industrial applications, two actual sets of data are employed to demonstrate the SISP's flexibility.
Citation: Mohammad Abiad, Md. Mahabubur Rahman, Oluwafemi Samson Balogun, Yusra A. Tashkandy, Mahmoud E. Bakr, M. Yusuf, Anoop Kumar, Haitham M. Yousof, Basma Ahmed. Sequential inspection sampling plan based on Burr-Ⅻ amputated life testing with numerical illustrations and industrial applications[J]. AIMS Mathematics, 2025, 10(6): 14917-14942. doi: 10.3934/math.2025669

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Abstract

It is often desired for practical reasons to cease a life test at a predetermined period $ {{𝓽}}_{0} $. In this study, we provide sequential inspection sampling plan (SISP) for amputated life tests underlying the Burr Ⅻ (BTXII) distribution. We considered the $ \rho ^{{\rm{th}}}$ percentile lifetime of a product as the quality parameter. The sequential sampling plan is a dynamic and efficient technique to quality control and statistical decision-making. Unlike fixed sample plans, which require a predetermined number of samples before deciding, sequential plan enables ongoing analysis as a batch is examined. This flexible plan enables decisions- such as rejecting, accepting or continuing the sampling process - to be made after each sample, which is cumulative data for the number of nonconforming items. Acceptance, rejection limit lines, and optimal sample size at levels of manufacturer and customer errors were analyzed. A technique is provided for calculating the operation characteristic (OC) function and average sample number (ASN) in the suggested SISP. The effectiveness of the SISP was compared to the single, double, and repeating sampling strategies. In comparison to the single, double, and repetitive acceptance sampling plans (RASPs) the proposed sequential sampling acceptance strategy requires fewer sample resources on average for amputated life testing. The suggested method's uses are demonstrated with illustrated instances. In industrial applications, two actual sets of data are employed to demonstrate the SISP's flexibility.

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