Bottles for room spray are supposed to weigh exactly 16 oz. Inspectors want to develop process control charts. They take five boxes of five bottles each and weigh them. They obtain the following data. The mean weights of each of the 5 samples are 15.2, 14.6, 16.5, 18.1, and 13.2 respectively. Likewise, the range values for the each of 5 samples are 0.4, 0.2, 0.4, 0.5, and 0.9 respectively. For the X-bar charts and R-charts, the Parameters, A2, D3 and D4 are respectively. a. 0.37,0.14, 1.86 O b. 0.25, 0.31, 1.69 Oc. 0.73,0.00, 2.28

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.

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 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. SAMPLE NUMBER 1 H234STO OHN345 5 6 7 8 9 10 11 ΕΕΕΕΕ 12 13 14 15 READINGS (IN OHMS) 1097 1094 978 1013 976 1016 977 986 983 1026 988 1014 991 1030 995 991 1023 1014 982 970 1030 1027 1017 1004 995 982 994 1008 1001 1004 995 1015 1026 978 1017 984 995 1007 988 970 1004 1028 1019 983 990 1026 1017 1010 987 994 1030 974 995 1012 1016 1011 983 1018 981 1020

Arana is a company that produces homemade Rotini pasta. They use statistical process control to monitor the manufacturing process. The company collects five samples, each containing six packs of pasta. Below is the sample data, but the standard deviation of the process output is unknown. If an R chart is created using three-sigma limits (i.e., z = 3) to monitor the variability of products, what would be the upper control limit for this R chart? Sample 1 Sample 2 Sample 3 Pack 1 452.3 451.6 448.6 Sample 4 454.7 Sample 5 448.9 7.614 9.328 11.653 13.427 Pack 2 452.8 451.2 455.6 451.7 453.4 Pack 3 456 454.6 456.5 451 456.7 Pack 4 457.2 455.3 451.9 452.6 456.3 Pack 5 457.8 452.2 455.6 454.7 452.4 Pack 6 451.8 451.9 448.3 458.4 456

In a fabric manufacturing factory, the quality control process using control charts from SPC. In an hour there are a total of 5 samples are taken each having 5 observations regarding the thickness of fabric in measured in millimeters. In a particular hour, the sample means (X-bar) are noted to be: 172.11, 219.51 . 208.24, 112.44 and 123.30 respectively. In the same sample, the corresponding ranges are: 13.1713.3815.34, 13.04, and 13.02 respectively What are the lower and upper control limits for the R chart?