Statistics for Business and Economics (13th Edition)
13th Edition
ISBN: 9780134506593
Author: James T. McClave, P. George Benson, Terry Sincich
Publisher: PEARSON
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Chapter 13, Problem 13.90ACI
Defects in graphite shafts. Over the last year, a company that manufactures golf clubs has received numerous com- plaints about the performance of its graphite shafts and has lost several market share percentage points. In response, the company decided to monitor its shaft production process to identify new opportunities to improve its product. The process involves pultrusion. A fabric is pulled through a thermosetting polymer bath and then through a long heated steel die. As it moves through the die, the shaft is cured. Finally, it is cut to the desired length. Defects that can occur during the process are internal voids, broken strands, gaps between successive layers, and microcracks caused by improper curing. The company’s newly formed quality department sampled 10 consecutive shafts every 30 minutes, and nondestructive testing was used to seek
| Shift Number | Number of Defective Shafts | Proportion of Defective Shafts |
| 1 | 9 | .05625 |
| 2 | 6 | .03750 |
| 3 | 8 | .05000 |
| 4 | 14 | .08750 |
| 5 | 7 | .04375 |
| 6 | 5 | .03125 |
| 7 | 7 | .04375 |
| 8 | 9 | .05625 |
| 9 | 5 | .03125 |
| 10 | 9 | .05625 |
| 11 | 1 | .00625 |
| 12 | 7 | .04375 |
| 13 | 9 | .05625 |
| 14 | 14 | .08750 |
| 15 | 7 | .04375 |
| 16 | 8 | .05000 |
| 17 | 4 | .02500 |
| 18 | 10 | .06250 |
| 19 | 6 | .03750 |
| 20 | 12 | .07500 |
| 21 | 8 | .05000 |
| 22 | 5 | .03125 |
| 23 | 9 | .05625 |
| 24 | 15 | .09375 |
| 25 | 6 | .03750 |
| 26 | 8 | .05000 |
| 27 | 4 | .02500 |
| 28 | 7 | .04375 |
| 29 | 2 | .01250 |
| 30 | 6 | .03750 |
| 31 | 9 | .05625 |
| 32 | 11 | .06875 |
| 33 | 8 | .05000 |
| 34 | 9 | .05625 |
| 35 | 7 | .04375 |
| 36 | 8 | .05000 |
Source: W. Kolarik. Creating Quality: Concepts. Systems, Strategies, and Tools. Copyright © 1995 by William J. Kolarik. Used by permission of William j. Kolarik.
out flaws in the shafts. The data from each 8-hour work shift were combined to form a shift sample of 160 shafts. Data on the proportion of defective shafts for 36 shift samples are presented in the table shown at the bottom of the previous column.
- a. Use the appropriate control chart to determine whether the process proportion remains stable over time.
- b. Does your control chart indicate that both common and special causes of variation are present? Explain.
- c. Data on the types of flaws identified are given in the table below. [Note: Each defective shaft may have more than one flaw.] To help diagnose the causes of variation in process output, construct a Pareto diagram for the types of shaft defects observed. Which are the “vital few”? The “trivial many"?
| Type of Defect | Number of Defects |
| Internal voids | 11 |
| Broken strands | 96 |
| Gaps between layer | 72 |
| Microcracks | 150 |
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Chapter 13 Solutions
Statistics for Business and Economics (13th Edition)
Ch. 13.4 - What is a control chart? Describe its use.Ch. 13.4 - Explain why rational subgrouping should be used in...Ch. 13.4 - When a control chart is first constructed, why are...Ch. 13.4 - Which process parameter is an x -chart used to...Ch. 13.4 - Even if all the points on an x -chart fall between...Ch. 13.4 - What must be true about the variation of a process...Ch. 13.4 - Use the six pattern-analysis rules described in...Ch. 13.4 - Consider the x -chart shown below. a. Is the...Ch. 13.4 - Use Table IX on page 13-74 to find the value of A2...Ch. 13.4 - Twenty-five consecutive samples of size n = 5 were...
Ch. 13.4 - The data in the following table were collected for...Ch. 13.4 - Prob. 13.12ACBCh. 13.4 - Active pharmaceutical ingredient. During the...Ch. 13.4 - Detecting gender-related employment disparities....Ch. 13.4 - Pain levels of ICU patients. Various interventions...Ch. 13.4 - Quality control for irrigation data. Most farmers...Ch. 13.4 - Improving public health waiting times. Statistical...Ch. 13.4 - Cereal box manufacturing. A machine at K-Company...Ch. 13.4 - Detecting under-reported emissions. The...Ch. 13.4 - 13 20 Selecting the best wafer-slicing machine....Ch. 13.4 - Chunky data. BPI Consulting, a leading provider of...Ch. 13.4 - Military aircraft bolts. A precision parts...Ch. 13.5 - What characteristic of a process is an R-chart...Ch. 13.5 - Prob. 13.24LMCh. 13.5 - Use Table IX on page 13-74 to find the values of...Ch. 13.5 - Construct and interpret an R-chart for the data in...Ch. 13.5 - Construct and interpret an R-chart for the data in...Ch. 13.5 - Construct and interpret an R-chart and an x -chart...Ch. 13.5 - Weight of packed frozen scallops. In Quality...Ch. 13.5 - Detecting gender-related employment disparities....Ch. 13.5 - Pain levels of ICU patients. Refer to the Research...Ch. 13.5 - Quality control for irrigation data. Refer to...Ch. 13.5 - Lowering the thickness of an expensive blow-molded...Ch. 13.5 - Cola bottle filling process. A soft-drink bottling...Ch. 13.5 - Chunky data. Refer to Exercise 13.21e (p. 13-40)...Ch. 13.5 - Replacement times for lost ATM cards. In an effort...Ch. 13.5 - Military aircraft bolts. Refer to the...Ch. 13.5 - Precision of scale weight measurements. The...Ch. 13.6 - What characteristic of a process is a p-chart...Ch. 13.6 - In each of the following cases, use the sample...Ch. 13.6 - The proportion of defective items generated by a...Ch. 13.6 - To construct a p-chart for a manufacturing...Ch. 13.6 - To construct a p-chart, 20 samples of size 150...Ch. 13.6 - Academic failure rates in Nigeria. The quality...Ch. 13.6 - Monitoring surgery complications. An article on...Ch. 13.6 - Rental car call center study. A worldwide rental...Ch. 13.6 - Defective micron chips. A manufacturer produces...Ch. 13.6 - Hand break cable defects. In Control Engineering...Ch. 13.6 - Monitoring newspaper typesetters. Accurate...Ch. 13.6 - Quality of rewritable CDs. A Japanese compact disc...Ch. 13.6 - Leaky process pumps. Quality (February 2008)...Ch. 13.6 - Rubber company lire tests. Goodstone Tire Rubber...Ch. 13.7 - Explain why it is inappropriate to conduct a...Ch. 13.7 - Explain the difference between process spread and...Ch. 13.7 - Describe two different ways to assess the...Ch. 13.7 - Why is it recommended to use and interpret Cp in...Ch. 13.7 - For a process that is in control and follows a...Ch. 13.7 - Find the specification spread for each of the...Ch. 13.7 - Find (or estimate) the process spread for each of...Ch. 13.7 - Find the value of Cp for each of the following...Ch. 13.7 - Upper specification limit of a process. An...Ch. 13.7 - Capability of an in-control process. A process is...Ch. 13.7 - Water use at a thermal power plant. Thermal power...Ch. 13.7 - Cereal box filling process. Refer to the data on...Ch. 13.7 - Military aircraft bolts. Refer to Exercise 13.22...Ch. 13.7 - Bioreactor production of antibodies. Benchtop...Ch. 13.7 - Driver gear bore holes. During the manufacture of...Ch. 13.7 - Lowering the thickness of an expensive blow-molded...Ch. 13 - Define quality and list its important dimensions.Ch. 13 - What is a process? Give an example of an...Ch. 13 - What is a system? Give an example of a system with...Ch. 13 - Describe the six major sources of process...Ch. 13 - Suppose all the output of a process over the last...Ch. 13 - Processes that are in control are predictable;...Ch. 13 - Compare and contrast special and common causes...Ch. 13 - Explain the difference between control limits and...Ch. 13 - Should control charts be used to monitor a process...Ch. 13 - Under what circumstances is it appropriate to use...Ch. 13 - A process is under control and follows a normal...Ch. 13 - Weight of a product. Consider the time series data...Ch. 13 - Lengths of pencils. The length measurements of 20...Ch. 13 - Applying pattern-analysis rules. Use the...Ch. 13 - Defective plastic mold. A company that...Ch. 13 - Robotics clamp gap width. Control chart...Ch. 13 - Package sorting time. AirExpress. an overnight...Ch. 13 - Waiting times of airline passengers. Officials at...Ch. 13 - Defects in graphite shafts. Over the last year, a...Ch. 13 - New iron-making process. Mining Engineering...Ch. 13 - CPU of a computer chip. The central processing...Ch. 13 - Bayfield Mud Company case. The text Quantitative...
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