Introduction to Industrial Engineering

By Jane M. Fraser

Chapter 10

Operations research and other mathematical methods

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Consider the following example. You have looked at data on the elapsed time to serve a customer for two clerks and find that Clerk 1 has an average of 189 seconds, while Clerk 2’s average is 211 seconds. Perhaps Clerk 1 is using a better process and Clerk 2 could learn from that process, or perhaps Clerk 2 tends to have customers with more items or more complicated orders. However, before you start thinking about reasons for the difference in averages, you should ask yourself first whether the averages really are different.

This table shows the check out times for Clerk 1 and Clerk 2 for the most recent 25 customers that each served. The first feature we might note about the data is that the times vary quite a bit about the averages.

Clerk 1 | Clerk 2 |
---|---|

176 | 170 |

A boxplot may help us visualize the data better and here is a figure showing the boxplot for each clerk. In a boxplot:

- The bottom line of the box is the first quartile, or 25th percentile; 25% of the data points lie below that value and 75% lie above it.
- The middle line of the box is the second quartile, or 50th percentile, also called the median; 50% of the data points lie below that value and 50% lie above it.
- The top line of the box is the third quartile, or 75th percentile, 75% of the data points lie below that value and 75% lie above it.
- Thus, the box covers 50% of the data.
- The top point is the largest value in the data.
- The bottom point is the smallest value in the data.

Now we can see that while the means are different, the variability within each clerk’s data really overwhelms that difference. You might still want to talk to each to see whether they have ideas for how the clerks can serve customers quickly and you might still want to see if different features of customers affect the check out time (and, if so, whether the process can adapt to those features), but you really don’t need to focus on the difference in averages between the two clerks.

Statistical analysis can be done to check more analytically whether your conclusion of little difference is valid, but often a well designed display of information can help you reach quick conclusions, especially conclusions about where to focus your attention for improvement of a process. Human beings are good at detecting visual patterns. For example, this graph shows data on square footage of a company's retail stores and annual dollar sales in each store. You can quickly detect that there is a generally upward trend, but you can also quickly see that one point doesn’t fit that pattern well at all. Based on this graph, the analyst would want to find out what is different about that store.

You should use well designed visual displays of data. Any visual display of data (a graph, a boxplot, etc.) should also have a short description of the data, the source of the data, and the conclusion you draw from the graph.

Edward R. Tufte, a professor at Yale University, has written a great deal on how to design a good visual display of data - and how to avoid misleading and distracting visual displays. Tufte used this figure (created by Charles Joseph Minard in 1861) of the 1812 campaign of Napoleon’s army to illustrate the use of several dimensions in a graphic.

The movement of the army is shown as a line on a two dimensional map, the
number of men is shown by the width of the line, the progress to and retreat
from Moscow are shown in two patterns, and the temperature (in degrees below
zero) and dates of the retreat are shown on the graph at the bottom. Only a
few moments with this graphic image makes clear the terrible fate of
Napoleon’s army. Tufte says “It may be the best statistical graphic every
drawn” (*The Visual Display of Quantitative Information*, Edward R. Tufte,
page 41).

You won’t create such a stunning image every time, but a carefully designed graphic can often convey your results much more persuasively than words. The first graph on this web page nicely displays world population growth through history. Graphical images can be used to convey understanding, but they can also be used to mislead. The second graph on the same web page is misleading because of the truncated vertical axis. That graph projects the US population in 2050 and uses colors to indicate how much of the population would be Immigrants and Descendants since 1970 (colored red) and Growth from Descendants of 1870 Residents (colored green). By 2050 the size of the immigrant population (red) appears to be over 3 times the size of the 1970 resident population (green), but this impression is incorrect because the vertical axis does not start at 0 but at 203 million. In fact, the total population is about 390 million, the red population is about 132 million and the green population is about 248 million. The red population is less than half the total population. The use of red and green colors is another way the viewer is influenced. This web page discusses another graph with a truncated vertical axis.

Tufte warns against the use of what he calls “chartjunk, ” that is,
ornamentation that attracts and diverts attention but does not add to
understanding (*Envisioning Information*, Edward R. Tufte, page 33). He warns
against the use of distracting patterns (see
this
example), three dimensional displays (see
this example),
and overly busy grids (see
this example).
Displaying
areas can distort the viewer’s perception of one-dimensional data (see
the first graph, with cows, on
this page).
While this
article was written to show teh capabilities of a graphing package, it
has some very bad graphs.
Tufte argues: “Cosmetic decoration, which frequently distorts the
data, will never salvage an underlying lack of content” (page 34).

On the positive side, this web page has a collection of nice graphs on disease rates over time. Stephen Few shows some poor graphs and then the improved versions.

One of the most important types of graphs for an IE is a graph with time on the horizontal axis. Such a graph allows tracking and monitoring data such as the number of units produced each shift or the number of defects by type each week. The IE can quickly detect problems. For example, the figure below shows ... [use data that I’ll use for QC chart in section 10.5]