Calculate the overall fraction defective from all of sample:

ABC insurance company desires to design a control chart to check whether insurance claim forms are being correctly completed. The company intends to utilize the chart to see if improvements in the design of the form are effective. To begin the procedure the company gathered data on the number of incorrect completed forms over the past 10 days. The insurance company processes thousands of these forms each of day, and because of the high cost of inspecting each form, only a small representative sample was gathered each day. The data and analysis are given in Table

Solution                                   

To build the control chart, first calculate the overall fraction defective from all of samples. This sets the centre line for the control chart.

p' =   91 /3000 = 0.03033

After that calculate the sample standard deviation :

At last calculate the upper and lower control limits. For z = 3, we have

UCL = p' + 3s p  = 0.03033 + 3 (0.00990) = 0.06004

LCL = p' - 3s p  = 0.03033 - 3 (0.00990) = 0.00063

Table: Insurance Company Claim Form