Reliability assessment through group acceptance sampling under the Darna distribution

Amer Ibrahim Al-Omari; Ehab M. Almetwally; Harsh Tripathi; Ahmad A. Hanandeh; Amer Ibrahim Al-Omari; Ehab M. Almetwally; Harsh Tripathi; Ahmad A. Hanandeh

doi:10.3934/math.2025851

AIMS Mathematics

2025, Volume 10, Issue 8: 19033-19057. doi: 10.3934/math.2025851

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Reliability assessment through group acceptance sampling under the Darna distribution

1.
Department of Mathematics, Faculty of Science, Al Al-Bayt University, Mafraq 25113, Jordan
2.
Department of Mathematics and Statistics, Faculty of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi Arabia
3.
Symbiosis Statistical Institute, Symbiosis International (Deemed University), Pune, India
4.
Department of Mathematics, Faculty of Science, Islamic University of Madinah, Madinah 42351, Saudi Arabia

Received: 19 July 2025 Revised: 07 August 2025 Accepted: 11 August 2025 Published: 21 August 2025
MSC : 62D05, 62N05, 62P30

In this study, a group acceptance sampling plan was proposed when the lifetime of an item follows the Darna distribution (DD). The mean served as a quality parameter to determine the design parameters, including the acceptance number and minimum group size, under a specified test termination time and consumer risk. The operating characteristic values were presented graphically and in tabular form. The minimum group size and operating characteristic values were obtained for various values of the distribution parameters, and the results were illustrated with an example. To illustrate the applicability of the proposed plan, two real-life data sets of failure times in minutes and weeks were analyzed as practical examples. It is preferable to choose higher $ t/\mu_0 $ ($ \mu_0 $ is a given mean value) values to minimize the required number of groups and, hence, reduce the overall cost and inspection effort. In addition, choosing suitable values of $ r $ ($ r $ is the size of the group) and $ t/\mu_0 $ ensures a balance between the inspection effort and the risk of the producer.
- acceptance sampling inspection plan,
- consumer's risk,
- Darna distribution,
- operating characteristic function,
- producer's risk,
- truncated life test
Citation: Amer Ibrahim Al-Omari, Ehab M. Almetwally, Harsh Tripathi, Ahmad A. Hanandeh. Reliability assessment through group acceptance sampling under the Darna distribution[J]. AIMS Mathematics, 2025, 10(8): 19033-19057. doi: 10.3934/math.2025851

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Abstract

In this study, a group acceptance sampling plan was proposed when the lifetime of an item follows the Darna distribution (DD). The mean served as a quality parameter to determine the design parameters, including the acceptance number and minimum group size, under a specified test termination time and consumer risk. The operating characteristic values were presented graphically and in tabular form. The minimum group size and operating characteristic values were obtained for various values of the distribution parameters, and the results were illustrated with an example. To illustrate the applicability of the proposed plan, two real-life data sets of failure times in minutes and weeks were analyzed as practical examples. It is preferable to choose higher $ t/\mu_0 $ ($ \mu_0 $ is a given mean value) values to minimize the required number of groups and, hence, reduce the overall cost and inspection effort. In addition, choosing suitable values of $ r $ ($ r $ is the size of the group) and $ t/\mu_0 $ ensures a balance between the inspection effort and the risk of the producer.

References

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