A New Markov Chain Based Acceptance Sampling Policy via the Minimum Angle Method

We develop an optimization model based on Markovian approach to determine the optimum value of thresholds in a proposed acceptance sampling design. Consider an acceptance sampling plan where items are inspected and when the number of conforming items between successive defective items falls below a lower control threshold value, then the batch is rejected, and if it falls above a control threshold value, then the batch is accepted and if it falls within the thresholds, the process of inspecting the items continues. A decision is made to accept or reject the batch. We begin with developing a Markov model for determining performance measures of sampling designs, resulting in an acceptance sampling plan optimized based on the minimum angle method. Then, the performance measures of the acceptance sampling plan are determined and the optimum values of thresholds are selected in order to optimize the objective functions. In order to demonstrate the application of the proposed methodology, numerical examples are illustrated.