Single acceptance sampling plans based on truncated lifetime tests for two-parameter Xgamma distribution with real data application

Ghadah Alomani; Amer I. Al-Omari; Ghadah Alomani; Amer I. Al-Omari

doi:10.3934/mbe.2022624

Mathematical Biosciences and Engineering

2022, Volume 19, Issue 12: 13321-13336. doi: 10.3934/mbe.2022624

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Single acceptance sampling plans based on truncated lifetime tests for two-parameter Xgamma distribution with real data application

Ghadah Alomani ^{1
,
,},
Amer I. Al-Omari ^{2
,
,}

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, Faculty of Science, Al al-Bayt University, Mafraq, Jordan

Received: 03 August 2022 Revised: 26 August 2022 Accepted: 30 August 2022 Published: 13 September 2022

Recently, the two-parameter Xgamma distribution (TPXGD) is suggested as a new lifetime distribution for modeling some real data. The TPXGD is investigated in different areas and generalized to other forms by many of the researchers. The acceptance sampling plans are one of the main important statistical tools in production and engineering fields. In this paper, modified acceptance sampling plans for the TPXGD are proposed with the assumption that the lifetime is truncated at a predetermined level. The mean of the TPXGD model is utilized as a quality parameter. The variables of the acceptance sampling plans including the acceptance numbers, the minimum sample sizes, operating characteristic function and the producer's risk are investigated for various values of the model parameters. Numerical examples are offered to illustrate the process of the proposed plans. Also, a real data is fitted to the TPXGD and an application based on the suggested acceptance sampling plans is considered for explanation.
- two-parameter Xgamma distribution,
- acceptance sampling plans,
- truncated lifetime test,
- producer's risk,
- operating characteristic function,
- minimum sample size,
- consumer's risk
Citation: Ghadah Alomani, Amer I. Al-Omari. Single acceptance sampling plans based on truncated lifetime tests for two-parameter Xgamma distribution with real data application[J]. Mathematical Biosciences and Engineering, 2022, 19(12): 13321-13336. doi: 10.3934/mbe.2022624

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Abstract

Recently, the two-parameter Xgamma distribution (TPXGD) is suggested as a new lifetime distribution for modeling some real data. The TPXGD is investigated in different areas and generalized to other forms by many of the researchers. The acceptance sampling plans are one of the main important statistical tools in production and engineering fields. In this paper, modified acceptance sampling plans for the TPXGD are proposed with the assumption that the lifetime is truncated at a predetermined level. The mean of the TPXGD model is utilized as a quality parameter. The variables of the acceptance sampling plans including the acceptance numbers, the minimum sample sizes, operating characteristic function and the producer's risk are investigated for various values of the model parameters. Numerical examples are offered to illustrate the process of the proposed plans. Also, a real data is fitted to the TPXGD and an application based on the suggested acceptance sampling plans is considered for explanation.

References

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