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91影视

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 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.


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: R Chart Let each subgroup consist of the 6 values within a year. Construct an R chart and determine whether the process variation is within statistical control. If it is not, identify which of the three out-of-control criteria lead to rejection of statistically stable variation

Short Answer

Expert verified

The following is the constructed R chart for the given samples:

Since none of the three out-of-control criteria are met, the constructed R chart depicts the process variation within statistical control.

Step by step solution

01

Given information

Data values are given for eightyears on the energy consumed (in kWh) in a two-month period.

The sample size for each of the eightyears is equal to 6.

02

Important lines in R Chart

For constructing the R chart, the values of the central line\(\bar R\), the lower control limit (LCL), and the upper control limit (UCL) need to be determined.

Referring to Exercise 1 CRE, the values are as follows:

\(\begin{aligned}{l}\bar R = 1729\;{\rm{kWh}}\\LCL = 0\;{\rm{kWh}}\\UCL = 3465\;{\rm{kWh}}\end{aligned}\)

03

Construction of R chart

Follow the given steps to construct the R chart:

  • Mark the values 1, 2, ..., 8 on the horizontal axis and label the axis as 鈥淪ample.鈥
  • Mark the values 0, 500, 1000, 鈥., 3500 on the vertical axis and label the axis as 鈥淪ample Range.鈥
  • Plot a straight line corresponding to the value 鈥1729鈥 on the vertical axis and label the line (on the left side) as 鈥淺(\bar R\)=1729.鈥
  • Plot ahorizontal line corresponding to the value 鈥0鈥 on the vertical axis and label the line as 鈥淟CL=0.鈥
  • Similarly, plot a horizontal line corresponding to the value 鈥3465鈥 on the vertical axis and label the line as 鈥淯CL=3465.鈥
  • Mark the following sample ranges on the graph corresponding to the sample number and join the dots using straight lines:

Sample No.

Sample Ranges

1

1345

2

2175

3

1302

4

1020

5

3214

6

1131

7

2342

8

1306

The following R chart is plotted:

04

Analysis of the R chart

The chart does not seem to show any of the three out-of-control criteria.

Thus, it can be concluded that the process variation is within statistical control.

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Most popular questions from this chapter

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

Service Times The Newport Diner records the times (min) it takes before customers are asked for their order. Each day, 50 customers are randomly selected, and the order is considered to be defective if it takes longer than three minutes. The numbers of defective orders are listed below for consecutive days. Construct an appropriate control chart and determine whether the process is within statistical control. If not, identify which criteria lead to rejection of statistical stability.

3 2 3 5 4 6 7 9 8 10 11 9 12 15 17

Listed below are annual sunspot numbers paired with annual high values of the Dow Jones Industrial Average (DJIA). Sunspot numbers are measures of dark spots on the sun, and the DJIA is an index that measures the value of select stocks. The data are from recent and consecutive years. Use a 0.05 significance level to test for a linear correlation between values of the DJIA and sunspot numbers. Is the result surprising?

Sunspot

DJIA

45

10941

31

12464

46

14198

31

13279

50

10580

48

11625

56

12929

38

13589

65

16577

51

18054

What is the difference between random variation and assignable variation?

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?

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