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Symmetry
Volume 15
Issue 12
10.3390/sym15122187
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Article

A New Cosine-Originated Probability Distribution with Symmetrical and Asymmetrical Behaviors: Repetitive Acceptance Sampling with Reliability Application

by
Huda M. Alshanbari
1,
Gadde Srinivasa Rao
2,
Jin-Taek Seong
3,*,
Sultan Salem
4 and
Saima K. Khosa
5
1
Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia
2
Department of Mathematics and Statistics, University of Dodoma, Dodoma P.O. Box 259, Tanzania
3
Graduate School of Data Science, Chonnam National University, Gwangju 61186, Republic of Korea
4
Department of Economics, Birmingham Business School, College of Social Sciences, University of Birmingham, Edgbaston, Birmingham B15 2TT, UK
5
Department of Mathematics and Statistics, University of Saskatchewan, Saskatoon, SK S7N 5A2, Canada
*
Author to whom correspondence should be addressed.
Symmetry 2023, 15(12), 2187; https://doi.org/10.3390/sym15122187
Submission received: 8 September 2023 / Revised: 14 November 2023 / Accepted: 15 November 2023 / Published: 12 December 2023
(This article belongs to the Special Issue Skewed (Asymmetrical) Probability Distributions and Applications across Disciplines III)
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Abstract

Several new acceptance sampling plans using various probability distribution methods have been developed in the literature. However, there is no published work on the design of new sampling plans using trigonometric-based probability distributions. In order to cover this amazing and fascinating research gap, we first introduce a novel probabilistic method called a new modified cosine-G method. A special member of the new modified cosine-G method, namely, a new modified cosine-Weibull distribution, is examined and implemented. The density function of the new model possesses symmetrical as well as asymmetrical behaviors. The usefulness and superior fitting power of the new modified cosine-Weibull distribution are demonstrated by analyzing an asymmetrical data set. Furthermore, based on the new modified cosine-Weibull distribution, we develop a new repetitive acceptance sampling strategy for attributes with specified shape parameters. Finally, a real-world application is presented to illustrate the proposed repetitive acceptance sampling strategy.
Keywords: cosine function; weibull model; acceptance sampling plan; producer’s risk; consumer’s risk; median life; repetitive sampling; statistical modeling cosine function; weibull model; acceptance sampling plan; producer’s risk; consumer’s risk; median life; repetitive sampling; statistical modeling

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MDPI and ACS Style

Alshanbari, H.M.; Rao, G.S.; Seong, J.-T.; Salem, S.; Khosa, S.K. A New Cosine-Originated Probability Distribution with Symmetrical and Asymmetrical Behaviors: Repetitive Acceptance Sampling with Reliability Application. Symmetry 2023, 15, 2187. https://doi.org/10.3390/sym15122187

AMA Style

Alshanbari HM, Rao GS, Seong J-T, Salem S, Khosa SK. A New Cosine-Originated Probability Distribution with Symmetrical and Asymmetrical Behaviors: Repetitive Acceptance Sampling with Reliability Application. Symmetry. 2023; 15(12):2187. https://doi.org/10.3390/sym15122187

Chicago/Turabian Style

Alshanbari, Huda M., Gadde Srinivasa Rao, Jin-Taek Seong, Sultan Salem, and Saima K. Khosa. 2023. "A New Cosine-Originated Probability Distribution with Symmetrical and Asymmetrical Behaviors: Repetitive Acceptance Sampling with Reliability Application" Symmetry 15, no. 12: 2187. https://doi.org/10.3390/sym15122187

APA Style

Alshanbari, H. M., Rao, G. S., Seong, J.-T., Salem, S., & Khosa, S. K. (2023). A New Cosine-Originated Probability Distribution with Symmetrical and Asymmetrical Behaviors: Repetitive Acceptance Sampling with Reliability Application. Symmetry, 15(12), 2187. https://doi.org/10.3390/sym15122187

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