Supplier selection critical decision values for processes with multiple independent lines

The process yield is the most common criterion considered for decision making in supplier selection problem. For normally distributed processes with multiple independent lines, the SpkM index provides an exact measurement for the overall yield. Therefore, the SpkM index can be implemented to deal with the supplier selection problem with processes having multiple independent lines. In this article, a test statistic obtained by a division method is employed to establish a hypothesis testing procedure, with two phases, which is developed to determine whether two suppliers are equally capable or not. The sampling distribution and the probability density function of the test statistic are derived. For various minimum requirements of process capability, number of lines, sample sizes, magnitudes of the difference between the two suppliers and the type I error, the critical values for decision making are presented. The required sample sizes for various designated powers at given type I error are tabulated. A thin-film transistor type liquid-crystal display application example is provided to demonstrate the testing procedure.