Avoiding the p-chart for enterprise quality tracking

Part of the teachings of Forrest Breyfogle, and even his recent correspondence partner Donald Wheeler, is that the individuals chart (I-chart) is a better method to monitor a process defect rate than using a p-chart.

Yes, I know that we were all taught that a p-chart is the correct Shewhart chart to use for defect rates when we have an unequal (and equal) sample size. One of my mentors told me, in jest, that the p in a p-chart meant “probably should use an I-chart.” I always thought it was cute until I began examining my history of p-chart success. I found it was nearly always out of control, even when applied to processes that were producing the same average defect rate month to month over many years. You may have seen the same things.

I now teach people the unspoken assumptions to a p-chart and just like Breyfogle and Wheeler, recommend people avoid the p-chart. What we were never taught was that the p-chart control limits are are based on an ideal binomial distribution data population. If the data stream is not producing perfect binomial data, it will be out of control.

What is a perfect binomial, this would mean that every item or transaction has an identical probability of being defective. When is this ever true? Every place I have ever worked experiences defect causes that come and go based on interactions, product mix, raw material batches, personnel changes……….. Some days are better than others. But over time, the average defect rate is consistent, because it is a function of how the process is managed. The defect rate is not constant at every moment, but it drifts up and down around an average. Because of the non-constant defect rate, the i-chart is the best chart to show time dependent performance.

OK, but what if the data is truly a perfect binomial, is the i-chart still a good choice? This is the question I asked myself this morning. To answer it, I used Minitab and simulated a 10 step process where each step and a .002 defect probability for 1000 lots of 300 units. I summed up the number of defects produced at each step to represent the total defectives per lot. This data was plotted with a p-chart, c-chart, and an Individuals chart of the defect rate. This is a true binomial process, so if all three charts show the same out of control conditions, then I can believe the i-chart is also acceptable when the p-chart assumptions are met.

Here is the p-chart of the data

p-chart
p-chart

Here is the c-chart of the data

C-chart
C-chart

Here is the i-chart

Individuals chart
Individuals chart

As you can see, all three charts provide the identical insight into the process behavior, three points above the upper control limit. Now these are all random/common cause events, but 4 out of 1000 data points is reasonable for 3 sigma limits. This demonstrates that the choice of an I-chart is appropriate for defect rates, even if the p-chart assumptions are met.

Join the legion of practitioners working to eliminate the p-chart from scorecards and performance reporting.

Please comment if you have also experienced p-charts reporting OOC when the process was really predictable.