Question

0 X 1.TX T 1 .III .2. 3 .III.4. III .5. III .6. II . , 7 . i. 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) 1000 992 1014 1026 1006 977 1027 1016 985 1029 1018 992 1001 1006 971 1000 1028 970 979 1025 997 1026 1007 1016 1003 987 1006 995 1029 978 1027 995 1003 1009 991 987 981 996 994 1000 978 971 999 983 973 1005 1003 993 974 1002 1005 972 994 1000 1012 1018 982 1014 0019 LIITILISIIII.7.IIIIII6.IIII.5. III.4.IIII.3.III.2III.1.IIII 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 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.) 13 15 e. What comments can you make about the process? Process is in statistical control Process is out of statistical control

Answer 1

# SAMPLE	1	2	3	4	AVERAGE	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
AVERAGE					999.25	35.733

XBAR = 999.25

RBAR = 35.733

A2 VALUE CORRESPONDING TO N = 4 = 0.73

D3 & D4 VALUES CORRESPONDING TO N = 0, 2.28

CONTROL LIMITS FOR XBAR

UCL X = XBAR + (A2 * RBAR) = 999.25 + (0.73 * 35.733) = 1025.335

LCL X = XBAR - (A2 * RBAR) = 999.25 - (0.73 * 35.733) = 973.165

CONTROL LIMITS FOR RBAR

UCL R = RBAR * D4 = 35.733 * 2.28 = 81.471

LCL R = RBAR * D3 = 35.733 * 0 = 0

THE PROCESS IS IN STATISTICAL CONTROL AS ALL THE POINTS ARE WITHIN THE CONTROL LIMITS.