18. Amertron produces electrical wiring in 100-foot rolls. The quality inspectionprocess involves selecting rolls of wire at random and counting the number of de-fects on each roll. The last 20 rolls examined revealed the following numbers ofdefects:RollNumber of DefectsRollNumber of Defects14112212531354414711516487178181943310204a. If the number of defects per 100-foot roll of wire follows a Poisson distribution,what is the estimate of c obtained from these observations?b. Using a normal approximation to the Poisson, what are the three-sigma controllimits that you would use to monitor this process?c. Are all 20 observations within the control limits?

Answered: 18. Amertron produces electrical wiring…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter2: Introduction To Spreadsheet Modeling

Section: Chapter Questions

Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...

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Suppose that a quality characteristic is normally distributed with specifications at 100 ± 20. The process standard deviation is 6.(a) Suppose that the process mean is 100. What are the natural tolerance limits? Calculate Cp and Cpk and interpret these ratios. What fraction of parts do you expect to be defective?(b) Suppose that the process mean is 106. What are the natural tolerance limits? What is thefraction defective? Calculate Cp and Cpk and interpret these ratios.
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.
Rolls of coiled wire are monitored using a c-chart. Twenty rolls have been examined, and the number of defects per roll has been recorded in the following table. Using the set of 20 observations, perform run tests on the data. What can you conclude about the data? Sample Number of Defects Sample Number of Defects 11 1 2 3 4 5 167390 Test First Second 297445TASA 6 8 12 13 14 15 16. 17 18 19 20 Conclusion 6 7 5 7 5 106
. Inspection results of video-of-the-month shipments to customers for 25 consecutive days are given in the following table. What central line and control limits should be established and posted if it is assumed that any out of-control points have assignable causes? The number of inspections each day is constant and equals 1750. Date Nonconforming Date Nonconforming July 6 47 July 23 37 7 42 26 39 8 48 27 51 9 58 28 44 12 32 29 61 13 38 30 48 14 53 Aug 2 56 15 68 3 48 16 45 4 40 19 37 5 47 20 57 6 25 21 38 9 35 22 53
In the past, Alpha Corporation has not performed incoming quality control inspections but has taken the word of its vendors. However, Alpha has been having some unsatisfactory experience recently with the quality of purchased items and wants to set up sampling plans for the receiving department to use. For a particular component, X, Alpha has a lot of tolerance percentage defective of 10 percent. Zenon Corporation, from which Alpha purchases this component, has an acceptable quality level in its production facility of 3 percent for component X. Alpha hasa consumer’s risk of 10 percent and Zenon has a producer’s risk of 5 percent.a. When a shipment of product X is received from Zenon Corporation, what sample size should the receiving department test?b. What is the allowable number of defects in order to accept the shipment?
70 In the past, Alpha Corporation has not performed incoming quality control inspections but has taken the word of its vendors. However, Alpha has been having some unsatisfactory experience recently with the quality of purchased items and wants to set up sampling plans for the receiving department to use. For a particular component, X, Alpha has a lot tolerance percentage defective of 38 percent. Zenon Corporation, from which Alpha purchases this component, has an acceptable quality level in its production facility of 13 percent for component X. Alpha has a consumer's risk of 10 percent, and Zenon has a producer's risk of 5 percent. a. When a shipment of Product X is received from Zenon Corporation, what sample size should the receiving department test? Use ¡Exhibit 10.16; Note: if the exact value of the computed LTPD/AOQ ratio does not appear in Exhibit 10.16, use the next higher ratio "Note: Round up your answer to the next whole number. b. What is the allowable number of defects…
The measurement of 85 automotive cables gave an arithmetic mean of the inner diameters of 3.51 mm and a standard deviation of 0.02 mm.The value required by the manufacturer is 3.5 upper/lower tolerance +0.04/ -0.12It is requested : a. Calculate the capability coefficients Cp, Cpk and state whether or not the machine is capable of producing compliant parts, i.e. whether or not the data dispersion is well centred. If applicable, calculate the adjustment coefficient Cr.b. If scrap is obtained, state whether it is recoverable or non-recoverable and calculate the percentage of scrap.c. Plot the limits of the tolerance field and the distribution of the measured data (using mean and standard deviation).
380,000 automotive A-Frame brackets are stamped in a year with a complex process involving shearing, forming, stamping, and heat treating. Each bracket has 6 Critical To Quality features. 627 brackets had at least one defect. Evaluation of the 627 brackets showed a total of, 1191 defects. Calculate the defects per million opportunities (DPMO). Calculate the defects per million (DPM). Calculate the defective units per million (DUPM).
Jason's house was built in 1968. He's looking to sell his house in the next 6 months, but first wants to be sure there are no material defects with the house. What should Jason test for first? O Electrical charge in each outlet. Lead-based paint since his house was built prior to 1978. O Water temperatures in the bathrooms. • Argon gas since his house was built prior to 1988.
Using samples of 200 credit card statements, an auditor found the following: Sample 1 2 3 4 Number with errors 4 2 5 9 a. Determine the fraction defective in each sample. b. If the true fraction defective for this process is unknown, what is your estimate of it? c. What is your estimate of the mean and standard deviation of the sampling distribution of fractions defective for samples of this size? d. What control limits would give an alpha risk of .03 for this process? Page 457 e. What alpha risk would control limits of .047 and .003 provide? f. Using control limits of .047 and .003, is the process in control? g. Suppose that the long-term fraction defective of the process is known to be 2 percent. What are the values of the mean and standard deviation of the sampling distribution? h. Construct a control chart for the process, assuming a fraction defective of 2 percent, using two-sigma control limits. Is the process in control? Can you show me the steps and formulas using excel
Using samples of 200 credit card statements, an auditor found the following:Sample 1 2 3 4Number with errors 4 2 5 9a. Determine the fraction defective in each sample.b. If the true fraction defective for this process is unknown, what is your estimate of it?c. What is your estimate of the mean and standard deviation of the sampling distribution of fractions defective for samples of this size?d. What control limits would give an alpha risk of .03 for this process?e. What alpha risk would control limits of .047 and .003 provide?f. Using control limits of .047 and .003, is the process in control?g. Suppose that the long-term fraction defective of the process is known to be 2 percent. What arethe values of the mean and standard deviation of the sampling distribution?h. Construct a control chart for the process, assuming a fraction defective of 2 percent, using twosigma control limits. Is the process in control?
Autopitch devices are made for both major- andminor-league teams to help them improve their batting averages.When set at the standard position, Autopitch can throw hardballstoward a batter at an average speed of 60 mph. To monitorthese devices and to maintain the highest quality, Autopitchexecutive Neil Geismar takes samples of 10 devices at a time. Theaverage range is 3 mph. Using this information, construct controllimits for:a) :X chart.b) R chart.

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