Statistical Control for Atribute Data. P Chart

The proportion of defectives in each subgroup is shown in this type of chart and indicates the lack of control in the process. Suppose that a furniture factory produces tables. The surface of it should be free of defects, meaning no scratches on it. Sampling the batches, quality inspector collected the following data:

Batch no.	Batch size	Number of defectives
1	100	10
2	100	8
3	125	9
4	95	6
5	100	7
6	100	7
7	125	7
8	110	8
9	90	7
10	100	7

Needed computations are:

• divide the number of defectives to batch size, thus resulting the proportion of detectives in each batch (10/100 = 0.1, 8/100 = 0.08, 9/125 = 0.072, etc.);
• sum separately the number of all batches and number of defectives (e.g. sum of batches is 1045 and sum of defectives is 79);
• divide the sum of defectives to the sum of batches and the result is mean of the proportion of defectives (in the example, the average is 0.07559);
• compute the lower and upper control limits (LCL and UCL) using the formulas: LCL = p -3 sqrt(p(1-p)/ni), where ni is the batch size and p is the mean computed previously. UCL = p +3 sqrt(p(1-p)/ni);
• if LCL is lower than 0 set it to 0. If UCL is greater than 1, set it to 1;
• plot the computed data on the chart and observe if there is any observation that fall outside the control limits.

P chart is shown above, near the table. Because all results fall within control limits, is concluded the existence of a control in production process. Assuming that run number 4 indicates a number of defectives of 22, for the same batch size of 95, the resulted P chart is shown below. Is observed that at inspection number 4, the proportion of defectives go beyond the upper control limit. This indicates a lack of control, and is a strong suggestion that a 100% inspection of batch no. 4 should be undertaken.