A machine has four heads. Samples of n= 3 units are selected from each head, and the x and Rvalues for an important quality characteristic are computed. The data are shown in the Table.Set up group control charts for this process. Interpret the charts.HEADSampleNo.1ла со ин234561899101xbar R2 1 4 73 75 4 73 72 1 7272717474713ANW241243ANA W1242xbar7 75 78 74 72 71 70 69 73 7277R212431NW N323xbar RNKNRF RENNR72757170747377727170WINA421322WN P11234xbar75 78 73 74 72 78 73 69 70 72RNW N NANA1212651232

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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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Control charts for X-bar and S are maintained for the fill volume of protein shake drink. The specifications are 330 + 10 mL. After 40 samples of size n=7 are analyzed, we find that: 40 40 = 13,200 Si = 296 i=1 i=D1 Find the best estimate of the process standard deviation. 7.498 7.400 7.570 2.737 7.713 8.032
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 10 pistons produced each day, the mean and the range of this diameter have been as follows: a) What is the value of X? x= mm (round your response to two decimal places). Day 1 2 3 4 5 Mean x (mm) 158.9 155.2 155.6 157.5 156.6 Range R (mm) 4.2 4.4 4.3 4.8 4.3
ory 5 Media telo Alan's Shop Once each day, a sample of 96 components is randomly taken and the # of defective components (out of 96), is recorded. Given the following results from 14 samples: Sample 1 2 3 4 5 6 7 0.1889 36812 0,2566 # Defects 8 4 11402 5 6 Ⓒ01366 7 4 5 Sample 8 What is the upper control limit for the most appropriate control chart? 9 10 11 12 13 14 # Defects 7 5 9 3 8 5 8
The weights of boxes of Oat Flakes within a large production lot are sampled each hour. Managers want to set control limits that include 99.73% of the sample means and given is the population (process) standard deviation, which is 1.13. You are in charge of randomly selecting four boxes each hour, for three hours. The data you collected is in the table below: Using an R Chart, what are the upper and lower control limits? Sample Lightest Obs. (n=4) Heaviest Obs. (n=4) Range (Ri) in difference 1 15.00 17.00 2.00 2 15.30 16.90 1.60 3 15.20 16.70 1.50
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 10 pistons produced each day, the mean and the range of this diameter have been as follows: a) What is the value of x? x= 156.76 mm (round your response to two decimal places). b) What is the value of R? Day 1 2 3 4 5 Mean x (mm) 158.9 155.2 155.6 157.5 156.6 R = 4.40 mm (round your response to two decimal places). c) What are the UCL and LCL using 3-sigma? Upper Control Limit (UCL) = mm (round your response to two decimal places). Range R (mm) 4.2 4.4 4.3 4.8 4.3 Ç
The weights of boxes of Oat Flakes within a large production lot are sampled each hour. Managers want to set control limits that include 99.73% of the sample means, and given is the population (process) standard deviation, which is 1.13. You are in charge of randomly selecting four boxes each hour, for three hours. The data you collected is located in the table below:Using an Xbar Chart, what are the upper and lower control limits? Sample Avg. of 4 boxes 1 16.8 2 17.1 3 17.2
Five data entry operators work at the data process-ing department of the Birmingham Bank. Each day for 30 days, the number of defective records in a sample of 250 records typedby these operators has been noted, as follows: a) Establish 3s upper and lower control limits.b) Why can the lower control limit not be a negative number? c) The industry standards for the upper and lower control lim-its are 0.10 and 0.01, respectively. What does this imply about Birmingham Bank’s own standards?
Specifications for a part for a 3-D printer state that the part should weigh between 24 and25 ounces. The process that produces the parts has a mean of 24.5 ounces and a standard deviation of .2 ounce. The distribution of output is normal. What percentage of parts will not meet the weight specs? Within what values will 95.44 percent of the sample means of this process fall if samples of n = 16 are taken and the process is in control (random)? Using the control limits from part b, would the following sample means be in control? 24.52, 24.53, 24.44, 24.51, 24.41, 24.39 An automatic filling machine is used to fill 1-liter bottles of cola. The machine’s output is approxi- mately normal with a mean of 1.0 liter and a standard deviation of .01 liter. Output is monitored using means of samples of 25 observations. Determine upper and lower control limits that will include roughly 97 percent of the sample means when the process is in control. Given the following sample means—1.005,…
The output of a certain integrated-circuit productionline is checked daily by inspecting a sample of 100 units.Over a long period of time, the process has maintaineda yield of 80 percent, that is, a proportion defective of 20 percent, and the variation of the proportion defec-tive from day to day is measured by a standard devi-ation of 0.04. If on a certain day the sample contains 38 defectives, find the mean of the posterior distribu-tion of as an estimate of that day’s proportion defec-tive. Assume that the prior distribution of Θ is a beta distribution.
Answer the given question with a proper explanation and step-by-step solution. Johnson & Johnson manufactures needles that are subjected to a bend test. They use statistical process control (SPC) and the results (measured in grams) are plotted on a chart. If the process average is 26,1 and the average range is 5; what will the control limits be if the sample size n=8? The factor for calculation of control limits is 0,373 for sample size n=8. Which statement(s) is/are true? a The process is "out of control". b The process is "in control". c The upper control limit equals 27,965. d The upper control limit equals 24,235. e The lower control limit equals 27,965. 1. a 2. b, c 3. a, c 4. b, c, d 5. a, d, e
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 10 pistons produced each day, the mean and the range of this diameter have been as follows: a) What is the value of x? = x= 155.56 mm (round your response to two decimal places). b) What is the value of R? R 4.48 mm (round your response to two decimal places). c) What are the UCL; and LCL; using 3-sigma? Day 1 2 3 4 5 Upper Control Limit (UCL) = 156.94 mm (round your response to two decimal places). Lower Control Limit (LCL-) = 154.18 mm (round your response to two decimal places). d) What are the UCLR and LCLR using 3-sigma? Upper Control Limit (UCL) = 7.96 mm (round your response to two decimal places). Mean x (mm) 154.9 153.2 155.6 155.5 158.6 Range R (mm) 4.0 4.8 3.9 5.0 4.7 Lower Control Limit (LCL) = 1.00 mm (round your response to two decimal places). e) If the true diameter mean should be 155 mm and you want…
Control charts for X-bar and R are maintained for the tensile strength of fibers used in composite materials. The specifications are 440+40. After 25 samples of size n=10 are analyzed, we find that: 25 25 X¡ = 12,870 Ri = 1,350 i=1 What are the limits of the R chart? UCL=65.54 and LCL=2.56 UCL=74.97 and LCL=9.41 UCL=79.96 and LCL=10.03 UCL=95.96 and LCL=12.04 UCL=72.82 and LCL=2.85

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