An acceptance sampling plan for the odd exponential-logarithmic Fréchet distribution: applications to quality control data

Abstract

This study focuses on implementing a group acceptance sampling plan (GASP) for simultaneous inspection of objects with complex lifespan patterns described by the odd exponential logarithmic (OEL) Fréchet distribution. The inspiration from the proposed model stems from the challenges posed by the objects that exhibited right-skewed, j-shaped, reversed j-shaped and nearly symmetric densities, along with decreasing and increasing hazard rates. A mathematical function is derived to identify key points in the distribution, crucial for designing the inspection process based on factors like testing duration and acceptable risk levels. Performance is assessed across various quality levels, with a simulation study providing insights into parameter changes. The results are clarified via visual representations. The minimum ratios of actual to expected lifespan at specific risk levels, utilizing real-world data to validate the approach are computed. Finally, a comparison is driven in the quest of highlighting the efficacy and versatility of the proposed acceptance sampling plan (ASP) under the inverse log-logistic and generalized exponential (GE) models.

Keywords:

• Odd exponential-logarithmic Fréchet distribution
• producer’s risk
• consumer’s risk
• operating characteristic function
• group acceptance sampling plan

REVIEWING EDITOR:

• Jones Ian Philip PhD, Senior Editor, The University of Birmingham, Metallurgy & Materials, Elms Rd, Birmingham, UNITED KINGDOM, N/A, B15 2TT

Subjects:

• Applied Mathematics
• Mathematics Education
• Statistics & Probability

Classification codes::

• 62E15
• 62E05
• 62E10

Disclosure statement

No potential conflict of interest was reported by the author(s).