Question

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	992	992	1000	1027
2	978	994	985	1018
3	1021	998	1018	994
4	974	1022	999	1026
5	1000	1012	1030	991
6	974	987	985	987
7	1005	973	1011	1001
8	983	1024	1012	977
9	990	1004	973	999
10	990	1018	1024	1001
11	998	976	1029	980
12	1024	1020	1020	976
13	1026	1018	1029	971
14	982	979	982	989
15	991	988	980	994

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

Sample Number	Mean	Range
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15

b. Determine X=X= and R−R−. (Round your answers to 3 decimal places.)

X=X=
R−R−

c. Determine the UCL and LCL for a X−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?

	The process is in statistical control.
	The process is out of statistical control.

Answer 1

Answers a are in BOLD

sample		1	2	3	4	R= Max- Min	X-bar= average of sample
1		992	992	1000	1027	35	1002.75
2		978	994	985	1018	40	993.75
3		1021	998	1018	994	27	1007.75
4		974	1022	999	1026	52	1005.25
5		1000	1012	1030	991	39	1008.25
6		974	987	985	987	13	983.25
7		1005	973	1011	1001	38	997.50
8		983	1024	1012	977	47	999.00
9		990	1004	973	999	31	991.50
10		990	1018	1024	1001	34	1008.25
11		998	976	1029	980	53	995.75
12		1024	1020	1020	976	48	1010.00
13		1026	1018	1029	971	58	1011.00
14		982	979	982	989	10	983.00
15		991	988	980	994	14	988.25

Answer b

35.933	999.017	AVERAGE(all X-bar samples)
R-bar	X-bar-bar

Answer c:

control limits for x-bar, z=3
UCL= Xbar-bar+ z*STD			1027.725
CL= X-bar-bar			999.017
LCL= Xbarbar- z*STD			970.308
Standard deviation= STD=		STDEV(select all X-bar values)	9.5695

Answer d:

R-bar
control limits for Range, z=3
UCL=R-bar+ z*STD			80.740
CL= R-bar			35.933
LCL=R-bar- z*STD	0 if negative	-8.873	0.000
Standerd deviation= STD=	STDEV(select all range values)		14.9354

Answer e:

The process is in control: As we can see that NO sample is beyond control limits in charts. Every sample is within the UCL and LCL