Question

A process considered to be in control measures an ingredient in ounces. A quality inspector took 10 samples, each with 5 observations as follows:

Samples	Observations
	1	2	3	4	5
1	10	9	10	9	12
2	9	9	11	11	10
3	13	9	10	10	9
4	10	10	11	10	10
5	12	10	9	11	10
6	10	10	8	12	9
7	10	11	10	8	9
8	13	10	8	10	8
9	8	8	12	12	9
10	10	12	9	8	12

a) Using this information, obtain three-sigma (i.e., z=3) control limits for a mean control chart and control limits for a range chart, respectively. It is known from previous experience that the standard deviation of the process is 1.36.

b) Discuss whether the process is in control or not.

Answer 1

a)

b) The process is in control

a) Compute X and R for each subgroup Plot control charts using Xbar, R and control limits Observations Sample #1 #2 #3 #4 #5 #6 #7 #8 #9 #10 10 10 13 10 12 10 10 13 12.00 10.00 9.00 10.00 10.00 9.00 9.00 8.00 9.00 12.00 9.80 7.54 12.06 3.10 0.00 7.07 TRUETRUE 9.80 7.54 12.06 3.10 0.00 7.07 TRUETRUE 9.80 7.54 12.06 3.10 0.00 7.07 TRUETRUE 9.80 7.54 12.06 3.10 0.00 7.07 TRUETRUE 9.80 7.54 12.06 3.10 0.00 7.07 TRUETRUE 9.80 7.54 12.06 3.10 0.00 7.07 TRUETRUE 9.80 7.54 12.06 3.10 0.00 7.07 TRUETRUE 9.80 7.54 12.06 3.10 0.00 7.07 TRUETRUE 9.80 7.54 12.06 3.10 0.00 7.07 TRUETRUE 9.80 7.54 12.06 3.10 0.00 7.07 TRUETRUE 10 10 10 10 10 10 3 10 3 10 10 10 12 Average9.800 3.100 b) Compute X and R R-Chart 9.800 R3.100 Control chart constants corresponding to sample size N Sample size, N D4 2.282 0.729 1 2 345 6 7 8910 c) Control limits for X-chart d) Control limits for R-chart X-Chart 14.00 7.07412.00 10.00 8.00 6.00 4.00 2.00 0.00 UCLr D4R 12.060 LCLr DR - 7.540 - 0.000 e) Process control 0 X-value lie outside of control limits. Therefore based on X-chart, the process is In Control 0 R-value lie outside of control limits. 1 2 345 6 7 8 910 Therefore based on R-chart, the process is In Control