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 NOEM 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 1003 1016 1003987 1006 995 1029 978 986 1027 995 1003 1008 991 987 981 996 994 1000 978 971 999 983 973 1005 1003 993 974 1002 1005972 994 1000 1012 1018 982 1014 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

Answer 1

number number number 1,008 JO Number of Sample Size of each sample (n) = 4. Sample Mean of each samples sum of observ sum of observations Creadirge) @ Range of each sample= Maximum value- Minimum Value Sample mear Range Sample Mean Range. 9 34 (1,008.25 32 1,00615) 988.75 15 3 ₂006 44 on 985.75 29 4 994.5. 35 990 32 1,000. 5 58 6 1,008.25 29 992.75 33 1,006.5 11,36 12 99329 IP ↑ 1,003 29 8 997 51 999.25 R = 35.733 O Ž - average of all meang=1999.257 Ř = average of range values = 1391733 © Uch and act for a un charts uchař +d2 R = 999.25+ (0.729) 35.733=999.25 +26.049 Uch=1,025.299

for n= 4, LCL = -Az = 999.25- (0.729)35.733 = 999.252 LCL = 1973,201) Note: @ uch and uch for R-chart A2=0.729 Du=2.282 och = DR = (2.282)35.733 =181.542) ach = DUR= (0)35-733 = ] @ Comments about the process is The process is in statistical conteol as all the mean values fall within the control limits. D3=0