Question

The College of Business has been having trouble with errors on student admittance records and you have been asked to investigate the cause of the problem. A form is considered defective if it has one or more errors. You think you have found one of the main reasons for the errors but in order to prove it, you decide to develop a process control chart to follow the current process for a few days. On the next three days, you collect 15 samples of 25 forms each and observe the following number of forms with errors on them:

Sample Number	# of forms in sample with errors		Sample Number	# of forms in sample with errors
1	4		9	6
2	3		10	8
3	6		11	5
4	9		12	4
5	4		13	6
6	3		14	10
7	7		15	3
8	7

A.) Develop the appropriate process control chart(s) using 3 sigma control limits.

B.) You follow the process for two more days, obtain results similar to that shown above, and correct any special causes that may exist. In an effort to improve the process, you make some changes and after the changes are made, collect five more samples of 25 forms each. The number of defects found is shown below:

Sample Number	1	2	3	4	5
# of Defects	5	4	3	5	3

**Plot and label these five observations on the same control chart(s) developed in part A. What comments can be made about the process now? Should any changes be made to the old control chart(s) given the new evidence? If so, describe the changes that should be made and explain why. If not, explain why not?**

Answer 1

(A)

Here we are considering 'Defectives'. So, the appropriate control chart will be a 'p-chart'.

(B)

Sample Number	# of forms in sample with errors (N.p)	p = N.p/N
16	5	0.20
17	4	0.16
18	3	0.12
19	5	0.20
20	3	0.12

The nature of the plot suggests that the countermeasures taken have yielded reduction in proportion defectives than the previous trend. The nature of the change reveals that the mean proportion defective have reduced along with the dispersion.

However, only 5 samples are too early to make changes in UCL and LCL of the control chart. The change may be proposed after monitoring a few more number of samples and if it is established that the countermeasures are effective permanently to bring changes the process.