Understanding the Effect of Large Subgroup Sizes on Overdispersion and Using Laney’s P’ Chart to Monitor Overdispersed Data

Abstract

Background The traditional Shewhart’s P chart is an important statistical process control tool that’s used to monitor processes that yield binary data. However, it has been known for showing a high rate of false alarms (i.e. overdispersion) when handling data with large subgroup sizes. Large subgroup sizes were usually considered to be the cause of overdispersion while no solid evidence actually exists to support this believe. In an effort to manage overdispersion Laney’s P’ chart was proposed in 2002 as a superior alternative to the traditional P chart. And the P chart diagnostic test was also introduced in some software packages to detect any overdispersion in the data and to recommend the suitable chart. Aim In this study we aimed at exploring the effect of large subgroup sizes on the overdispersion of data and we also attempted to test Laney’s P’ chart and the P chart diagnostic test in detecting and handling overdispersed data. Method An Experimental study was conducted using a single set of real data in addition to nine sets of simulated data with variable characteristics. All data sets were used to perform the P chart diagnostic test and to plot Shewhart P chart and Laney’s P’ chart. Results Large subgroup sizes proved to have no effect on binomially distributed data but if the data is not truly binomial, increasing the subgroup sizes will exaggerate overdispersion. In this case using Laney’s P’ chart will successfully resolve the problem. Conclusion The problem of overdispersion is not due to large subgroup sizes rather than it’s due to the false assumption that the data follows a binomial distribution when it frequently doesn’t. An ideal remedy for this problem is to discover a better fitting distribution for the data. Till then Laney’s P’ chart is a practical and capable remedy. Recommendations The P chart diagnostic tool should be used to detect any overdispersion before using Shewhart’s P chart. And if overdispersion is detected Laney’s P’ chart is a recommended alternative. We also recommend Further study of the performance of Laney’s P’ chart and other suggested distributions that can outperform the binomial distribution as a basis for the P chart.