Designing of Variables Modified Chain Sampling Plan Based on the Process Capability Index with Unknown Mean and Variance

Abstract

SYNOPTIC ABSTRACTThis article proposes a variables-modified chain sampling plan based on the process capability index Cpk for the inspection of normally distributed quality characteristics with unknown mean and variance. The modified chain sampling plan is one of the conditional sampling procedures and this plan under variables inspection will be very useful, particularly in compliance testing. Tables are also constructed to select the optimal parameters of the variables modified chain sampling plan for specified two points on the operating characteristic curve by minimizing the average sample number. Symmetric and asymmetric cases based on the fraction nonconforming by the lower and the upper specification limits are also considered. The optimization problem is formulated as a nonlinear programming problem where the objective function to be minimized is the average sample number, and the constraints are related to lot acceptance probabilities at acceptable quality level and limiting quality level under the operating characteristic curve.