P-Chart or Fraction non-confirming chart
In process quality check, we inspect many quality characteristic of a product to verify the product parameters. If all product parameters meets with the requirement or standard then product called as a conforming product. And if any parameters does not meet the requirement then product is called as a non-confirming product. A product may have one or more product parameters or requirements.
Let us consider a sample of 50 numbers taken from a batch during processing & during inspection 10 numbers from sample found non-confirming. Then fraction of non-confirming (P) is 0.2 or in percentage 20%. The fraction nonconforming is defined as the ratio of the number of nonconforming items in a population to the total number of items in that population.
A control chart used for this fraction non confirming is called as P-Chart. P-chart is based on the Binomial Distribution.
Calculation of Control Limit
Example:
30 samples of n = 50 cans each were selected at half-hour intervals over a three-shift period in which the machine was in continuous operation. The data are shown in below Table
Calculation
Since the 30 samples contain nonconforming products, Using as an estimate of the true process fraction nonconforming, we can now calculate the upper and lower control limits as given below:
Construction of P-Chart
Plot the fraction non-confirming with UCL (upper control limit) & (LCL) Lower control limit.
The control chart with center line at and the above upper and lower control limits is shown below. The sample fraction nonconforming from each preliminary sample is plotted on this chart.
We note that two points, those from samples 15 and 23, plot above the upper control limit, so the process is not in control. These points must be investigated to see whether an assignable cause can be determined.
The np Control Chart. It is also possible to base a control chart on the number nonconforming rather than the fraction nonconforming. This is often called an number nonconforming (np) control chart.