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- Auto pistons at Wemming Chung's plant in Shanghai are produced in a forging process, and the diameter is a critical factor that must be controlled. From sample sizes of 5 pistons produced each day, the mean and the range of this diameter have been as follows: Day Mean (mm) Range R (mm) 158 4.3 151.2 4.4 155.7 4.2 153.5 4.8 156.6 4.5 What is the UCL using 3-sigma?(round your response to two decimal places). 1. 2. 4.3. A large beverage company would like to use statistical process control to monitor a new bottlingmachine designed to load liquid into 350-ml bottles. This company knows that the exact amountthe machine places in each bottle can naturally vary by a small amount but does not have any more specific information about the process. The company operated this new machine under careful supervision, confident that the machine was under complete control, for 7 hours. Each hour, a sample of nine bottles was taken off the line and the amount of liquid in each bottle was carefully measured. This is the resulting data: Sample Sample Mean (ml) Sample Range (ml) 350.85 0.6 350.80 0.8 0.5 351.20 351.00 1.0 350.62 0.8 351.12 0.7 0.8 351.50 a. Where should the control limits be placed on a mean chart intended to monitor thismachine in the future, using the same sampling procedure that produced this data? b. Where should the control limits be placed on a range chart intended to monitor thismachine in the…West Battery Corp. has recently been receiving complaints from retailers that its 9-volt batteries are not lasting as long as other name brands. James West, head of the TQM program at West's Austin plant, believes there is no problem because his batteries have had an average life of 60 hours, about 10% longer than competitors' models. To raise the lifetime above this level would require a new level of technology not available to West. Nevertheless, he is concerned enough to set up hourly assembly line checks. Previously, after ensuring that the process was running properly, West took samples of 5 9-volt batteries for 25 test to establish the standards for control chart limits. Those 25 tests are shown in the following table: Sample Data Sample Data Hour Hour Sample Taken 1 Sample Taken 1 2 4 5 R 2 3 4 R 1 60 61 60 59 67 61.4 8 14 62 69 51 62 56 60.0 18 55 57 70 56 46 56.8 24 15 67 53 63 69 70 64.4 17 60 45 58 49 57 53.8 15 16 72 58 51 44 64 57.8 28 66 81 61 51 60 63.8 30 17 49 49 58 68…
- Construct a p-chart that plots the percentage of patients unsatisfied with their meals. Set the control limits to include 99.73% of the random variation in meal satisfaction. Comment on your results. (Z=3)West Battery Corp. has recently been receiving complaints from retailers that its 9-volt batteries are not lasting as long as other name brands. James West, head of the TQM program at West's Austin plant, believes there is no problem because his batteries have had an average life of 60hours, about 10% longer than competitors' models. To raise the lifetime above this level would require a new level of technology not available to West. Nevertheless, he is concerned enough to set up hourly assembly line checks. Previously, after ensuring that the process was running properly, West took samples of 5 9-volt batteries for 25 test to establish the standards for control chart limits. Those 25 tests are shown in the following table: Sample Data Sample Data Hour Sample Taken 1 2 3 4…At Gleditsia Triacanthos Company, a certain manufactured part is deemed acceptable if its length is between 12.45 to 12.55 inches. The process is normally distributed with an average of 12.49 inches and a standard deviation of 0.014 inches. a) is the process capable of meeting specifications? b) Does the process meet specifications?
- Ettlie Engineering has a new catalyst injection system for your countertop production line. Your process engineering departmenthas conducted experiments and determined that the mean is 8.01 grams with a standard deviation of .03. Your specificationsare: m = 8.0 and s = .04, which means an upper specification limit of 8.12 [ = 8.0 + 3(.04)] and a lower specification limit of7.88 [= 8.0 - 3(.04)].What is the Cpk performance of the injection system?The IRS is concerned with improving the accuracy of tax information given by its representatives over the telephone. Previous studies involved asking a set of 25 questions of a large number of IRS telephone representatives to determine the proportion of correct responses. Historically, the averageproportion of correct responses has been 72 percent. Recently, IRS representatives have been receiving more training. On April 26, the set of 25 tax questions were again asked of 20 randomly selected IRS telephone representatives. The numbers of correct answers were 18, 16, 19, 21, 20, 16,21, 16, 17, 10, 25, 18, 25, 16, 20, 15, 23, 19, 21, and 19. a. What are the upper and lower control limits for the appropriate p-chart for the IRS? Use z = 3. b. Is the tax information process in statistical control?In a sausage factory, quality managers are studying the compliance of the sausages with the requirements. Any sausage having pin holes, air pockets, deformation or breakage in its casings is counted as defective and total number of such defective sausages alone is noted in each shift. The following data represents the number of defective sausages in samples of 200 sausages taken from 10 shifts. Sample Defectives Percent Defective 1 40 20% 2 28 14% 3 15 8% 4 23 (a) 5 20 10% 6 21 11% 7 19 10% 8 15 8% 9 16 8% 10 17 9% Calculate the value for (a) in the table above. Calculate p-bar based on the samples above. What is the UCL and LCL for a p chart based on the data provided and a desired control level of 99.74%? Use your control limits from part b along with the data provided to draw a p-chart. Is the process in control? Why or why not? If not in control, suggest some potential reasons.
- The specifications for a gasket that installs between two engine parts calls for a thickness of 6.0 mm ± .2 mm. The standard deviation of the process is estimated to be 0.05 mm. The process is known to operate at a mean thickness of 6.1 mm What are the upper and lower specification limits for the gasket? What are the Cp and Cpk values for this process? Is this process capable of producing the desired part?Consider 2.5 kg of austenite containing 0.65 wt% C, cooled to 726 ° C a)Is the steel hypereutectoid or hypoeutectoid b)What is the primary microconstituent (proeutectoid)phase? c)How many kilograms of total ferrite and cementite form? d)How many kilograms each of pearlite and the proeutectoid phase form? Weight percent carbonNanosElectron, Inc. manufactures 75,000 circuit boards per month. A random sample of 800 boards is inspected every week for three characteristics. During a recent week, four defects were found for one characteristic, two defects were found for another characteristic, and one defect was found for the third characteristic. If these inspections produced defect counts that were representative of the population, what is the overall sigma level for this process? What is the sigma level for the characteristic that showed four defects?