Repetitive Group Sampling Plan Based on Truncated Tests for Weibull Models

Muhammad Aslam,Chi-Hyuck Jun,Munir Ahmad,Mujahid Rasool,Arturo J Fernandez

doi:10.19026/rjaset.7.483

Muhammad Aslam, Chi-Hyuck Jun + Show 3 more

Open Access

https://doi.org/10.19026/rjaset.7.483

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Abstract

This study proposes a new repetitive group sampling plan by attributes based on truncated life test under the Weibull distributions with known shape parameter. The constrained optimization problem is formulated as a nonlinear integer programming to determine the sample size and the acceptance criterion of the proposed plan. The objective function to be minimized is the average sample number, whereas the constraints are related to the lot acceptance probabilities at the acceptable and limiting quality levels. Tables containing the optimal design parameters are constructed for various values of the Weibull shape parameter and the results are explained with several examples. Minimum producer's and consumer's risks are also determined. The proposed sampling plan reduces significantly the average sample number as compared with the traditional single sampling plan. The effect of the mis-specification of shape parameters is also discussed.

Highlights

Two types of censoring known as Type-I and Type-II censoring schemes are commonly used in medical sciences and in life testing experiments
We developed an attributes repetitive sampling plan for the truncated life tests assuming that the lifetime of products follows the Weibull distribution with known shape parameter and that the quality level is represented by the ratio of mean life to the specified life
The probability of lot acceptance is determined by using the Operating Characteristic (OC) function, which is derived to be: Attributes repetitive group sampling plan for weibull models: The Weibull distribution is an important statistical model which has been widely used in many areas, including quality control, reliability analysis and life testing

Summary

Introduction

Two types of censoring known as Type-I and Type-II censoring schemes are commonly used in medical sciences and in life testing experiments. No attempt has been made to study attributes repetitive sampling plans based on truncated life tests for a Weibull distribution.

Results

Conclusion