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		986	987	1014	1001
2		994	993	973	972
3		983	1022	981	983
4		1022	989	1007	994
5		1015	988	1020	1027
6		1013	998	990	1002
7		986	998	977	1021
8		995	1026	1016	1002
9		1023	991	993	990
10		1002	1012	1008	998
11		996	987	1017	1023
12		972	1018	1005	1018
13		1007	1007	992	998
14		978	982	986	984
15		1012	1023	1001	1003

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

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

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.)

e. What comments can you make about the process?

• The process is in statistical control.

• OR

• The process is out of statistical control.

Answer 1

(a)

Mean and range

SAMPLE NUMBER	READINGS (IN OHMS)	Mean	Range Maximum of row – Minimum of row
1	986	987	1014	1001	(986+987+1014+1001)/4= 997.00	1014-986 = 28
2	994	993	973	972	983.00	22
3	983	1022	981	983	992.25	41
4	1022	989	1007	994	1003.00	33
5	1015	988	1020	1027	1012.50	39
6	1013	998	990	1002	1000.75	23
7	986	998	977	1021	995.50	44
8	995	1026	1016	1002	1009.75	31
9	1023	991	993	990	999.25	33
10	1002	1012	1008	998	1005.00	14
11	996	987	1017	1023	1005.75	36
12	972	1018	1005	1018	1003.25	46
13	1007	1007	992	998	1001.00	15
14	978	982	986	984	982.50	8
15	1012	1023	1001	1003	1009.75	22

(b)

(c)

Sample size in each sample = 4

(d)

(e)

The process is in statistical control

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