Question

In quality control, statistical process control (SPC ) is often employed to analyze the process capability in manufacturing or service operations. Explain the following with an example each :

• What is a p chart  ?
• What is a c chart ?

There are 3 machines in your factory which can produce a ruler. The rulers as produced has a spread in length between 12.5 thru 12.4 inch.

Given the standard deviation of the 3 machines are as follows, calculate the process capability of each machine. Which of the 3 machines has the best process capability index ?

Answer 1

A p chart is a control chart for measuring process variability when the data being measured is attribute data. An attribute data refers to discrete quantity values such as count, proportion, number, etc. In this case a p chart usually utilizes samples and the count of defect. The count of defect divided by sample size for each observation is considered as fraction and the p (stands for proportion) is calculated. These proportion values are then used to calculate the control limits and plotted p values are measured against them. For example, a machine produces 5 defects in the product when 1000 units are observed in sample 1 then it produces 3 defects in the next sample of 500 observation. The p values are 5/1000 = 0.005 and 0.006 respectively.

A c chart is another control chart for measuring attribute data. Here, c stands for count. In contrast to the previous approach of p chart, c chart directly counts the number of defects for each sample. These counts are then used to calculate control limits and then the c values are observed. For example, a plant performs quality control by taking samples of 500 units every hour. The defects observed in the first 2 hours are 2 and 6. The c values for 2 and 6 for the first two samples.