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Chapter 18: A. Basic Statistics and Applications 225
to reduce the overall rejection amount, one should first attempt to eliminate or at
least reduce defects due to corrugation, then blistering, then streaks, and so on.
By eliminating these three types of defects, one would change dramatically the
percentage of rejected paper and reduce those losses. It is important to note that if
one can eliminate more than one defect simultaneously then one should consider
eliminating them even though some of them are occurring less frequently. Furthermore,
after one or more defects are either eliminated or reduced, one should
collect data again and reconstruct the Pareto chart to find out if the priority has
changed, if another defect is now occurring more frequently, so that one may
divert the resources to eliminate that defect first. Note that in this example there
may 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 resources
on this category until all other defects are eliminated.
Sometimes all the defects are not equally important. This is true particularly
when some defects are life threatening while other defects are merely a nuisance
or a matter of inconvenience. It is quite common to allocate weights to each defect
and then plot the weighted frequencies versus defects to construct the Pareto
chart. For example, consider the following scenario. Suppose a product has five
types 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 as
shown in Table 18.7.
Note that the Pareto chart using these weighted frequencies in Figure 18.13
presents a completely different picture. That is, by using weighted frequencies the
order of priority of removing the defects is C, A, B, D, and E whereas without using
the weighted frequencies this order would have been E, C, D, B, and A.
Scatter Plot
When studying two variables simultaneously, the data obtained from such a study
is known as bivariate data. In examining bivariate data, the first question to emerge
is whether there is any association between the two variables of interest. One
Part IV.A.4
Table 18.7
Frequencies and weighted frequencies when different
types of defects are not equally important.
Defect type Frequency Weighted frequencies
A 5 50
B 6 45
C 15 75
D 12 24
E 25 12.5