When is a p-chart the best choice?

In class on Tuesday this topic came up.  A student was concerned that we are teaching that an individuals chart is a better way to plot defect rates at a business level.  How can the student explain it when he gets back to his organization.  So here is a shot at an explanation.

A p-chart is based on a binomial distribution, the distribution of pass/fail data.  The control limits are calculated based on the variability you would see, randomly, from a binomial distribution.  A process would be in control (with a p-chart) if the variation in the percentages does not exceed what you would randomly expect from a population with a known constant defect rate.  This variability is known as the sampling variation.  If the percentage changes more than you would have expected with random sampling variation, then the p-chart would be out of control.

The real question is if a set of defect data, from a real process, is truly a binomial distribution.  Does every transaction/unit have the same probability of being defective?  If not, then the defect data would not be a binomial distribution, and the p-chart is not appropriate.  In most business conditions, a defect rate is derived from multiple causes.  Each defect cause comes and goes as the process is executed.  At times, multiple causes are acting on the process, so the defect rate cycles up and down as the process is executed.  The variation in the defect rate exceeds what is expected for a pure binomial distribution, because it is really a mixture of many binomial distributions that all have changing rates of occurrence.

Since the defect rate is not a binomial, the next logical choice is an individuals chart.  This chart sets its control limits based on the time-to-time variation in the individual values, percentages in this case.  If the variation in the percentages is predictable, which it should be because you are measuring a managed process, all of the process controls and requirements keep it consistent.  The individuals chart then assesses if the data is consistently varying around a mean value.  If it is, the process is considered as stable and predictable.

In my view, both charting methods have value, but they ask different questions of the data.  A p-chart asks if the defect rate fits a pure binomial distribution; an i-chart asks only  if it is consistent.  Both are important, but the i-chart is the best choice for Lean Six Sigma tracking.

So, when is a p-chart the best choice?  It is the best choice when you are examining a single process that is under identical conditions and you are tracking a single defect rate.  In this case, the p-chart will be in control if the defect rate is truly constant over time.  If it is out of control, you know that the defect cause is coming and going, not constant.

1 thought on “When is a p-chart the best choice?”

  1. Comment received by email

    “I tried to leave a comment, but I was blocked because I’m behind a proxy.

    “This is a well articulated and compelling argument for using I-charts when tracking processes driven by multiple inputs.”

    Reed”

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