Repetitive Group Sampling Plan Based on Truncated Tests for Weibull Models

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.