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. *ONLY ANSWER b,c,d, e please. Thank you!*

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	1002.75	35
2	933.75	40
3	1007.75	27
4	1005.25	52
5	1008.25	39
6	983.25	13
7	997.50	38
8	999	47
9	991.50	31
10	1008.25	34
11	995.75	53
12	1010	48
13	1011	58
14	983	10
15	988.25	14

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

Solution(a)

Sample Number					Xbar	Range
1	992	992	1000	1027	1002.75	35
2	978	994	985	1018	993.75	40
3	1021	998	1018	994	1007.75	27
4	974	1022	999	1026	1005.25	52
5	1000	1012	1030	991	1008.25	39
6	974	987	985	987	983.25	13
7	1005	973	1011	1001	997.5	38
8	983	1024	1012	977	999	47
9	990	1004	973	999	991.5	31
10	990	1018	1024	1001	1008.25	34
11	998	976	1029	980	995.75	53
12	1024	1020	1020	976	1010	48
13	1026	1018	1029	971	1011	58
14	982	979	982	989	983	10
15	991	988	980	994	988.25	14

Solution(b)
Xdoublebar = (1002.75+993.75+1007.75+1005.25+1008.25+983.25+997.5+999+991.5+1008.25+999.75+1010+1011+983+988.25)/15 = 999.012
Rbar = (35+40+27+52+39+13+ 38+47+31+34+53+48+58+10+14)/15 = 35.933
Solution(c)

LCL = Xdoublebar - A2*Rbar = 999.02 - 0.729*35.93 = 972.827

UCL = Xdoublebar + A2*Rbar = 999.02 + 0.729*35.93 = 1025.213
Solution(d)
LCL = D3*Rbar = 0*35.93 = 0
UCL = D4*Rbar = 2.282*35.93 = 81.992

Solution(e)
From the LCL and UCL limits of Range and Mean, we can say that the process is in statistical control.