Resistors for electronic circuits are manufactured on a high-speed automated mac

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) 972 990 997 1000 994 1005 996 994 1029 1022 1028 972 994 1025 1004 993 1009 1016 986 973 1003 987 982 977 988 998 985 982 1021 1013 1027 1010 1003 989 1028 997 1002 978 1013 1029 1011 975 1029 1026 979 985 1003 987 980 1022 986 1028 983 998 1023 1027 1021 a. Calculate the mean and range for the above samples. (Round "Mean" to 2 decimal places and "Range" to the nearest whole number.) 989.75 C 997.25 1012.75 28 1003 1005.5 987.25 986.25 1000.25 1007.25 100125 1013 1002.25 57 31 23 30 21 39 38 50 30 54 23 45 29 4 9 10 988.75 14 15 1004.75 101725 b. Determine X and R, (Round your answers to 3 decimal places.) 1001.100 33.933 c. Determine the UCL and LCL for a Xchart. (Round your answers to 3 decimal places.) 1008.667 993.532 LCL d. Determine the UCL and LCL for R-chart. (Leave no cells blank be certain to enter "O" wherever required. Round your answers to 3 decimal places.) 56057 LCL

Explanation / Answer

Following are given :

Xbar = 1001.100

Rbar = 33.933

Sample size = n = 4

Following are the values of relevant constants derived from standard table for Xbar and Range chart for n = 4:

A2 = 0.729

D4 = 2.282

D3 = 0

CONTROL LIMITS FOR Xbar CHART:

UCLx =   1001.100 + 0.729x33.933 = 1001.100 +24.737 = 1025.837
LCLx   =   1001.100 – 0.729 x 33.933 = 1001.100 – 24.737 = 976.363

Control Limits for R Chart :

UCLr = D4.Rbar = 2.282 x 33.933 = 77.437

LCLr = D3.Rbar = 0

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