Optimal Designing of Variables Chain Sampling Plan by Minimizing the Average Sample Number

We investigate the optimal designing of chain sampling plan for the application of normally distributed quality characteristics. The chain sampling plan is one of the conditional sampling procedures and this plan under variables inspection will be useful when testing is costly and destructive. The advantages of this proposed variables plan over variables single sampling plan and variables double sampling plan are discussed. Tables are also constructed for the selection of optimal parameters of known and unknown standard deviation variables chain sampling plan for specified two points on the operating characteristic curve, namely, the acceptable quality level and the limiting quality level, along with the producer’s and consumer’s risks. The optimization problem is formulated as a nonlinear programming 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.