Question

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	9.104	0.044	7	9.103	0.021
2	9.100	0.051	8	9.103	0.058
3	9.089	0.042	9	9.097	0.039
4	9.108	0.037	10	9.103	0.038
5	9.097	0.048	11	9.103	0.054
6	9.097	0.053	12	9.108	0.061

For the given data, the X (double bar) =______inches (round your response to four decimal places)

Based on the sampling done, the control limits for 3-sigma x-bar chart are:
Upper Control Limit (UCLxbar ) =______ Inches (round your response to four decimal places)
Lower Control Limit (LCLxbar ) =______ Inches (round your response to four decimal places)

Based on the x-bar chart, the process is a) OUT OF CONTROL or b) IN CONTROL

For the given data, the R (average range of the samples) =______ Inches (Round to four decimal places)

The control limits for the 3-sigma R-chart are:
Upper Control Limit (UCLR) =_______inches (round your response to for decimal places)
Lower Control Limit (LCLR) =______ inches (round your response to four decimal places)

Based on the R-chart, the wire cutting process is a) OUT OF CONROL OR b) IN CONTROL

Answer 1

Answer: R bar is the mean of all Range. The formula used is = sum of all range/12.

Similarly, X-bar-bar is mean of all X-bar. The formula used is = sum of all X bar/12.

R= Max- Min	X-bar
9.104	0.044
9.1	0.051
9.089	0.042
9.108	0.037
9.097	0.048
9.097	0.053
9.103	0.021
9.103	0.058
9.097	0.039
9.103	0.038
9.103	0.054
9.108	0.061
9.101	0.046
R-bar	X-bar-bar

Answers related to X bar

control limits for x-bar
UCL= Xbar-bar+ 3*STD			0.0773
CL= X-bar-bar			0.0455
LCL= Xbarbar- 3*STD			0.0137
standard deviation X-bar=			0.0106

Yes, the process is in control. Because all the points lie within its control limits. And all the points of X-bar lies in X-bar control limits

Answers related to Range

control limits for R
UCL=R-bar+ 3*STD	9.1164
CL= R-bar	9.1010
LCL=R-bar- 3*STD	9.0856
standard deviation R=	0.0051

Yes, the process is in control. Because all the points lie within its control limits. And all the points of range lies in Range control limits

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