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224 Part IV: Quality AssuranceContinued141210Frequency86420ABCDefect typeDEFigure 18.11 Bar graph for the data in Example 18.21.Types of DefectsPart IV.A.4Frequency7060504030201010080604020Percent0 0Types of defects Corrugation Blistering Streaks Pin holes Dirt OthersFrequency 28 11 10 9 7 5Percent 40.0 15.7 14.3 12.9 10.0 7.1Cumulative % 40.0 55.7 70.0 82.9 92.9 100.0Figure 18.12 Pareto chart for the data in Example 19.1.the use of his/her resources to eliminate first those defects that affect the qualityof the product most. For instance, the Pareto diagram in Figure 18.12 indicatesthat 40 percent of the paper rolls rejected are because of the corrugation problem.Corrugation and blistering together are responsible for 55.7 percent of the rejectedpaper. Corrugation, blistering, and streaks are responsible for 70 percent. Thus,

Chapter 18: A. Basic Statistics and Applications 225to reduce the overall rejection amount, one should first attempt to eliminate or atleast reduce defects due to corrugation, then blistering, then streaks, and so on.By eliminating these three types of defects, one would change dramatically thepercentage of rejected paper and reduce those losses. It is important to note that ifone can eliminate more than one defect simultaneously then one should considereliminating them even though some of them are occurring less frequently. Furthermore,after one or more defects are either eliminated or reduced, one shouldcollect data again and reconstruct the Pareto chart to find out if the priority haschanged, if another defect is now occurring more frequently, so that one maydivert the resources to eliminate that defect first. Note that in this example theremay be several defects that are included under the category others, such as porosity,grainy edges, wrinkles, or brightness, that are not occurring very frequently.Thus, if one has very limited resources then one should not use his/her resourceson this category until all other defects are eliminated.Sometimes all the defects are not equally important. This is true particularlywhen some defects are life threatening while other defects are merely a nuisanceor a matter of inconvenience. It is quite common to allocate weights to each defectand then plot the weighted frequencies versus defects to construct the Paretochart. For example, consider the following scenario. Suppose a product has fivetypes of defects, which are denoted by A, B, C, D, and E, where A is life threatening,B is not life threatening but very serious, C is serious, D is somewhat serious,and E is not serious or merely a nuisance. Suppose we assign a weight of 10 to A,7.5 to B, 5 to C, 2 to D, and 0.5 to E. The data collected over a period of study is asshown in Table 18.7.Note that the Pareto chart using these weighted frequencies in Figure 18.13presents a completely different picture. That is, by using weighted frequencies theorder of priority of removing the defects is C, A, B, D, and E whereas without usingthe weighted frequencies this order would have been E, C, D, B, and A.Scatter PlotWhen studying two variables simultaneously, the data obtained from such a studyis known as bivariate data. In examining bivariate data, the first question to emergeis whether there is any association between the two variables of interest. OnePart IV.A.4Table 18.7Frequencies and weighted frequencies when differenttypes of defects are not equally important.Defect type Frequency Weighted frequenciesA 5 50B 6 45C 15 75D 12 24E 25 12.5

224 Part IV: Quality Assurance

Continued

14

12

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Frequency

8

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2

0

A

B

C

Defect type

D

E

Figure 18.11 Bar graph for the data in Example 18.21.

Types of Defects

Part IV.A.4

Frequency

70

60

50

40

30

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10

100

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Percent

0 0

Types of defects Corrugation Blistering Streaks Pin holes Dirt Others

Frequency 28 11 10 9 7 5

Percent 40.0 15.7 14.3 12.9 10.0 7.1

Cumulative % 40.0 55.7 70.0 82.9 92.9 100.0

Figure 18.12 Pareto chart for the data in Example 19.1.

the use of his/her resources to eliminate first those defects that affect the quality

of the product most. For instance, the Pareto diagram in Figure 18.12 indicates

that 40 percent of the paper rolls rejected are because of the corrugation problem.

Corrugation and blistering together are responsible for 55.7 percent of the rejected

paper. Corrugation, blistering, and streaks are responsible for 70 percent. Thus,

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