17. Over a period of 12 consecutive production hours, samples of size 50 resulted inthe following proportions of defective items:ProportionDefectiveProportionDefectiveSample NumberSample Number1.047.10.02.06.088.103910.064.0856.08.04.04.041112a. What are the three-sigma control limits for this process?b. Do any of the sample points fall outside of the control limits?c. The company claims a defect rate of 3 percent for these items. Are the observedproportions consistent with a target value of 3 percent defectives? What diffi-culty would arise if the control limits were based on a target value of 0.03? Inview of the company's claims, what difficulty would arise if the control limitscomputed in part (a) were used?

a) Calculation of the value of p Calculation of the upper control limits Thus, UCL = 0.127…

Answered: 17. Over a period of 12 consecutive…

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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An inspector counted the number of defective monthly billing statements of a telephonecompany in each of 20 samples. Using the following information, construct a control chartthat will describe 99.74 percent of the chance variation in the process when the process is incontrol. Each sample contained 100 statements.Sample Number ofDefectivesSample Number ofDefectivesSample Number ofDefectivesSample Number ofDefectives1 7 6 11 11 8 16 102 10 7 10 12 12 17 83 12 8 18 13 9 18 124 4 9 13 14 10 19 105 9 10 10 15 16 20 21220
Organic Grains LLC uses statistical process control to ensure that its health-conscious, low-fat, multigrain sandwich loaves have the proper weight. Based on a previously stable and in-control process, the control limits of the x- and R-charts are: UCL-4.86, LCL- = 4.52, UCLR=1.344, LCLR = 0. Over the past few days, they have taken five random samples of four loaves each and have found the following: Based on the x-chart, is one or more samples beyond the control limits? Sample 1 2 3 4 5 Yes No Loaf # 1 4.8 4.4 4.5 4.6 5.0 Net Weight Loaf # 2 4.7 4.8 4.5 4.9 4.8 Loaf # 3 5.0 4.7 4.9 4.7 4.7 Loaf # 4 4.7 4.8 4.6 4.5 4.6
4. Organic Grains LLC uses statistical process control to ensure that its health-conscious, low-fat, multigrain sandwich loaves have the proper weight. Based on a previously stable and in-control process, the control limits of the x- and R-charts are: UCLx = 5.35, LCLx = 4.93; UCLR = 0.894, LCLR = 0. Over the past few days, they have taken five random samples of four loaves each and have found the following: Net Weight Sample Loaf # 1 Loaf # 2 Loaf # 3 Loaf # 4 1 4.9 5.2 5.1 5.0 2 5.3 5.1 5.2 5.3 3 4.9 5.2 4.9 5.2 4 5.5 5.5 5.3 5.5 5 5.3 5.2 5.3 5.0 Part 2 Based on the x-chart, is one or more samples beyond the control limits? ▼ No Yes .
6 of 11 5 3. The manager of a building-supplies company randomly samples incoming lumber to see whether it meets quality specifications. From each shipment, 100 pieces of 2 x 4 lumber are inspected and judged according to whether they are first (acceptable) or second (defective) grade. The proportions of second-grade 2 x 4s recorded for 30 shipments were as follows: a. Construct a control chart for the proportion of second-grade 2 x 4s in samples of 100 pieces of lumber. b. Explain how the control chart can be of use to the manager of the building supplies company. Shipment No. Proportion of second grade 1 0.14 2 0.22 3 0.21 4 0.15 0.19 0.26 7 0.18 8 0.22 9 0.23 10 0.21 11 0.2 12 0.14 13 0.25 14 0.2 15 0.19 16 0.18 17 0.22 18 0.22 19 0.17 20 0.21 21 0.21 22 0.13 23 0.15 24 0.2 25 0.23 26 0.23 27 0.12 28 0.19 29 0.19 30 0.26
Using samples of 197 credit card statements, an auditor found the following: Sample 1 3 errors Sample 2 3 errors Sample 3 5 errors Sample 4 9 errors 1. what alpha risk would control limits of .0470 and .0038 provide? 2. Using control limits of .0470 and .0038, is the process in control? 3. Construct a control chart for the process, assuming a fraction defective of 2 percent, using two-sigma control limits. Is the process in control?
Five data entry operators work at the data processing department of the Birmingham Bank. Each day for 30 days, the number of defective records in a sample of 250 records typed by these operators has been noted, as follows: Sample No. 12 2 3 4 5 6 7 8 9 10 No. Defectives 8 5 18 9 18395 10 14 Sample No. 11 12 13 14 15 16 17 18 19 20 No. Defectives 7 4 a) Establish 30 upper and lower control limits. 54697496 15 10 11 19 16 Sample No. 21 222222NERS 23 24 25 26 27 28 29 30 No. Defectives 16 12 8726668 12 11 13 6, 12 UCLp = (enter your response as a number between 0 and 1; rounded to three decimal places).
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
Boxes of Honey-Nut Oatmeal are produced to contain14 ounces, with a standard deviation of .I ounce. Set up the3-sigma :X-charl for a sample size of 36 boxes
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.
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1. Boxes of Honey-Nut Oatmeal are produced to contain 14.0 ounces, with a standard deviation of 0.10 ounce. For a sample size of 64, the 3-sigma x chart control limits are: Upper Control Limit (UCLx) = 14.0414.04 ounces (round your response to two decimal places). Lower Control Limit (LCLx) =?ounces (round your response to two decimal places). 2. The overall average on a process you are attempting to monitor is 55.0 units. The process population standard deviation is 1.84. Sample size is given to be 16. a) Determine the 3-sigma x-chart control limits. Upper Control Limit (UCLx)=56.3856.38 units (round your response to two decimal places). Lower Control Limit (LCLx)=? units (round your response to two decimal places). 3. Refer to Table S6.1 - Factors for Computing Control Chart Limits (3 sigma) LOADING... for this problem. Thirty-five samples of size 7 each were taken from a fertilizer-bag-filling machine at Panos Kouvelis Lifelong Lawn Ltd.…
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.

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