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. 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 SAMPLE NUMBER READINGS (IN OHMs) 985 1015 1005 1010 986 1003 1020 1015 993 005 1020 989 1001 992 979 006 101 003 984 981 989 14 013 1002 1005

Develop an X bar chart and an r-chart and plot the values. From the charts, what comments can you make about the process?

Answer 1

	sample	1	2	3	4	Mean	Range
	1	1010	991	985	986	993	25
	2	995	996	1009	994	998.5	15
	3	990	1003	1015	1008	1004	25
	4	1015	1020	1009	998	1010.5	22
	5	1013	1019	1005	993	1007.5	26
	6	994	1001	994	1005	998.5	11
	7	989	992	982	1020	995.75	38
	8	1001	986	996	996	994.75	15
	9	1006	989	1005	1007	1001.75	18
	10	992	1007	1006	979	996	28
	11	996	1006	997	989	997	17
	12	1019	996	991	1011	1004.25	28
	13	981	991	989	1003	991	22
	14	999	993	988	984	991	15
	15	1013	1002	1005	992	1003	21
					Average	999.1	21.733
	X chart control limits			N	A2	D3	D4
	UCL = x + A2R			2	1.88	0	3.27
	LCL = x- A2R			3	1.02	0	2.57
				4	0.73	0	2.28
				5	0.58	0	2.11
	R chart Control Limits			6	0.48	0	2
	UCL = D4R			7	0.42	0.08	1.92
	LCL = D3R			8	0.37	0.14	1.86
				9	0.34	0.18	1.82
				10	0.31	0.22	1.78
				11	0.29	0.26	1.74
	X BAR CHART
	UCL = X + A2R = 999.1 + 0.73(21.733) = 1014.965
	LCL = X - A2R = 999.1 - 0.73(21.733) = 989.235
	R CHART
	UCL = D4R = (2.28)(21.733) = 49.551
	LCL = D3R = (0) (21.733) = 0
	CONCLUSION
	All the points are well within control limits
	The process is controlled