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

Ghadah Alomani1, Amer I Al-Omari2

  • 1Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia.

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Summary

This study introduces modified acceptance sampling plans for the two-parameter Xgamma distribution (TPXGD), a new lifetime model. These plans are crucial for quality control in production and engineering, ensuring product reliability.

Keywords:
acceptance sampling plansconsumer's riskminimum sample sizeoperating characteristic functionproducer's risktruncated lifetime testtwo-parameter Xgamma distribution

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Area of Science:

  • Statistics
  • Engineering Quality Control

Background:

  • The two-parameter Xgamma distribution (TPXGD) is a recently proposed lifetime distribution with growing applications.
  • Acceptance sampling plans are vital statistical tools in manufacturing and engineering for quality assurance.

Purpose of the Study:

  • To develop and investigate modified acceptance sampling plans specifically for the TPXGD.
  • To utilize the mean of the TPXGD as a quality parameter within these sampling plans.

Main Methods:

  • Proposed modified acceptance sampling plans for the TPXGD under a truncated lifetime assumption.
  • Investigated key variables: acceptance numbers, minimum sample sizes, operating characteristic function, and producer's risk.
  • Employed numerical examples and a real-data application for illustration.

Main Results:

  • The study details the performance of the proposed sampling plans across various TPXGD parameter values.
  • Demonstrated the practical application of these plans using real-world data analysis.

Conclusions:

  • The developed modified acceptance sampling plans offer a robust framework for quality assessment using the TPXGD.
  • These plans provide valuable tools for engineers and quality control professionals dealing with TPXGD-modeled data.