Time left 0:58:00Bottles for room spray are supposed to weigh exactly 16 oz. Inspectors want to develop process control charts. Theytake six boxes of five bottles each and weigh them. They obtain the following data. The mean weights of each of the 6samples are 15.2, 14.6, 16.5, 18.1, 13.2, and 14.8 respectively. Likewise, the range values for the each of 6 samples are1.8, 0.7,0.5,0.4, 0.2, and 0.9 respectively. Find out Grand Mean (X double bar), and mean range (R bar)O a.15.04, 0.75O b. 15.53,0.67C.16.53,0.86O d. 0,0O e. 15.53, -0.67AGENEXT PAGE78PsDELL

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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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2) The specification for a Lindemann’s stainless steel chimney liner requires a thickness of 7.1 mm ± 0.1 mm. The firm’s quality analyst determines that the liner process operates at a mean thickness of 7.13 mm with the standard deviation of the process being 0.02 mm. a) Calculate the upper and the lower limits for the stainless steel chimney liner. b) Calculate the Cpand Cpkfor this process. Hint: Cp = (Upper Specification Limit – Lower Specification Limit)/6sigma Cpk = minimum of [(Upper Specification Limit – Xbar)/3sigma], [(Xbar – Lower Specification Limit)/3sigma]
Quality control programs often establish control limits that are three standard deviationsfrom the target mean of a process. If the mean of a sample taken from the process iswithin the control limits, the process is deemed satisfactory.A process is designed to fill bottles with 16 ounces of soda with a standard deviationof 0.5 ounces. Determine the control limits above and below the mean for this processusing a sample size of n = 30.
A microbrewery tracks its output in gallons over a five hour period for each of seven days. Their data is in the table below, and they went ahead and calculated the averages and ranges for the individual samples and the overall averages Their data and the factors tables can be found below. Calculate the upper (LCL) and lower (UCL) control limits for X bar, and R charts for their process. Day (X values) X̅ R 1 46 49 45 47 48 47.0 4 2 43 52 46 52 44 47.4 9 3 45 55 46 51 43 48.0 12 4 39 44 42 43 40 41.6 5 5 45 50 48 50 42 47.0 8 6 44 48 45 45 40 44.4 8 7 41 44 52 50 47 46.8 11 X̿ = 46.03 R̅ 8.14 Xbar chart - LCL = 40.48, UCL=46.25, R chart LCL=0, UCL=14.01 Xbar chart - LCL = 44.21, UCL=48.41, R chart LCL=0.49, UCL=17.18 Xbar chart - LCL = 42.61, UCL=49.45, R chart LCL=0.65, UCL=15.63 Xbar chart - LCL = 44.21, UCL=51.62, R chart LCL=0, UCL=17.18 Xbar chart - LCL = 41.31, UCL=50.75, R chart LCL=0, UCL=17.18
Aspen Plastics produces plastic bottles to customer order. The quality inspector randomly selects four bottles from the bottle machine and measures the outside diameter of the bottle neck, a critical quality dimension that determines whe the bottle cap will fit properly. The dimensions (in.) from the last six samples are Bottle Sample 1 2 4 1 0.602 0.601 0.604 0.594 2 0.588 0.581 0.612 0.573 0.588 0.571 0.578 0.574 4 0.582 0.612 0.603 0.582 5 0.596 0.602 0.597 0.609 6 0.583 0.602 0.615 0.579 Click the icon to view the table of factors for calculating three-sigma limits for the x-chart and R-chart. Suppose that the specification for the bottle neck diameter is 0.600 ± 0.050 in. and the population standard deviation i 0.012 in. a. What is the process capability index? The Cok is 1.19. (Enter your response rounded to two decimal places.) b. The process capability ratio? The Cp is (Enter your response rounded to two decimal places.)
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BlueMoon Bottlers has a bottle-filling process with a mean value of 64 ounces and a standard deviation of 8 ounces. Suppose the upper and lower specification limits are 71 and 57 ounces, respectively. What is the process capability index of this process? (Note: You MUST show every single step and detailed derivation for full credit)
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 b. 0.25, 0.31, 1.69 С. 0.73,0.00, 2.28 d. None of them e. 0.58, 0.00, 2.11
How is a process operating in statistical control distinguished from one that is not
A metal fabricator produces connecting rods with an outer diameter that has a 1± 0.02 inch specification. A machine operator takes several sample measurements over time and determines the sample mean outer diameter to be 1.005 inches with a standard deviation of 0.003 inch. Calculate the process capability index for this example. Note: Round your answer to 3 decimal places. Process capability index
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 6 observations regarding the thickness of fabric in measured in millimeters. In a particular hour, the sample means (X-bar) are noted to be: 156.46, 199.62, 189.31, 102.22, and112.09 respectively. In the same sample, the corresponding ranges are: 11.97, 12.17, 13.94, 11.86, and 11.83 respectively. What are the lower and upper control limits for the X-bar chart? O a. None is correct O b. 146.01, 157.87 Oc. 142.92, 160.66 Od. 143.55, 165.47 Oe. 156.55, 170.47 Of. 144.78, 159.11
A manufacturer is selling pharmaceuticals that have a weight specification 199.8 to 200.2 mg, with a target value of 200 mg. Before sending its next shipment, the company collects a large sample of product and determines the mean weight of the sample is 199.89 mg, with a standard deviation of 0.035 mg. The process capability index for the current process is ____. Round to three decimal places.
Sam’s Long Life 60-watt light bulbs are designed to have a life of 1,350 hours with tolerance of ± 340 hours. A recent representative sample from the process that makes these light bulbs revealed a mean of 1,290 hours, with a standard deviation of 94 hours. Compute a. Compute the process capability ratio and the process capability index, and comment on the overall capability of the process b. Explain to what extent the process for producing Sam’s Long Life 60-watt light bulbs would have to be improved to achieve 4-sigma quality. c. show detail work

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