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Chapter 14: Q4BSC (page 654)

Euro Coins After constructing a control chart for the proportions of defective one-euro coins, it is concluded that the process is within statistical control. Does it follow that almost all of the coins meet the desired specifications? Explain.

Short Answer

Expert verified

No, it cannot be concluded that the coins follow the required specifications.

A control chart only examines whether the process mean/process variation is within statistical control. It does not establish any conclusion on whether the goods follow the given specifications.

Step by step solution

01

Given information

A control chart is plotted for the proportions of defective coins. By observing the control chart, it is concluded that the process is under statistical control.

02

No Information on Process Specifications Using Control Charts

The process's actual behavior and not the desired behaviordeterminesthe upper and lower control boundaries of a control chart for a proportion p.

If a process is concluded to be under control using the control chart, it does not guarantee whether the goods produced satisfy the required specifications.

Thus, it cannot be said that all coins meet the desired specifications.

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Most popular questions from this chapter

Quarters. In Exercises 9–12, refer to the accompanying table of weights (grams) of quarters minted by the U.S. government. This table is available for download at www.TriolaStats.com.

Day

Hour 1

Hour 2

Hour 3

Hour 4

Hour 5

\(\bar x\)

s

Range

1

5.543

5.698

5.605

5.653

5.668

5.6334

0.0607

0.155

2

5.585

5.692

5.771

5.718

5.72

5.6972

0.0689

0.186

3

5.752

5.636

5.66

5.68

5.565

5.6586

0.0679

0.187

4

5.697

5.613

5.575

5.615

5.646

5.6292

0.0455

0.122

5

5.63

5.77

5.713

5.649

5.65

5.6824

0.0581

0.14

6

5.807

5.647

5.756

5.677

5.761

5.7296

0.0657

0.16

7

5.686

5.691

5.715

5.748

5.688

5.7056

0.0264

0.062

8

5.681

5.699

5.767

5.736

5.752

5.727

0.0361

0.086

9

5.552

5.659

5.77

5.594

5.607

5.6364

0.0839

0.218

10

5.818

5.655

5.66

5.662

5.7

5.699

0.0689

0.163

11

5.693

5.692

5.625

5.75

5.757

5.7034

0.0535

0.132

12

5.637

5.628

5.646

5.667

5.603

5.6362

0.0235

0.064

13

5.634

5.778

5.638

5.689

5.702

5.6882

0.0586

0.144

14

5.664

5.655

5.727

5.637

5.667

5.67

0.0339

0.09

15

5.664

5.695

5.677

5.689

5.757

5.6964

0.0359

0.093

16

5.707

5.89

5.598

5.724

5.635

5.7108

0.1127

0.292

17

5.697

5.593

5.78

5.745

5.47

5.657

0.126

0.31

18

6.002

5.898

5.669

5.957

5.583

5.8218

0.185

0.419

19

6.017

5.613

5.596

5.534

5.795

5.711

0.1968

0.483

20

5.671

6.223

5.621

5.783

5.787

5.817

0.238

0.602

Quarters: R Chart Treat the five measurements from each day as a sample and construct an R chart. What does the result suggest?

Identify three specific criteria for determining when a process is out of statistical control.

Lake Mead Elevations Many people in Nevada, Arizona, and California get water and electricity from Lake Mead and Hoover Dam. Shown in Exercise 4 are an x chart (top) and an R chart (bottom) obtained by using the monthly elevations (ft) of Lake Mead at Hoover Dam (based on data from the U.S. Department of the Interior). The control charts are based on the 12 monthly elevations for each of 75 consecutive and recent years. What does the x chart tell us about Lake Mead?

Control Charts for p. In Exercises 5–12, use the given process data to construct a control chart for p. In each case, use the three out-of-control criteria listed near the beginning of this section and determine whether the process is within statistical control. If it is not, identify which of the three out-of-control criteria apply

Aspirin Tablets Bottles of aspirin tablets typically have labels indicating that each tablet contains 325 mg of aspirin, but the actual amounts can vary between 315 mg and 335 mg. A tablet is defective if it has less than 315 mg of aspirin or more than 335 mg of aspirin. Listed below are numbers of defects found in batches of 1000 tablets.

16 18 13 9 10 8 6 5 5 3

Control Charts for p. In Exercises 5–12, use the given process data to construct a control chart for p. In each case, use the three out-of-control criteria listed near the beginning of this section and determine whether the process is within statistical control. If it is not, identify which of the three out-of-control criteria apply

Cola Cans In each of several consecutive days of production of cola cans, 50 cans are tested and the numbers of defects each day are listed below. Do the proportions of defects appear to be acceptable? What action should be taken?

8 7 9 8 10 6 5 7 9 12 9 6 8 7 9 8 11 10 9 7
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