Operations Management
13th Edition
ISBN: 9781259667473
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
the same product, are under control with regard to a particular quality variable. Accordingly, he sampled four
units of output from each machine, with the following results:
Machine
Measurements
#1
17
15
15
17
#2
16
25
18
25
# 3
23
24
23
22
What is the estimate of the process mean for whenever it is under control?
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
Operations Management
Ch. 10.2 - A potato chip is a delicate thing Fragile A pound...Ch. 10.2 - A potato chip is a delicate thing Fragile A pound...Ch. 10.5 - It's estimated that more than 7 000 hospital...Ch. 10.5 - It's estimated that more than 7 000 hospital...Ch. 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 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
- 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) = mmarrow_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 can filling process at a beverage manufacturing factory is assumed to be in control with limits of 84 ±3 had sample averages for the x-bar chart of the following:87.1,87, 87.2, 89, 90, 88.5, 89.5, and 88. Which of the following statement ?below are correct Not enough information to determine .a O None is correct b O Process mean is in-control .c O Process mean is out-of-control .d O أخل اختياري 4) E ENG acerarrow_forward
- Refer to Table 56.1-Factors for Computing Control Chart Limits.(3.sigma) for this problem. 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? mm (round your response to two decimal places). b) What is the value of R? R=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;)mm (round your response to two decimal places) Lower Control Limit (LCL;)mm (round your response to two decimal places). d) What are the UCL and LCL using 3-sigma? Upper Control Limit (UCLR)-mm (round your response to two decimal places). Lower Control Limit (LCL)-mm (round your response to two decimal places) Mean x (mm) 154.9 151.2 155.6 155.5 154.6 Range R (mm) 4.4 4.8 4.3 5.0 4.7 Nextarrow_forwardA Quality Analyst wants to construct a control chart for determining whether three machines, all producing the same product, are under control with regard to a particular quality variable. Accordingly, he sampled four units of output from each machine, with the following results : Machine #1 measurements [17, 12, 21, 12]; Machine #2 measurements [ 14, 22, 16, 13]; Machine #3 measurements [ 13, 19, 14, 23]. Using the factors for three sigma control limits, what are x-bar chart upper and lower control limits? O a. 23.15and 9.52 O b. 44.33and -11.67 Oc. 25.85and 6.813 O d. 18.85and 13.81arrow_forwardAt Gleditsia Triacanthos Company, a certain manufactured part is deemed acceptable if its lengthis between 12.45 to 12.55 inches. The process is normally distributed with an average of 12.49inches and a standard deviation of 0.014 inches. A) Is the process capable of meeting specifications? B) Does the process meet specifications?arrow_forward
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