| Abstract: | Statistical process control based on the cumulative counts of conforming items instead of occurrences of non-conformances has proved to be useful for the manufacture of high-quality products. In this paper we study some interesting and useful issues of using cumulative counts in practice. The general problem in the control of high-quality products is first discussed, which leads to the calculation of the probability that a process is out of control when a single non-conforming item is detected. A decision graph is introduced with which we can easily judge whether the process is out of control when a non-conforming item is observed after a number of conforming ones, accompanied by the certainty level of this judgement. Next, using the equivalence of information on one non-conforming item found in a number of inspected items to that on zero non-conforming items in a smaller sample, we give a method for choosing a new starting point to reset the cumulative count after the detection of the non-conforming item. The procedures are all statistically justified and have the practical merit of simplicity in actual applications. |
