Efficiency Comparison in Detecting of Nonconforming Fractional Changing by Using p, PM and EWMA Control Charts

Abstract

This research aims to compare the efficiency of the three control charts in detecting of nonconforming fractional changing: p, PM, and EWMA control charts by using average run length (ARL) as the criterion. In the research, the Monte Carlo technique simulates data as binomial distribution with the nonconforming fractions (p0) of 0.05, 0.2, and 0.4. The sample sizes (n) are 50, 100, 200, and 500. The shifts of nonconforming fraction (δ) are 1.1, 1.2, 1.3, 1.4, and 1.5, and the smooth parameters (λ) for the EWMA control chart are 0.05, 0.2, and 0.4. The results found that the PM control chart is the best in detecting nonconforming fractional changing for all situations. In case of the shift of nonconforming fraction increases, it is shown that the EWMA control chart with almost of λs has the same efficiency as the PM control chart. The p control chart tends to increase efficiency when δ increases. Moreover, when sample size increases, PM and EWMA control charts provide better efficiency. However, the efficiency of detecting nonconforming fractional changing of p control chart is less than the PM and the EWMA control charts for all situations.