Question

Each value represents the number of mistakes (defects) found on a student loan application. Values for 50 consecutive loan applications are given. Calculate the appropriate centerline and 3-sigma control limits for the c-chart, and then plot the data and create a control chart. Does the process appear to be in a state of statistical control? Why or why not?

Upper control limit (UCL) =

Centerline (CL) =

Lower control limit (LCL) =

Process in statistical control?

Expense Report Auditing

Week	Number of Reports Reviewed	Reports Non-conforming	Proportion Non-conforming
4-Nov	30	8	0.267
11-Nov	30	6	0.200
18-Nov	30	9	0.300
25-Nov	30	7	0.233
2-Dec	30	4	0.133
9-Dec	30	10	0.333
16-Dec	30	7	0.233
23-Dec	30	7	0.233
30-Dec	30	7	0.233
6-Jan	30	7	0.233
13-Jan	30	8	0.267
20-Jan	30	11	0.367
27-Jan	30	9	0.300
3-Feb	30	8	0.267
10-Feb	30	4	0.133
17-Feb	30	6	0.200
24-Feb	30	8	0.267
3-Mar	30	8	0.267
10-Mar	30	8	0.267
17-Mar	30	4	0.133

Answer 1

Answer:

The given data is,

Week	Number of Reports Reviewed	Reports Non-conforming	Proportion Non-conforming
04-Nov	30	8	0.267
11-Nov	30	6	0.2
18-Nov	30	9	0.3
25-Nov	30	7	0.233
02-Dec	30	4	0.133
09-Dec	30	10	0.333
16-Dec	30	7	0.233
23-Dec	30	7	0.233
30-Dec	30	7	0.233
06-Jan	30	7	0.233
13-Jan	30	8	0.267
20-Jan	30	11	0.367
27-Jan	30	9	0.3
03-Feb	30	8	0.267
10-Feb	30	4	0.133
17-Feb	30	6	0.2
24-Feb	30	8	0.267
03-Mar	30	8	0.267
10-Mar	30	8	0.267
17-Mar	30	4	0.133

We have to calculate the average number of non-conforming reports.

where N is the total number of items and c_i the number of reports non-conforming per item.

Therefore,

Centerline, upper control limit and the lower control limit can be determined as below:

Centerline (CL) = = 7.3

Uppler control limit (UCL) =

Lower control limit (LCL) =

Practically, the lower control limit cannot be negative; hence, the lower control limit is taken as zero.

i.e. Lower control limit (LCL) = 0.

Then after plotting the above control limits and the reports non-conforming, the c-chart is as below:

The above c-chart clearly exhibits that all the points are within the control limits. Hence, it can be said that the process is in statistical control with an average of 7.3 non-conforming reports per lot reviewed.