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Chapter 14: Q3CQQ (page 654)

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

Short Answer

Expert verified

When a statistical process shows one of the following features, then it is said to be out of control:

  • There is a distinguishably visible pattern, trend, or cycle.
  • At least one point exceeds the upper control limit, and at least one point falls below the lower control limit.
  • The points follow the Run of 8 Rule, which states that there must be at least eight points above or below the centerline in a row.

Step by step solution

01

Given information

The conditions for identifying when a statistical process is out of control are to be determined.

02

Criteria of determining when the statistical process is out of control

If a statistical process possesses one of the following characteristics, then it is said to be unstable or out of control:

  • There is a clearly identifiablepattern, trend, or cycle which is not of random nature.
  • At least one point is above the upper control limit(UCL),and at least one point falls below the lower control limit (LCL).
  • The points depict the Run of 8 Rule, which can be determined as that eight or more consecutive points above or below the centerline.

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Most popular questions from this chapter

Quarters. In Exercises 9鈥�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: Run Chart Treat the 100 consecutive measurements from the 20 days as individual values and construct a run chart. What does the result suggest?

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b. Find the probability that 4 randomly selected men have heights with a mean greater than 70 in.

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3 4 2 5 3 6 8 9 12 14 17 20

Energy Consumption. Exercises 1鈥�5 refer to the amounts of energy consumed in the author鈥檚 home. (Most of the data are real, but some are fabricated.) Each value represents the energy consumed (kWh) in a two-month period. Let each subgroup consist of the six amounts within the same year. Data are available for download at www.TriolaStats.com.


Jan.-Feb.

Mar.-April

May-June

July-Aug.

Sept.-Oct.

Nov.-dec.

Year 1

3637

2888

2359

3704

3432

2446

Year 2

4463

2482

2762

2288

2423

2483

Year 3

3375

2661

2073

2579

2858

2296

Year 4

2812

2433

2266

3128

3286

2749

Year 5

3427

578

3792

3348

2937

2774

Year 6

4016

3458

3395

4249

4003

3118

Year 7

4016

3458

3395

4249

4003

3118

Year 8

4016

3458

3395

4249

4003

3118

Energy Consumption: Run Chart Construct a run chart for the 48 values. Does there appear to be a pattern suggesting that the process is not within statistical control?

Quarters. In Exercises 9鈥�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: \(\bar x\)-Chart Treat the 5 measurements from each day as a sample and construct an \(\bar x\)- chart. What does the result suggest?
See all solutions

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