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, Problem 69AP
Summary Introduction
Interpretation: Mean and Range needs to be determined with the help of given data.
Concept Introduction: X bar chart monitors the change in mean over time and R chart monitors the change in range over time and helps organizations makes better improvement decisions.
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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 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.
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 Sample Mean (in.) Range (in.) Sample Sample Mean (in.) Range (in.)1 9.700 0.044 7 9.703 0.0212 9.700 0.051 8 9.707 0.0583 9.689 0.042 9 9.695 0.0394 9.706 0.037 10…
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
Sample Mean(in.)
Range (in.)
Sample
Sample Mean (in.)
Range (in.)
1
9.402
0.033
7
9.401
0.041
2
9.404
0.041
8
9.407
0.034
3
9.391
0.034
9
9.393
0.027
4
9.406
0.051
10
9.401
0.029
5
9.397
0.031
11
9.403
0.039
6
9.399
0.036
12
9.404
0.047
Part 2
For the given data, the
x
=
enter your response here
inches (round your response to four decimal places).
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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- 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 Sample Mean (in.) Range (in.) Sample Sample Mean (in.) Range (in.) 1 13.502 0.033 7 13.501 0.041 2 13.500 0.041 8 13.507 0.034 3 13.489 0.034 9 13.493 0.027 4 13.508 0.051 10 13.501 0.029 5 13.497 0.031 11 13.501 0.039 6 13.499 0.036 12 13.506 0.047 For the given data, the x = nothing 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 (UCLx) = nothing inches (round your response…arrow_forwardTwelve 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 Sample Mean (in.) Range (in.) Sample Sample Mean (in.) Range (in.) 1 11.404 0.044 7 11.403 0.021 2 11.400 0.051 8 11.407 0.058 3 11.389 0.042 9 11.397 0.039 4 11.406 0.037 10 11.403 0.038 5 11.395 0.048 11 11.401 0.054 6 11.397 0.053 12 11.406 0.061 Part 2 For the given data, the x = enter your response here inches (round your response to four decimal places). The control limits for the 3-sigma R-chart are (round all intermediate calculations to three decimal places before…arrow_forwardThe time to replace vehicle wiper blades at a service center was monitored using a mean and a rangechart. Six samples of n = 20 observations were obtained and the sample means and ranges computed:Sample Mean Range Sample Mean Range1 3.06 .42 4 3.13 .462 3.15 .50 5 3.06 .463 3.11 .41 6 3.09 .45 a. Using the factors in Table 10.3, determine upper and lower limits for mean and range charts.b. Is the process in control?arrow_forward
- 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 Sample Mean (in.) Range (in.) Sample Sample Mean (in.) Range (in.) 1 9.602 0.033 7 9.603 0.041 2 9.602 0.041 8 9.605 0.034 3 9.593 0.034 9 9.597 0.027 4 9.606 0.051 10 9.601 0.029 5 9.599 0.031 11 9.603 0.039 6 9.599 0.036 12 9.606 0.047 Part 2 For the given data, the x double overbarx = 9.6013 inches (round your response to four decimal places). Part 3 Based on the sampling done, the control limits for 3-sigma x overbarx chart are: Upper Control Limit (UCL Subscript x…arrow_forwardTwelve 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 Sample Mean (in.) Range (in.) Sample Sample Mean (in.) Range (in.) 1 9.602 0.033 7 9.603 0.041 2 9.602 0.041 8 9.605 0.034 3 9.593 0.034 9 9.597 0.027 4 9.606 0.051 10 9.601 0.029 5 9.599 0.031 11 9.603 0.039 6 9.599 0.036 12 9.606 0.047 Part 2 For the given data, the x double overbarx = (inches (round your response to four decimal places)arrow_forwardRefer 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).arrow_forward
- 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 Sample Mean (in.) Range (in.) Sample Sample Mean (in.) Range (in.) 1 10.802 0.044 7 10.803 0.021 2 10.800 0.051 8 10.807 0.058 3 10.791 0.042 9 10.793 0.039 4 10.808 0.037 10 10.803 0.038 5 10.797 0.048 11 10.803 0.054 6 10.801 0.053 12 10.806 0.061 Part 2 For the given data, the x = enter your response here inches (round your response to four decimal places).arrow_forwardA production manager at a Contour Manufacturing planthas inspected the number of defective plastic molds in 5 randomsamples of 20 observations each. Following are the number ofdefective molds found in each sample: Construct a 3-sigma control chart (z = 3) with this informationarrow_forwardDistinguish between a sampling error and a nonsampling error.How can each be reduced?arrow_forward
- 4: A production manager at a Contour Manufacturing plant has inspected the number of defective plastic molds in 5 random samples of 20 observations each. Following are the number of defective molds found in each sample: Sample N Number of observations Number of defections 1 1 20 2 2 20 3 2 20 4 1 20 5 0 20 a) Construct a 3-sigma control chart (P-chart) with this information.arrow_forwardAt Webster Chemical Company, lumps in the caulking compound could cause difficulties in dispensing a smooth bead from the tube. Testing for the presence of lumps destroys the product, so an analyst takes random samples. The following results are obtained: Tube No. Lumps Tube No. Lumps Tube No. Lumps 1 6 5 6 9 0 2 7 6 5 10 5 3 2 7 5 11 2 4 4 8 8 12 3 Determine the c-chart two-sigma upper and lower control limits for this process. Is the process in statistical control? The UCLc equals ------ and the LCLc equals ------ (Enter your responses rounded to two decimal places.)arrow_forward4. Organic Grains LLC uses statistical process control to ensure that its health-conscious, low-fat, multigrain sandwich loaves have the proper weight. Based on a previously stable and in-control process, the control limits of the x- and R-charts are: UCLx = 5.35, LCLx = 4.93; UCLR = 0.894, LCLR = 0. Over the past few days, they have taken five random samples of four loaves each and have found the following: Net Weight Sample Loaf # 1 Loaf # 2 Loaf # 3 Loaf # 4 1 4.9 5.2 5.1 5.0 2 5.3 5.1 5.2 5.3 3 4.9 5.2 4.9 5.2 4 5.5 5.5 5.3 5.5 5 5.3 5.2 5.3 5.0 Part 2 Based on the x-chart, is one or more samples beyond the control limits? ▼ No Yes .arrow_forward
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