Fraction nonconforming control charts with m-of-m runs rules

Abstract

In this article, we proposed m-of-m control chart for fraction nonconforming to increase sensitivity of the standard p-chart. The m-of-m control chart for fraction nonconforming is described, and the 3-of-3 control chart is discussed in detail as an illustration of the m-of-m control chart. The performance of proposed control charts is measured in terms of average run length, standard deviation of run length and quartiles under zero-state and steady-state modes. The Markov chain approach is used to compute average run length, standard deviation of run length and quartiles. Comparison study revealed that the performance proposed m-of-m control chart with m = 2, 3 is significantly better than the standard p-chart. Average run length values of the proposed control charts are at least 15 % less than that of the standard p-chart values for small to moderate shifts. Standard deviation of run length values of the proposed control charts is also at least 18 % less than the standard p-chart. An example is given to illustrate an application of procedures discussed.