Hassan was the company plotter. Give him any data set and he could plot a graph that was not only accurate, but also aesthetically pleasing. One afternoon he took some attribute data and plotted it as a p-chart

Question

When Saba, his supervisor, saw the plot he insisted it be discarded and in its place a c-chart should be constructed. Hassan made the c-chart and noticed that when he placed the two charts one on top of the other, the lines created by the data points were exactly the same shape. Has our plotting colleague made a mistake? If not, why should there be these two types of charts when the data generate identical lines?

Answer 1

The p-chart uses a yes-no type of classification—typically "defective or not defective." This yes/no, two-valued data is binomially distributed, and one way to consider the "p" in p-chart is the proportion defective. The c-chart is used for situations in which a product can have more than one defect per unit. The "c" in c-chart is therefore the count of defects in an item. This data is governed by the Poisson distribution. It is natural that the two plots would display the same shape; the binomial distribution is a special case of the Poisson distribution. The p-chart allows the user to work with a variable sample size, either by averaging samples sizes or dealing with specific sample sizes on a point by point basis. The c-chart requires a constant sample size. For a constant sample size and attribute data, the two charts should arrive at the same conclusion of either in or out of control and can be superposed.