Question

Problem 10-25

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		1097	1094	983	1026
2		978	1013	988	1014
3		976	991	1030	995
4		1016	991	1023	1014
5		977	1016	982	970
6		986	1011	1030	1027
7		1026	983	1017	1004
8		1017	1018	995	982
9		1010	981	994	1008
10		987	1020	1001	1004
11		994	995	1015	1026
12		1030	978	1017	984
13		974	995	1007	988
14		995	970	1004	1028
15		1012	1019	983	990

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

Answer 1

SAMPLE NUMBER	READINGS (IN OHMS)				X bar or Mean	Minimum	Maximum	Range = Maximum - Minimum	Upper Control Limit or UCL for X bar Chart	Lower Control Limit or LCL for X bar Chart
1	1097	1094	983	1026	1050.00	983	1097	114	1037.601	971.699
2	978	1013	988	1014	998.25	978	1014	36	Upper Control Limit or UCL for R Chart	Lower Control Limit or LCL for R Chart
3	976	991	1030	995	998.00	976	1030	54	103.146	0.000
4	1016	991	1023	1014	1011.00	991	1023	32	Here, 0.729, 2.282, 0 are constant and used here as Number of X = 4
5	977	1016	982	970	986.25	970	1016	46
6	986	1011	1030	1027	1013.50	986	1030	44
7	1026	983	1017	1004	1007.50	983	1026	43
8	1017	1018	995	982	1003.00	982	1018	36
9	1010	981	994	1008	998.25	981	1010	29
10	987	1020	1001	1004	1003.00	987	1020	33
11	994	995	1015	1026	1007.50	994	1026	32
12	1030	978	1017	984	1002.25	978	1030	52
13	974	995	1007	988	991.00	974	1007	33
14	995	970	1004	1028	999.25	970	1028	58
15	1012	1019	983	990	1001.00	983	1019	36
		X Double Bar or Mean Value of X bar			1004.650	R bar or Mean Value of R		45.200

Formula

1	B	C	D	E	F	G	H	I	J	K	L
2	SAMPLE NUMBER	READINGS (IN OHMS)				X bar or Mean	Minimum	Maximum	Range = Maximum - Minimum	Upper Control Limit or UCL for X bar Chart	Lower Control Limit or LCL for X bar Chart
3	1	1097	1094	983	1026	=AVERAGE(C3:F3)	=MIN(C3:F3)	=MAX(C3:F3)	=I3-H3	=G18+(0.729*J18)	=G18-(0.729*J18)
4	2	978	1013	988	1014	=AVERAGE(C4:F4)	=MIN(C4:F4)	=MAX(C4:F4)	=I4-H4	Upper Control Limit or UCL for R Chart	Lower Control Limit or LCL for R Chart
5	3	976	991	1030	995	=AVERAGE(C5:F5)	=MIN(C5:F5)	=MAX(C5:F5)	=I5-H5	=2.282*J18	=0*J18
6	4	1016	991	1023	1014	=AVERAGE(C6:F6)	=MIN(C6:F6)	=MAX(C6:F6)	=I6-H6	Here, 0.729, 2.282, 0 are constant and used here as Number of X = 4
7	5	977	1016	982	970	=AVERAGE(C7:F7)	=MIN(C7:F7)	=MAX(C7:F7)	=I7-H7
8	6	986	1011	1030	1027	=AVERAGE(C8:F8)	=MIN(C8:F8)	=MAX(C8:F8)	=I8-H8
9	7	1026	983	1017	1004	=AVERAGE(C9:F9)	=MIN(C9:F9)	=MAX(C9:F9)	=I9-H9
10	8	1017	1018	995	982	=AVERAGE(C10:F10)	=MIN(C10:F10)	=MAX(C10:F10)	=I10-H10
11	9	1010	981	994	1008	=AVERAGE(C11:F11)	=MIN(C11:F11)	=MAX(C11:F11)	=I11-H11
12	10	987	1020	1001	1004	=AVERAGE(C12:F12)	=MIN(C12:F12)	=MAX(C12:F12)	=I12-H12
13	11	994	995	1015	1026	=AVERAGE(C13:F13)	=MIN(C13:F13)	=MAX(C13:F13)	=I13-H13
14	12	1030	978	1017	984	=AVERAGE(C14:F14)	=MIN(C14:F14)	=MAX(C14:F14)	=I14-H14
15	13	974	995	1007	988	=AVERAGE(C15:F15)	=MIN(C15:F15)	=MAX(C15:F15)	=I15-H15
16	14	995	970	1004	1028	=AVERAGE(C16:F16)	=MIN(C16:F16)	=MAX(C16:F16)	=I16-H16
17	15	1012	1019	983	990	=AVERAGE(C17:F17)	=MIN(C17:F17)	=MAX(C17:F17)	=I17-H17
18			X Double Bar or Mean Value of X bar			=AVERAGE(G3:G17)	R bar or Mean Value of R		=AVERAGE(J3:J17)