Question

Problem 10-25 (Algo)

Resistors for electronic circuits are manufactured on a high-speed automated machine. The machine is set up to produce a large run of resistors of 1,000 ohms each. Use Exhibit 10.13.
To set up the machine and to create a control chart to be used throughout the run, 15 samples were taken with four resistors in each sample. The complete list of samples and their measured values are as follows: Use three-sigma control limits.

SAMPLE NUMBER		READINGS (IN OHMS)
1		1027	994	977	994
2		975	1013	999	1017
3		988	1016	974	997
4		998	1024	1006	1010
5		990	1012	990	1000
6		1016	998	1001	1030
7		1000	983	979	971
8		973	982	975	1030
9		992	1028	991	998
10		997	1026	972	1021
11		990	1021	1028	992
12		1021	998	996	970
13		1027	993	996	996
14		1022	981	1014	983
15		977	993	986	983

a. Calculate the mean and range for the above samples. (Round "Mean" to 2 decimal places and "Range" to the nearest whole number.)

b. Determine [Math Processing Error]X= and [Math Processing Error]R− . (Round your answers to 3 decimal places.)

Xbar
Rbar

c. Determine the UCL and LCL for a [Math Processing Error]X− chart. (Round your answers to 3 decimal places.)

UCL
LCL

d. Determine the UCL and LCL for R-chart. (Leave no cells blank - be certain to enter "0" wherever required. Round your answers to 3 decimal places.)

UCL
LCL

e. What comments can you make about the process?

• Process is in statistical control
• Process is out of statistical control

Answer 1

Answers a and b:

READINGS (IN OHMS)				R= Max- Min	X-bar= average of sample
1027	994	977	994	50.000	998.00
975	1013	999	1017	42.000	1001.00
988	1016	974	997	42.000	993.75
998	1024	1006	1010	26.000	1009.50
990	1012	990	1000	22.000	998.00
1016	998	1001	1030	32.000	1011.25
1000	983	979	971	29.000	983.25
973	982	975	1030	57.000	990.00
992	1028	991	998	37.000	1002.25
997	1026	972	1021	54.000	1004.00
990	1021	1028	992	38.000	1007.75
1021	998	996	970	51.000	996.25
1027	993	996	996	34.000	1003.00
1022	981	1014	983	41.000	1000.00
977	993	986	983	16.000	984.75
				38.067	998.850
				R-bar (Average of above values)	X-bar-bar (average of above values)

D4, D3 and A2 are taken from table of factors computing 3 sigma control limits, sample size=4

Answer c: X bar limits

A2 (n=4)			0.729
control limits for X bar,
CL or Xbarbar			998.850
UCL=Xbarbar+ (A2)*Rbar			1026.601
LCL=Xbarbar- (A2)*Rbar			971.099

Answer d: Range limits

D4 (n=4)=			2.282
D3 (n=4)=			0
control limits for Range,
CL or R-bar=			38.067
UCL=R-bar*D4			86.868
LCL=R-bar*D3			0.000

Answer e: Process is in statistical control.  As we can see that NO sample is beyond control limits in charts

X-bar= average of sample	UCL	CL	LCL
998.00	1026.601	998.850	971.099
1001.00	1026.601	998.850	971.099
993.75	1026.601	998.850	971.099
1009.50	1026.601	998.850	971.099
998.00	1026.601	998.850	971.099
1011.25	1026.601	998.850	971.099
983.25	1026.601	998.850	971.099
990.00	1026.601	998.850	971.099
1002.25	1026.601	998.850	971.099
1004.00	1026.601	998.850	971.099
1007.75	1026.601	998.850	971.099
996.25	1026.601	998.850	971.099
1003.00	1026.601	998.850	971.099
1000.00	1026.601	998.850	971.099
984.75	1026.601	998.850	971.099