Operations Management
14th Edition
ISBN: 9781260238891
Author: Stevenson
Publisher: MCG
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Chapter 10, Problem 2P
(a)
Summary Introduction
To determine: The upper and lower control limits that include roughly 97% of the sample means when an automatic machine filled a one-liter bottle of cola with a mean of 1 liter, a standard deviation of 0.1 liters, and samples of 25 observations are used to monitor the output.
Introduction: To monitor the process dispersion, range control charts are used and the mean control limit charts are based on a
(b)
Summary Introduction
To determine: Whether the process is in control at the sample means: 1.005, 1.001, .998, 1.002, .995, .999 when an automatic machine filled a one-liter bottle of cola with a mean of 1 liter, a standard deviation of 0.1 liters and samples of 25 observations are used to monitor the output.
Introduction: To monitor the process dispersion, range control charts are used and the mean control limit charts are based on a normal distribution.
(c)
Summary Introduction
To determine: Whether the process is in control at sample means of 1.003, .999, .997, 1.002, .998, and 1.004. when an automatic machine filled a one-liter bottle of cola with a mean of 1 liter, a standard deviation of 0.1 liters and samples of 25 observations are used to monitor the output.
Introduction: To monitor the process dispersion, range control charts are used and the mean control limit charts are based on a normal distribution.
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An automatic filling machine is used to fill 1-liter bottles of cola. The machine’s output is approximately normal with a mean of 1.0 liter and 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% of the sample means when the process is in control. Using Appendix B, Table A to find the value of Z corresponding to the mean control limits.
Develop a p chart with 3 sigma control limits and evaluate whether the process is in statical control
Factors for Computing Control Chart Limits (3 sigma)
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:
Day
Mean x
(mm)
Range R
(mm)
1
156.9
4.2
2
153.2
4.6
3
153.6
4.1
4
155.5
5.0
5
156.6
4.5
Part 4 c) What are the (UCLx) and (LCLx) using 3-sigma?
(UCLx) = mm (round your response to two decimal places).
(LCLx) = mm
Chapter 10 Solutions
Operations Management
Ch. 10.2 - Prob. 1.1RQCh. 10.2 - Prob. 1.2RQCh. 10.4 - Prob. 1.1RQCh. 10.4 - Prob. 1.2RQCh. 10 - Prob. 1DRQCh. 10 - Prob. 2DRQCh. 10 - Prob. 3DRQCh. 10 - Prob. 4DRQCh. 10 - Prob. 5DRQCh. 10 - Prob. 6DRQ
Ch. 10 - Prob. 7DRQCh. 10 - Prob. 8DRQCh. 10 - Prob. 9DRQCh. 10 - Prob. 10DRQCh. 10 - Prob. 11DRQCh. 10 - Prob. 12DRQCh. 10 - Prob. 13DRQCh. 10 - Prob. 14DRQCh. 10 - Prob. 15DRQCh. 10 - Prob. 16DRQCh. 10 - Prob. 1TSCh. 10 - Prob. 2TSCh. 10 - Prob. 3TSCh. 10 - Prob. 1CTECh. 10 - Prob. 2CTECh. 10 - Prob. 3CTECh. 10 - Prob. 4CTECh. 10 - Prob. 1PCh. 10 - Prob. 2PCh. 10 - Prob. 3PCh. 10 - Prob. 4PCh. 10 - Prob. 5PCh. 10 - Prob. 6PCh. 10 - Prob. 7PCh. 10 - Prob. 8PCh. 10 - Prob. 9PCh. 10 - Prob. 10PCh. 10 - Prob. 11PCh. 10 - Prob. 12PCh. 10 - Prob. 13PCh. 10 - Prob. 14PCh. 10 - Prob. 15PCh. 10 - Prob. 16PCh. 10 - Prob. 17PCh. 10 - A production process consists of a three-step...Ch. 10 - Prob. 19PCh. 10 - Prob. 20PCh. 10 - Prob. 21PCh. 10 - Prob. 22PCh. 10 - Prob. 23PCh. 10 - Prob. 24PCh. 10 - Prob. 25PCh. 10 - Prob. 26PCh. 10 - Prob. 27PCh. 10 - Prob. 28PCh. 10 - Prob. 29PCh. 10 - Prob. 1.1CQCh. 10 - Prob. 2.1CQCh. 10 - Prob. 2.2CQCh. 10 - Prob. 2.3CQCh. 10 - Prob. 2.4CQ
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- A large beverage company would like to use a statistical process control to monitor how much liquid beverage it puts into each bottle. The company operated its bottle filling line under careful supervision, confident that the line was under complete control, for seven hours. Each hour, a sample of 20 bottles was taken off the line and the amount of liquid in each bottle was carefully measured. This is the resulting data: Sample Sample Sample Mean (ml) Range (ml) No. #1 350.4 0.5 349.6 0.5 #3 349.6 0.7 # 4 349.5 0.4 #5 349.8 0.5 #6 350.4 0.9 #7 349.8 0.3 Which of the following is closest to the upper control limit on the beverage company's range chart? O A. 0.86 ml O B. 351.15 ml O C. 350.68 ml O D. 1.92 ml O E. 0.5 ml 2. %23 %23arrow_forwardAt 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?arrow_forwardA large beverage company would like to use a statistical process control to monitor how much liquid beverage it puts into each bottle. The company operated its bottle filling line under careful supervision, confident that the line was under complete control, for seven hours. Each hour, a sample of 20 bottles was taken off the line and the amount of liquid in each bottle was carefully measured. This is the resulting data: Sample Mean (ml) Sample Range (ml) Sample No # 1 350.4 0.5 #2 349.6 0.5 #3 349.6 0.7 #4 349.5 0.4 #5 349.8 0.5 #6 350.4 0.9 #7 349.8 0.3 Which of the following is closest to the lower control limit on the beverage company's range chart? O a. 350.68 ml O b. 0.22 ml O. 351.15 ml O d. 1.92 ml O e. 0.86 mlarrow_forward
- Twelve samples, each containing five parts, were taken from a process that produces steel rods at Emmanual Kodzi's factory. The length of each rod in the samples was determined. The results were tabulated and sample means and ranges were computed. The results were: Sample Sample Mean (in.) Range (in.) Sample Sample Mean (in.) Range (in.) 1 9.602 0.033 7 9.603 0.041 2 9.602 0.041 8 9.605 0.034 3 9.593 0.034 9 9.597 0.027 4 9.606 0.051 10 9.601 0.029 5 9.599 0.031 11 9.603 0.039 6 9.599 0.036 12 9.606 0.047 Part 2 For the given data, the x double overbarx = 9.6013 inches (round your response to four decimal places). Part 3 Based on the sampling done, the control limits for 3-sigma x overbarx chart are: Upper Control Limit (UCL Subscript x…arrow_forwardAuto 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.arrow_forwardTwelve samples, each containing five parts, were taken from a process that produces steel rods at Emmanual Kodzi's factory. The length of each rod in the samples was determined. The results were tabulated and sample means and ranges were computed. The results were: Sample Sample Mean (in.) Range (in.) Sample Sample Mean (in.) Range (in.) 1 9.602 0.033 7 9.603 0.041 2 9.602 0.041 8 9.605 0.034 3 9.593 0.034 9 9.597 0.027 4 9.606 0.051 10 9.601 0.029 5 9.599 0.031 11 9.603 0.039 6 9.599 0.036 12 9.606 0.047 Part 2 For the given data, the x double overbarx = (inches (round your response to four decimal places)arrow_forward
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