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 12.1, Problem 2P
Summary Introduction
Interpretation: Histogram needs to be determined based on the given data.
Concept Introduction: Histogram helps in distributing the given data by grouping the numbers into some range. It helps to identify the outliers present in the data.
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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
Refer to Table S6.1 - Factors for Computing Control Chart Limits (3 sigma) for this problem.
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 Mean
(in.)
Range
(in.)
Sample
Sample Sample Mean (in.) Range (in.)
1
9.404
0.044
7
9.403
0.021
2
9.402
0.051
8
9.405
0.058
3
9.393
0.042
9.395
0.039
4
9.404
0.037
10
9.401
0.038
9.399
0.048
11
9.401
0.054
9.397
0.053
12
9.404
0.061
For the given data, the x =
inches (round your response to four decimal places).
Based on the sampling done, the control limits for 3-sigma x chart are:
Upper Control Limit (UCL;) = inches (round your response to four decimal places).
Lower Control Limit (LCL;) = inches (round your response to four decimal places).
Arana is a company that produces homemade Rotini pasta. They use statistical process control to monitor the
manufacturing process. The company collects five samples, each containing six packs of pasta. Below is the sample
data, but the standard deviation of the process output is unknown. If an R chart is created using three-sigma limits
(i.e., z = 3) to monitor the variability of products, what would be the upper control limit for this R chart?
Sample 1
Sample 2
Sample 3
Pack 1
452.3
451.6
448.6
Sample 4
454.7
Sample 5 448.9
7.614
9.328
11.653
13.427
Pack 2
452.8
451.2
455.6
451.7
453.4
Pack 3
456
454.6
456.5
451
456.7
Pack 4
457.2
455.3
451.9
452.6
456.3
Pack 5
457.8
452.2
455.6
454.7
452.4
Pack 6
451.8
451.9
448.3
458.4
456
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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