Question

A quality manager asked his team to implement p control chart for a process that was recently introduced. The team collected samples of size n = 100 parts hourly over a period of 30 hours and determined the proportion of nonconforming parts for each sample. The mean proportion of nonconforming parts for 30 samples turned out to be 0.025.

1. Determine the upper and lower control limits for the p chart.
2. Discuss how you will use the p Chart and what you will report to the manager.

Answer 1

For the p-chart,

Given,  The mean proportion of nonconforming parts for 30 samples each of size n = 100, is 0.025

i.e. C L : = 0.025

and, control limits(UCL,LCL) :

We have to calculate the p-values(fraction of defectives) for each sample. Then those values along with the average(C L), and the control limits are plotted. If most points are near the average or a few points are near the control limits, but no points are beyond the control limits, then we will report that the process is in statistical control i.e. a stable process.

If any points fall above the upper control limit or below the lower control limit,there will be no need to apply other tests for out of control situations and we will report a special cause is present in the process so that, actions can be taken to find the special cause and permanently remove it from the process . Points if lies on the control limits, will not considered to be out of statistical control.