Analysis of sequential monitoring schemes using natural conjugate priors

The complexity of modern manufacturing underscores the need for improved control strategies for these systems. We formulate a Bayesian attribute sequential monitoring plan useful for adaptive control of a production process. The Bayesian framework is based on natural informative conjugate priors that provide an optimal adjustment interval k in response to real-time changes in the operating characteristics of a process. The sampling and adjustment decisions are based on the tradeoffs between quality costs and quality parameters resulting from the process. The parameters include the fraction of nonconforming products p, and the number of nonconforming products r. The quality costs, which include the inspection, cost, repair cost, nonconformance cost, and adjustment cost are fixed and used to develop a breakeven relationship that that results in a sequential sampling construct that optimizes both the systems costs and process quality.