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Chapter 14: Q4CQQ (page 654)

What is the difference between an R chart and an\(\bar x\) chart?

Short Answer

Expert verified

The key difference between an\(\bar x\) chart and an R chart is that the \(\bar x\) chart is used to monitor the change in the average value of the variable over time. In contrast, the R chart monitors the change in the range/variability of the variable over time.

Step by step solution

01

Given information

An R chart and \(\bar x\) chart are plotted to identify whether a process is under statistical control or not.

02

Step 2:Difference between R chart and \(\bar x\) chart

An R chart is a plot that shows the sample ranges of all the samples varied over time.

It is plotted when the individual sample size is less than 10.

It examines the variation present in the process.

An\(\bar x\)chart is a plot that shows the sample means varied over time.

It examines the central value of the process.

The main difference between the two types of control charts is that the\(\bar x\)chart is used to assess the process mean,whereas the R chart isused to assess process variability.

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Most popular questions from this chapter

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

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

Smartphone Batteries TheSmartBatt company manufactures batteries for smartphones. Listed below are numbers of defects in batches of 200 batteries randomly selected in each of 12 consecutive days of production. What action should be taken?

5 7 4 6 3 10 10 13 4 15 4 19

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

Car Batteries Defective car batteries are a nuisance because they can strand and inconvenience drivers, and drivers could be put in danger. A car battery is considered to be defective if it fails before its warranty expires. Defects are identified when the batteries are returned under the warranty program. The Powerco Battery corporation manufactures car batteries in batches of 250, and the numbers of defects are listed below for each of 12 consecutive batches. Does the manufacturing process require correction?

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

Sunspots and the DJIA Use the data from Exercise 5 and find the equation of the regression line. Then find the best predicted value of the DJIA in the year 2004, when the sunspot number was 61. How does the result compare to the actual DJIA value of 10,855?

Energy Consumption. Exercises 1–5 refer to the amounts of energy consumed in the author’s 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 atwww.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: 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

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