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A Pareto diagram is a variation of a histogram forcategorical data resulting from a quality control study.Each category represents a different type of product non-conformity or production problem. The categories areordered so that the one with the largest frequencyappears on the far left, then the category with the secondlargest frequency, and so on. Suppose the following information on nonconformities in circuit packs isobtained: failed component, 126; incorrect component,210; insufficient solder, 67; excess solder, 54; missingcomponent, 131. Construct a Pareto diagram.

Short Answer

Expert verified

The frequenciesof occurrence, according to problem categories are provided which helps in designing the Pareto Chart. These four categories are given in the accompanying table:

Category

Frequency

failed component

126

incorrect component

210

insufficient solder

67

excess solder

54

missingcomponent

131

Step by step solution

01

Given information

The frequenciesof occurrence, according to problem categories are provided which helps in designing the Pareto Chart. These four categories are given in the accompanying table:

Category

Frequency

failed component

126

incorrect component

210

insufficient solder

67

excess solder

54

missingcomponent

131

02

Construct Pareto Chart of Problem Categories.

Following are the steps to construct a dot-plot of cylinder observations:

  1. Order all the problem categories from smallest to largest.
  2. Open Minitab and enter the given data into the worksheet.
  3. Choose Stat and select 鈥淨uality Tools鈥. Under quality tools select 鈥淧areto Chart鈥.
  4. Double click on C1 category to specify it in defects or attribute data. Similarly, Double click on C2 category to specify it in Frequency.
  5. All other values remain same and then click 鈥淥k鈥.

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Most popular questions from this chapter

The accompanying data set consists of observations on shear strength (lb) of ultrasonic spot welds made on a certain type of alclad sheet. Construct a relative frequency histogram based on ten equal-width classes with boundaries 4000, 4200, 鈥. [The histogram will agree with the one in 鈥淐omparison of Properties of Joints Prepared by Ultrasonic Welding and Other Means鈥 (J. of Aircraft, 1983: 552鈥556).] Comment on its features.

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5055

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The following categories for type of physical activityinvolved when an industrial accident occurred appearedin the article 鈥淔inding Occupational Accident Patternsin the Extractive Industry Using a Systematic DataMining Approach鈥 (Reliability Engr. and System

Safety, 2012: 108鈥122):

A. Working with handheld tools

B. Movement

C. Carrying by hand

D. Handling of objects

E. Operating a machine

F. Other

Construct a frequency distribution, including relative frequencies, and histogram for the accompanying data from 100 accidents (the percentages agree with those in the cited article):

A B D AA F C A C B E B A C

F D B C D AA C B E B C E A

B A AA B C C D F D B B A F

C B A C B E E D A B C E A A

F C B D DD B D C A F AA B

D E A E D B C A F A C D D A

A B A F D C A C B F D A E A

C D

Suppose your waiting time for a bus in the morning is uniformly distributed on\((0,8)\), whereas waiting time in the evening is uniformly distributed on\((0,10)\)independent of the morning waiting time.

a. If you take the bus each morning and evening for a week, what is your total expected waiting time?

b. What is the variance of your total waiting time?

c. What are the expected value and variance of the difference between morning and evening waiting times on a given day?

d. What are the expected value and variance of the difference between total morning waiting time and total evening waiting time for a particular week?

Allowable mechanical properties for structural design of metallic aerospace vehicles requires an approved method for statistically analyzing empirical test data. The article 鈥淓stablishing Mechanical Property Allowables for Metals鈥 (J. of Testing and Evaluation, 1998: 293鈥299) used the accompanying data on tensile ultimate strength (ksi) as a basis for addressing the difficulties in developing such a method.

122.2 124.2 124.3 125.6 126.3 126.5 126.5 127.2 127.3

127.5 127.9 128.6 128.8 129.0 129.2 129.4 129.6 130.2

130.4 130.8 131.3 131.4 131.4 131.5 131.6 131.6 131.8

131.8 132.3 132.4 132.4 132.5 132.5 132.5 132.5 132.6

132.7 132.9 133.0 133.1 133.1 133.1 133.1 133.2 133.2

133.2 133.3 133.3 133.5 133.5 133.5 133.8 133.9 134.0

134.0 134.0 134.0 134.1 134.2 134.3 134.4 134.4 134.6

134.7 134.7 134.7 134.8 134.8 134.8 134.9 134.9 135.2

135.2 135.2 135.3 135.3 135.4 135.5 135.5 135.6 135.6

135.7 135.8 135.8 135.8 135.8 135.8 135.9 135.9 135.9

135.9 136.0 136.0 136.1 136.2 136.2 136.3 136.4 136.4

136.6 136.8 136.9 136.9 137.0 137.1 137.2 137.6 137.6

137.8 137.8 137.8 137.9 137.9 138.2 138.2 138.3 138.3

138.4 138.4 138.4 138.5 138.5 138.6 138.7 138.7 139.0

139.1 139.5 139.6 139.8 139.8 140.0 140.0 140.7 140.7

140.9 140.9 141.2 141.4 141.5 141.6 142.9 143.4 143.5

143.6 143.8 143.8 143.9 144.1 144.5 144.5 147.7 147.7

a. Construct a stem-and-leaf display of the data by first deleting (truncating) the tenths digit and then repeating each stem value five times (once for leaves 1 and 2, a second time for leaves 3 and 4, etc.). Why is it relatively easy to identify a representative strength value?

b. Construct a histogram using equal-width classes with the first class having a lower limit of 122 and an upper limit of 124. Then comment on any interesting features of the histogram.

Every corporation has a governing board of directors. The number of individuals on a board varies from one corporation to another. One of the authors of the article 鈥淒oes Optimal Corporate Board Size Exist? An Empirical Analysis鈥 (J. of Applied Finance, 2010: 57鈥69) provided the accompanying data on the number of directors on each board in a random sample of 204 corporations.

No. directors: 4 5 6 7 8 9

Frequency: 3 12 13 25 24 42

No. directors: 10 11 12 13 14 15

Frequency: 23 19 16 11 5 4

No. directors: 16 17 21 24 32

Frequency: 1 3 1 1 1

a. Construct a histogram of the data based on relative frequencies and comment on any interesting features.

b. Construct a frequency distribution in which the last row includes all boards with at least 18 directors. If this distribution had appeared in the cited article, would you be able to draw a histogram? Explain.

c. What proportion of these corporations have at most 10 directors?

d. What proportion of these corporations have more than 15 directors?

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