Donald Wheeler in his classic book^{1} demonstrates why you can use process behavior charts for all your count-based data.

Wheeler uses the term *XmR *Chart in his description. An *XmR *Chart is the same chart we call an I Chart in the PBCharts Excel Add-In. For this article we use the term “process behavior chart” interchangeably with the term “I Chart.”

“Thus, while p-charts, np-charts, c-charts and u-charts use theoretical models to create theoretical limits, the *XmR *Chart lets the data define appropriate empirical limits. This means that you can use an *XmR *Chart with count-based data anytime you wish. Since the p-chart, the np-chart, the c-chart, and the u-chart are all special cases of the chart for individual values, the *XmR *chart will mimic these specialized charts when they would be appropriate. However, when the specialized charts are inappropriate, the *XmR *chart will still work because it uses an empirical approach rather than being based on a specific probability model. Therefore, if you do not know how to verify a particular probability model, or if do not care to do so, you can still use an *XmR *chart with your count-based data.

Thus, you can’t go wrong by placing your count-based data on an *XmR *Chart.”^{2}

He gives an illustration^{3} of an inappropriate use of a p-chart for On-Time Shipments, because p-charts are based on binominal distribution model.

“These theoretical p-chart limits are incorrect because the binominal model is inappropriate for these data. Specifically, the probability of a shipment being on time is not the same for all of the shipments in any given month. The empirical limits of the X Chart, which do not depend upon the appropriateness of any particular probability model, are the correct limits for the data in Figure A.12.”

In this case the limits of the p-chart are almost five times wider than those of the process behavior chart. Figure 2 is the process behavior chart made with the Excel PBCharts Add-In.

The limits produced by p-charts can also be narrower than those produced by process behavior charts. Wheeler gives a second example^{4} shown in Figure 3 and Figure 4.

- Donald J. Wheeler, Understanding Variation: The Key to Managing Chaos 2nd Edition (Knoxville, TN: SPC Press, 2000), 140-142.
- IBID 142
- IBID Figure A.12, 141. Reproduced using Minitab 21©, as Figure 1 in this article.
- IBID Figure A.13, 141. Reproduced using Minitab 21©, as Figure 2 in this article.

No responses / comments so far.