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		1000	992	1014	1026
2		1006	977	1027	1016
3		985	1029	1018	992
4		1001	1006	971	1000
5		1028	970	979	1025
6		997	1026	1007	1003
7		1016	1003	987	1006
8		995	1029	978	986
9		1027	995	1003	1008
10		991	987	981	996
11		994	1000	978	971
12		999	983	973	1005
13		1003	993	974	1002
14		1005	972	994	1000
15		1012	1018	982	1014

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

a.

Sample Mean and Sample Range for all the samples are calculated as per the below table:

	Sample Readings
Number	1	2	3	4	Sample Mean	Sample Range
1	1000	992	1014	1026	1008	34
2	1006	977	1027	1016	1006.5	50
3	985	1029	1018	992	1006	44
4	1001	1006	971	1000	994.5	35
5	1028	970	979	1025	1000.5	58
6	997	1026	1007	1003	1008.25	29
7	1016	1003	987	1006	1003	29
8	995	1029	978	986	997	51
9	1027	995	1003	1008	1008.25	32
10	991	987	981	996	988.75	15
11	994	1000	978	971	985.75	29
12	999	983	973	1005	990	32
13	1003	993	974	1002	993	29
14	1005	972	994	1000	992.75	33
15	1012	1018	982	1014	1006.5	36

b.

X double bar = Mean of Sample Ranges = ( 1008 + 1006.5 + 1006 + 994.5 + 1000.5 + 1008.25 + 1003 + 997 + 1008.25 + 988.75 + 985.75 + 990 + 993 + 992.75 + 1006.5) / 15 = 14988.75 / 15 = 999.25

R bar = Mean of Sample Rnages = ( 34 + 50 + 44 + 35 + 58 + 29 + 29 + 51 + 32 + 15 + 29 + 32 + 29 + 33 + 36) / 15 = 536 / 15 = 35.733

c.

X bar chart:

UCL = X double bar + ( R bar x A2)

LCL = X double bar - ( R bar x A2)

For a sample size of 4, A2 value is 0.729 ( From Control chart constant table)

So,

UCL = 999.25 + ( 35.733 x 0.729) = 999.25 + 26.049 = 1025.299

LCL = 999.25 - ( 35.733 x 0.729) = 999.25 - 26.049 = 973.201

d.

R bar chart:

UCL = R bar x D4

LCL = R bar x D3

For a sample size of 4, D4 value is 2.282 and D3 value is 0 ( From Control chart constant table)

So,

UCL = 35.733 x 2.282 = 81.543

LCL = 35.733 x 0 = 0

e.

All the Sample mean values are within the UCL and LCL values of X bar chart.

All the Sample range values are within the UCL and LCL values of R bar chart.

Therefore,

The process is in statistical control.