Concept explainers
a
Interpretation:The value ofa for the control chart is to be calculated.
Concept Introduction:Control charts are used to measure the effectiveness of the process determining the average value and control limits of the process. The Upper Control Limit (UCL) is the larger value and the Lower Control limit (LCL) is the smaller value of the sample. These limits gives a range to the data available.
b
Interpretation:The value of UCL and LCL based on three − sigma limits are to be calculated.
Concept Introduction:Control charts are used to measure the effectiveness of the process determining the average value and control limits of the process. The Upper Control Limit (UCL) is the larger value and the Lower Control limit (LCL) is the smaller value of the sample
c
Interpretation:The probability that the shift is detected on the first subgroup after the shift has occurred is to be determined.
Concept Introduction:Control charts are used to measure the effectiveness of the process determining the average value and control limits of the process. The Upper Control Limit (UCL) is the larger value and the Lower Control limit (LCL) is the smaller value of the sample
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Production and Operations Analysis, Seventh Edition
- 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 and their measured values are as follows: Sample Number Readings (in Ohms) 1 1010 991 985 986 2 995 996 1009 994 3 990 1003 1015 1008 4 1015 1020 1009 998 5 1013 1019 1005 993 6 994 1001 994 1005 7 989 992 982 1020 8 1001 986 996 996 9 1006 989 1005 1007 10 992 1007 1006 979 11 996 1006 997 989 12 1019 996 991 1011 13 981 991 989 1003 14 999 993 988 984 15 1013 1002 1005 992 Develop three-sigma appropriate control chart(s) from the chart(s) what comments can you make about the process? Explain and show workarrow_forwardA pharmaceutical company producing vitamin capsules desires a proportion of calcium content between 40 and 55 ppm. A random sample of 20 capsules chosen from the output yields a sample mean calcium content of 44 ppm with a standard deviation of 3 ppm. Find the natural tolerance limits of the process. If the process is in control at the present values of its parameters, what proportion of the output will be nonconforming, assuming a normal distribution of the characteristic? Answer letters a, b, and c. a. Find the Cp index. Comment on the ability of the process to meet specifications. b. What proportion of the specification range is used up by the process? c. If it is easier to change the process mean than to change its variability, to what value should the process mean be set to minimize the proportion of nonconforming product?arrow_forwardA metal fabricator produces connecting rods with an outer diameter that has a 1 ± .01–inch specification. A machine operator takes several sample measurements over time and determines the sample mean outer diameter to be 1.002 inches with a standard deviation of .003 inch.a. Calculate the process capability index for this example.b. What does this figure tell you about the process?arrow_forward
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- A component part for a motorcycle is manufactured by an investment casting process. The air vent opening on this casting is an important functional parameter of the part. The results for five samples are given in the table. The values given have been coded using the last two digits of the dimension Sample Air vent opening diameter (in mm 1 58 61 54 60 2 61 55 58 62 3 66 60 59 55 4 53 57 58 64 5 65 63 79 61 Determine the central line and control limits for the range and mean charts, and discuss whether or not the process is in statistical control.arrow_forwardResistors 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 13.7. 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. 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.)arrow_forwardOrlando Manufacturers has decided to use a c-Chart to monitor the number of defects per file cabinet produced by their manufacturing process. The c-Chart should be constructed with an alpha risk of 7%. The quality control manager randomly samples one file cabinet at 99 successively selected time periods and counts the number of defects in the file cabinet. Sample Defects1 112 83 74 145 56 117 48 69 13 Step 2 of 7: What is the Upper Control Limit? Round your answer to three decimal places.arrow_forward
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