Question

An accounts department is concerned about the number of internal purchase forms that its users completed incorrectly. As a result they are monitoring the proportion of purchase forms that were not completed correctly. This was chosen, rather than measuring the actual number of defects, because any number of defects on a form required about the same effort to revise. The following table shows number of forms completed incorrectly "out of 200 forms" that is processed each day. Construct a control chart for the data that monitors the proportion of incorrect forms. Is the process in control?

Day	Number of Incorrect Forms
1	18
2	19
3	18
4	18
5	25
6	18
7	20
8	20
9	18
10	20
Sum	194

IMPORTANT: In this problem, keep 3 decimal places in your calculations.

1. Which of the following charts is appropriate?
   1. P Chart
   2. C Chart
2. Based on your choice on the last question, calculate "one" of the followings: P (for P chart), or C (for C chart)
3. If you chose P Chart, how much is standard deviation of p (sigma_p)? (Leave empty if you are not doing P chart)
4. Upper Control Limit:
5. Lower Control Limit:
6. Is the proportion of incorrect forms in control?
   1. Yes
   2. No

Answer 1

a. Which of the following charts is appropriate ?

Ans : P Chart

P chart is used when defectives items are being monitored

C chart when number of defects are being monitored.

For the given problem, each day out of 200 form how many incorrect forms(Defective forms) , hence the p chart is appropriate.

Control Limit : CL : = Total number of defective forms / Total number of forms Inspected

Each day 200 forms being processed and inspected

Number of days = 10

Total number of forms inspected/processed = 200 x 10 =2000

Total number of defective forms = 194

= Total number of defective forms / Total number of forms Inspected = 194/2000=0.097

n : number of forms processed every day = 200

Upper Control limit : UCL

Lower Control Limit

Upper Control Limit: 0.1598

Lower Control Limit: 0.0342

p : proportion of defective for each day = Number of incorrect forms per day / Number of forms processed:200

proportion of defective for each day calculated and tabulated below

Day	Number of Incorrect Forms	p: Proportion of defectives
1	18	18/200 = 0.09
2	19	19/200 =0.095
3	18	18/200 =0.09
4	18	18/200 =0.09
5	25	25/200 = 0.125
6	18	18/200=0.09
7	20	20/200=0.1
8	20	20/200=0.1
9	18	18/200=0.09
10	20	20/200=0.1

As all the proportions : p are within the UCL and LCL. Hence the process is in control.

Is the proportion of incorrect forms in control?

Ans : Yes