Question

5. Metropolis Supply Company manufactures paper clips and other office products. Although inexpensive, paper clips have provided the firm with a high margin of profitability. So, it is important to monitor closely the number of clips produced that are bad and cannot be sold. Samples of size 200 are selected each day and the number of bad clips is determined, below are the results for the last 10 samples (remember each sample is 200 paper clips): 1 1 2 3 6 7 Sample Defectives 4 5 46 8 6 9 10 10 2 5 1 3 4 5 a) Establish upper and lower control limits for the control chart. b) Has the process been in control? (you may want to sketch a rough chart to answer this) c) A co-worker, unfamiliar with the control charting technique asks: when should the control limits be changed?

Answer 1

Answer a:

Sample	nonconformities	Observations
1	7	200
2	5	200
3	3	200
4	4	200
5	6	200
6	4	200
7	5	200
8	6	200
9	10	200
10	2	200
total	52	2000
steps and formulas, for z=3
Proportion of defects=P	total nonconformities/total observations	0.026
Q=	1-P	0.974
N=	average sample size	200
Standard deviation, Sp	squareroot(P*Q/N)	0.011
UCL=	P + z*Sp	0.060
LCL=	P - z*Sp	-0.008
	defects cannot be negative, therefore negative LCL is taken as '0'	0.000

Answer b:

P Chart 7 9 1 2 3 4 5 6 proportion of defect=defectives/observations 8 U 10 CL P CL L

The process is in control: As we can see that NO sample is beyond control limits in charts

Answer c: Usually control limits are changed after 20 samples. In this case, every sample is collected every day so control limits should be changed after 20 days.