Operations Management
2nd Edition
ISBN: 9781260484687
Author: CACHON, Gerard
Publisher: MCGRAW-HILL HIGHER EDUCATION
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Chapter 9, Problem 6PA
Summary Introduction
To determine: The center line while constructing an X-bar chart.
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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?
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 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.
You are an analyst for a company that produces parts for medical devices, and these parts must meet specifications required by your customer. You implement a process improvement to decrease the variation in diameter for one of the parts, and want to determine if the process improvement had any effect. What type of control chart would be most appropriate to determine if the process improvement did in fact reduce variation in the output of the process?
Group of answer choices
a X-bar
b R
c P
d C
e Cpk
Chapter 9 Solutions
Operations Management
Ch. 9 - Prob. 1CQCh. 9 - Prob. 2CQCh. 9 - Prob. 3CQCh. 9 - Prob. 4CQCh. 9 - Prob. 5CQCh. 9 - Prob. 6CQCh. 9 - Prob. 7CQCh. 9 - Prob. 8CQCh. 9 - Prob. 9CQCh. 9 - Prob. 10CQ
Ch. 9 - Prob. 11CQCh. 9 - Prob. 12CQCh. 9 - Prob. 13CQCh. 9 - Prob. 14CQCh. 9 - Prob. 15CQCh. 9 - Prob. 16CQCh. 9 - Prob. 17CQCh. 9 - Prob. 18CQCh. 9 - Prob. 1PACh. 9 - Prob. 2PACh. 9 - Prob. 3PACh. 9 - Prob. 4PACh. 9 - Prob. 5PACh. 9 - Prob. 6PACh. 9 - Prob. 7PACh. 9 - Prob. 8PACh. 9 - Prob. 9PACh. 9 - Prob. 10PACh. 9 - Prob. 11PACh. 9 - Prob. 12PACh. 9 - Prob. 2.1CCh. 9 - Prob. 2.2C
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- 1. The data shown in Table 1 are x and R values for 20 samples of size n= 5 taken from a process producing bearings. The measurements are made on the inside diameter of the bearing, with only the last three decimals recorded (i.e., 31.6 should be 0.50316). Please show all your work for full credit. (a) Set up x and R charts on this process. Does the process seem to be in statistical control? If necessary, revise the trial control limits. (b) Assume that diameter is normally distributed. Estimate the process standard deviation. Sample R Sample R 1 31.6 4 11 29.8 4 33.0 3 12 34.0 4 35.0 4 13 33.0 10 4 32.2 4 14 34.8 4 5 33.8 38.4 31.6 15 35.6 7 3 16 30.8 7 4 17 33.0 5 8 36.8 10 18 31.6 3 9. 35.0 15 19 28.2 9 10 34.0 6 20 33.8 Table 1: Bearing Diameter Dataarrow_forwardA process considered to be in control measures an ingredient in ounces. A quality inspector took 10 samples, each with 5 observations as follows: Using this information, obtain three-sigma (i.e., z=3) control limits for a mean control chart and control limits for a range chart, respectively. It is known from previous experience that the standard deviation of the process is 1.36. Discuss whether the process is in control or not.arrow_forwardCan someone please explain how to find upper and lower limits using Excel? I am trying to answer this question: The overall average on a process you are attempting to monitor is 50.0 units. The process population standard deviation is 1.84 Sample size is given to be 4.a) Determine the 3-sigma x-chart control limits. Upper Control Limit (UCL) = ____units (round your response to two decimal places).arrow_forward
- 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 4 observations regarding the thickness of fabric in measured in millimeters. In a particular hour, the sample means (X-bar) are noted to be: 172.11, 219.58, 208.24, 112.44, and 123.30 respectively. In the same sample, the corresponding ranges are: 13.17, 13.38, 15.34, 13.04, and 13.02 respectively What are the lower and upper control limits for the X-bar chart? O a. None is correct O b. 143.55, 165.47 Oc. 144.78, 159.11 O d. 157.21, 177.05 O e. 146.01, 157.87 Of. 142.92, 160.66arrow_forwardIn 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 4 observations regarding the thickness of fabric in measured in millimeters. In a particular hour, the sample means (X-bar) are noted to be: 172.11,219.58, 208.24, 112.44, and 123.30 respectively. In the same sample, the corresponding ranges are: 13.17, 13.38, 15.34, 13.04, and 13.02 respectively What are the lower and upper control limits for the R chart? O a. 0,31.47 O b. 0,30.99 Oc. None is correct O d. 0,29.17 O e. 0,31.17 O f. 0,28.17arrow_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
- 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.arrow_forwardIn 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 5 observations regarding the thickness of fabric in measured in millimeters. In a particular hour, the sample means (X-bar) are noted to be: 172.11, 219.51 . 208.24, 112.44 and 123.30 respectively. In the same sample, the corresponding ranges are: 13.1713.3815.34, 13.04, and 13.02 respectively What are the lower and upper control limits for the R chart?arrow_forwardCartons of Plaster are supposed to weigh exactly 32 ounces. Inspectors want to develop process control charts. They take five samples of six (6) boxes each and weigh them. Sample means (X-bar) are: 33.8, 34.6, 34.7, 34.1, and 34.2 respectively. Also, the corresponding ranges are: 1.1, 0.3, 0.4, 0.7, and 0.3, respectively. The lower and upper control limits of the xbar-chart are respectively O a. 33.12 and 34.12 b. 34.01 and 34.55 O c. 30.11 and 40.15 O d. None is correct O e. 37.01 and 39.23arrow_forward
- Cartons of Plaster are supposed to weigh exactly 32 ounces. Inspectors want to develop process control charts. They take five samples of six (5) boxes each and weigh them. Sample means (X-bar) are: 33.8, 34.6, 34.7, 34.1, and 34.2 respectively. Also, the corresponding ranges are: 1.1, 0.3, 0.4, 0.7, and 0.3, respectively. The lower and upper control limits of the R-chart are ,respectively O a. None is correct O b. O and O.15 O c. 0.01 and 1.13 O d. 0.03 and 1.18 O e. O and 1.18arrow_forwardCartons of Plaster are supposed to weigh exactly 32 ounces. Inspectors want to develop process control charts. They take five samples of six (5) boxes each and weigh them. Sample means (X-bar) are: 33.8, 34.6, 34.7, 34.1, and 34.2 respectively. Also, the corresponding ranges are: 1.1, 0.3, 0.4, 0.7, and 0.3, respectively. The lower and upper control limits of the R-chart are respectively O a. O and 0.15 O b. 0.01 and 1.13 O c. O and 1.18 O d. None is correct O e. 0.03 and 1.18arrow_forwardCartons of Plaster are supposed to weigh exactly 32 ounces. Inspectors want to develop process control charts. They take five samples of six (6) boxes each and weigh them. Sample means (X-bar) are: 33.8, 34.6, 34.7, 34.1, and 34.2 respectively. Also, the corresponding ranges are: 1.1,0.3, 0.4. 0.7, and 0.3, respectively. The lower and upper control limits of the xbar-chart are respectively O a. None is correct O b. 30.11 and 40.15 O c. 34.01 and 34.55 O d. 33.12 and 34.12 O e. 37.01 and 39.23arrow_forward
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