Loose-leaf for Operations Management (The Mcgraw-hill Series in Operations and Decision Sciences)
12th Edition
ISBN: 9781259580093
Author: William J Stevenson
Publisher: McGraw-Hill Education
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Chapter 10, Problem 2P
a)
Summary Introduction
To determine: The upper and lower control limits.
Introduction:
Control chart:
It is a graph used to analyze the process change over a time period. A control chart has a upper control limit, and lower control which are used plot the time order.
b)
Summary Introduction
To determine: Whether the process is in a controlled state.
Introduction:
Control chart:
It is a graph used to analyze the process change over a time period. A control chart has a upper control limit, and lower control which are used plot the time order.
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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.
A Quality Analyst wants to construct a control chart for determining whether three machines, all producing
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units of output from each machine, with the following results:
Machine
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#1
17
15
15
17
#2
16
25
18
25
# 3
23
24
23
22
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What is the sample average range based upon this limited sample?
What are the x-bar chart upper and lower control limits?
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.
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Chapter 10 Solutions
Loose-leaf for Operations Management (The Mcgraw-hill Series in Operations and Decision Sciences)
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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 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_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 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…arrow_forward1. 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)=53.6253.62 units (round your response to two decimal places). b) Now determine the 2-sigma x-chart control limits. Upper Control Limit (UCLx)=? units (round your response to two decimal places). 2. Sample Size, n Mean Factor, A2 Upper Range, D4 Lower Range, D3 2 1.880 3.268 0 3 1.023 2.574 0 4 0.729 2.282 0 5 0.577 2.115 0 6 0.483 2.004 0 7 0.419 1.924 0.076 8 0.373 1.864 0.136 9 0.337 1.816 0.184 10 0.308 1.777 0.223 12 0.266 1.716 0.284 Thirty-five samples of size 7 each were taken from a…arrow_forward
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