An algorithm for the determination of the optimum target values for two machines in series with quality sampling plans

Recently, there has been a lot of interest in the economics of quality control among researchers. The literature is rich in papers that address the determination of the optimum mean and control limits for a single machine with (and without) 100% inspection. However, it seems that the problem of analysing two machines in series (which has applications in electronics industries, and copper rolling amongst others) has not been addressed. Here an algorithm is developed for finding optimum target values for the two machines when a sampling plan is used. Numerical examples are also given.