Question

You manage a fabrication shop and have collected the following measurements (cm). You collected 7 random samples each day for a month. Below find the average of those 7 measurements and the range. You do not know the natural variation. Construct an x-bar and range chart. Include several sentences about your conclusions after analyzing your charts.

Sample	Sample mean (cm.)	Sample range
1	50	13
2	53	11
3	53	13
4	55	13
5	54	11
6	51	10
7	52	9
8	53	10
9	52	9
10	53	10
11	55	12
12	54	10
13	53	11
14	54	13
15	54	9
16	50	10
17	52	11
18	54	9
19	52	13
20	52	12
21	53	12
22	52	10
23	54	9
24	55	13
25	57	11
26	56	10
27	57	13
28	56	9
29	58	9
30	56	9
31	58	9

Continuing on with the data from the fabrication shop (cm. measurements), you have the following additional information. The standard deviation is 1.3 cm. The contract specifies that parts will be between 50 cm and 60 cm. What is the Cp? Express with 2 decimal places.

Answer 1

Conclusion:

There is a total of 210 observations. Each sub-group has 7 observations creating a total of 31data points. Both charts are in control and within the UCL and LCL. This indicates that there is no special cause of variation only natural, inherent cause of variation. The x bar chart is showing the mean of the first subgroup is 50. The centerline of 31 subgroups is 53.81, UCL is 58.31(3 sigmas above the center line) and LCL is 49.31 (3 sigmas below the centerline). The x bar is indicating that the process is within the defined limits of UCL and LCL. Two data points are near the UCL indicating natural variation in the process. R bar chart is in control and with the defined UCL and LCL limits.

Calculations:

Quality control/x-bar chart
Number of samples	31
Sample size	7
Data
Sample	Sample mean (cm.)	Sample range
1	50	13
2	53	11
3	53	13
4	55	13
5	54	11
6	51	10
7	52	9
8	53	10
9	52	9
10	53	10
11	55	12
12	54	10
13	53	11
14	54	13
15	54	9
16	50	10
17	52	11
18	54	9
19	52	13
20	52	12
21	53	12
22	52	10
23	54	9
24	55	13
25	57	11
26	56	10
27	57	13
28	56	9
29	58	9
30	56	9
31	58	9

Calculations:

Ans: Cp=1.28
Data
Upper tolerance limit	60
Lower tolerance limit	50
Mean (optional)
Standard deviation	1.3
Process Capability Ratio, Cp	1.28
Formula (Cp)
=(Upper tolerance limit-Lower tolerance limit)/(6* standard deviation)
=(60-50)/(6*1.3)
1.28