ACCEPTANCE SAMPLING AND COMPONENT REDUNDANCY: CHOOSING OPTIMAL SCENARIO IN K-OUT-OF-M SYSTEMS

In this paper, a sampling policy involving system reliability is proposed. A k-out-of-m system is considered for this purpose. Acceptance sampling and component redundancy both affect the reliability of k-out-of-m systems. According to the cost of sampling and redundancy, it is essential to define an economical procedure to achieve a specified value of reliability. In this paper, we propose a model to specify the optimal scenario considering both sampling and redundancy. A scenario consists of sample number, acceptance number and redundancy in a k-out-of-m system. Proper distributions to construct the reliability function are specified. Decision is made based on the number of defective items in an inspected sample. This is done by specifying a prior distribution on the number of defects in a lot, as the probability of detecting a defective is unknown, and then based on the information of the acceptance sample; the posterior distribution on the number of defects into a distribution on reliability for a given system is defined. Then a total cost function, including the cost of rejecting the batch, the cost of inspection, the cost of defective items detected during operation, the cost of system failure and the cost of redundancy, is defined as a criterion to choose the optimal scenario. The probability of the system failure is obtained based on the system reliability. Furthermore, based on lot defective items, two constraints for producer's risk and consumer's risk are developed. To choose the optimal scenario, an interval for reliability, serve as the target reliability, is considered and then based on the total cost, the best scenario is chosen. In order to demonstrate the application of the proposed model, a numerical example is illustrated. Furthermore, the results of the sensitivity analysis show that the cost of system failure and the cost of redundancy are two key factors to determine the optimal scenario. The variations of the other costs results in choosing scenarios without redundancy.