Production and Operations Analysis, Seventh Edition
7th Edition
ISBN: 9781478623069
Author: Steven Nahmias, Tava Lennon Olsen
Publisher: Waveland Press, Inc.
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Chapter 12.2, Problem 9P
Summary Introduction
Interpretation: Control Limits needs to be determined with the help of given data.
Concept Introduction: X bar chart monitors the change in mean over time helps organizations makes better improvement decisions.
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At Webster Chemical Company, lumps in the caulking compound could cause difficulties in dispensing a smooth bead from the tube. Even when the process is in control, an average of four lumps per tube of caulk will remain. Testing for the presence of lumps destroys the product, so an analyst takes random samples. The following results are obtained:
Tube No.
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Tube No.
Lumps
Tube No.
Lumps
1
6
5
6
9
5
2
5
6
4
10
0
3
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7
1
11
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4
4
8
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Determine the c-chart two-sigma upper and lower control limits for this process. Is the process in statistical control?
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?
R= 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
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,…
Chapter 12 Solutions
Production and Operations Analysis, Seventh Edition
Ch. 12.1 - Prob. 2PCh. 12.1 - Prob. 3PCh. 12.1 - Prob. 4PCh. 12.1 - Prob. 5PCh. 12.1 - Prob. 6PCh. 12.2 - Prob. 7PCh. 12.2 - Prob. 8PCh. 12.2 - Prob. 9PCh. 12.2 - Prob. 10PCh. 12.2 - Prob. 11P
Ch. 12.2 - Prob. 12PCh. 12.2 - Prob. 13PCh. 12.3 - Prob. 14PCh. 12.3 - Prob. 15PCh. 12.3 - Prob. 16PCh. 12.3 - Prob. 17PCh. 12.4 - Prob. 18PCh. 12.4 - Prob. 19PCh. 12.4 - Prob. 20PCh. 12.4 - Prob. 21PCh. 12.5 - Prob. 22PCh. 12.6 - Prob. 23PCh. 12.6 - Prob. 24PCh. 12.6 - Prob. 25PCh. 12.6 - Prob. 26PCh. 12.6 - Prob. 27PCh. 12.6 - Prob. 28PCh. 12.9 - Prob. 29PCh. 12.9 - Prob. 30PCh. 12.9 - Prob. 31PCh. 12.9 - Prob. 32PCh. 12.9 - Prob. 33PCh. 12.10 - Prob. 34PCh. 12.10 - Prob. 35PCh. 12.10 - Prob. 37PCh. 12.10 - Prob. 38PCh. 12.10 - Prob. 39PCh. 12.10 - Prob. 40PCh. 12.11 - Prob. 41PCh. 12.11 - Prob. 42PCh. 12.11 - Prob. 43PCh. 12.11 - Prob. 44PCh. 12.12 - Prob. 46PCh. 12.12 - Prob. 47PCh. 12.12 - Prob. 48PCh. 12 - Prob. 49APCh. 12 - Prob. 50APCh. 12 - Prob. 51APCh. 12 - Prob. 52APCh. 12 - Prob. 53APCh. 12 - Prob. 54APCh. 12 - Prob. 55APCh. 12 - Prob. 57APCh. 12 - Prob. 58APCh. 12 - Prob. 59APCh. 12 - Prob. 60APCh. 12 - Prob. 61APCh. 12 - Prob. 62APCh. 12 - Prob. 63APCh. 12 - Prob. 64APCh. 12 - Prob. 65APCh. 12 - Prob. 66APCh. 12 - Prob. 67APCh. 12 - Prob. 68APCh. 12 - Prob. 69APCh. 12 - Prob. 70AP
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- NauticaB is a company that makes little boats. This company controls its production process by periodically taking a sample of 100 units from the production line. Each product is inspected for defective features. Control limits are developed using three standard deviations from the mean as the limit. During the last 16 samples taken, the proportion of defective items per sample was recorded as follows: .01 .02 .01 .03 .02 .01 .00 .02 .00 .01 .03 .02 .03 02 .01 .00 The supply chain of Nautica has the following information: Supplier Factory Wholesale Retailer Inventory in days* Accounts 30 90 40 20 receivable in days 20 45 30 40 Accounts payable in days Purchasing unit cost Added unit cost Sales unit price On-time 30 45 60 37 $ 5 $10 $20 $20 $25 $55 $55 $10 $70 $ 70 $ 30 $110 delivery (%) 85 95 75 95 * This is also the throughput time in days. Compute the cash-to-cash cycle time for each of the four entities separately. Based on this calculation, who is benefiting the most?arrow_forwardThe Awake Coffee Company produces gourmet instantcoff ee. Th e company wants to be sure that the average fi ll of coff eecontainers is 12.0 ounces. To make sure the process is in control,a worker periodically selects at random a box of six containers ofcoff ee and measures their weight. When the process is in control,the range of the weight of coff ee samples averages 0.6 ounces.(a) Develop an R-chart and an x-chart for this process.(b) Th e measurements of weight from the last five samplestaken of the six containers follow Is the process in control? Explain your answer.arrow_forwardA woodworker is concerned about the quality of the finished appearance of her work. She has finished a total of 50 unit split-willow hand-woven baskets. However, she has found the following number of finish defects in ten units sampled: 4,0,3,1,2,0,1,2,0,2. Calculate the average number of defects per basket. If 3-sigma control limits are used, calculate the lower control limit and upper control limit.arrow_forward
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