Question

Refer to Table S6.1 - Factors for Computing Control Chart Limits (3 sigma)LOADING... for this problem. Twelve​ samples, each containing five​ parts, were taken from a process that produces steel rods at Emmanual​ Kodzi's factory. The length of each rod in the samples was determined. The results were tabulated and sample means and ranges were computed. The results​ were:                                                                                                                           

Sample Sample Mean​ (in.) Range​ (in.) Sample Sample Mean​ (in.) Range​ (in.) 1 8.502 0.033 7 8.503 0.041 2 8.502 0.041 8 8.507 0.034 3 8.489 0.034 9 8.495 0.027 4 8.506 0.051 10 8.501 0.029 5 8.499 0.031 11 8.503 0.039 6 8.497 0.036 12 8.506 0.047

For the given​ data, the x double overbar ​= 8.5007 inches ​(round your response to four decimal​ places). Based on the sampling​ done, the control limits for ​3-sigma x overbar chart​ are: Upper Control Limit ​(UCL Subscript x overbar​) ​= 8.5269 inches ​(round your response to four decimal​ places). Lower Control Limit ​(LCL Subscript x overbar​) ​= 8.4744 inches ​(round your response to four decimal​ places). Based on the x overbar​-chart, is one or more samples beyond the control​ limits? No . For the given​ data, the Upper R overbar ​= 0.0 inches ​(round your response to four decimal​ places). The control limits for the ​3-sigma​ R-chart are: Upper Control Limit ​(UCL Subscript Upper R​) ​= nothing inches ​(round your response to four decimal​ places). Lower Control Limit ​(LCL Subscript Upper R​) ​= nothing inches ​(round your response to four decimal​ places). Based on the​ R-chart, is one or more samples beyond the control​ limits? ▼ Yes No . Enter your answer in each of the answer boxes.

Answer 1

X double Bar= average of all sample mean

R Bar = average of all the ranges

Sub group size = 5

UCL for X Bar Chart=X double Bar+(0.577*R Bar) for subgroup size = 5, A2 = 0.577

LCL for X bar Chart=X double Bar-(0.577*R Bar) for subgroup size = 5, A2 = 0.577

UCL for R Chart==2.114*R bar

LCL for R chart= 0*R Bar

1	B	C	D	E
2	Sample	Sample Mean	Range	UCL for X Bar Chart
3	1	8.502	0.033	8.522
4	2	8.502	0.041	LCL for X bar Chart
5	3	8.489	0.034	8.480
6	4	8.506	0.051	UCL for R Chart
7	5	8.499	0.031	0.078
8	6	8.497	0.036	LCL for R chart
9	7	8.503	0.041	0.000
10	8	8.507	0.034
11	9	8.495	0.027
12	10	8.501	0.029
13	11	8.503	0.039
14	12	8.506	0.047
15		X double Bar	R Bar
16		8.501	0.037

X Bar Chart:

R chart:

Conclusion: as all the points are within UCL and LCL, hence, we can conclude that both X bar and Range data are in statistical control, no assignable causes are found.