Page 289 - Six Sigma Demystified

Part 3 s i x s i g m a to o l s 269

Interpretation

This method will let you see where you can afford delays. On the critical path,
any delay will result in a change in the process/project completion time. Ac-
tivities not on the critical path have slack time. In Figure F.15, the Begin Layout
Editing task has a slack time of 4 days. This implies that the task does not need
to begin as soon as possible (day 1, its earliest start time) but must begin by day
4 (its latest start time).
There is, by definition, no slack time on the critical path. That is, all tasks on
the critical path must be completed as soon as possible (i.e., each task’s earliest
start time) or the project will be delayed.
Program evaluation and review techniques (PERT) analysis, discussed below,
allows probabilistic estimates to be applied to a task’s duration.

goodness-of-Fit Tests

Popular goodness-of-fit tests include the chi-square, Kolmogorov-Smirnov
(K-S), and Anderson-Darling tests. They are often reported with probability
plots provided as a graphic aid.

When to Use

Measure to Control Stages

• To verify an assumed distribution to ensure validity of statistical tests, in-
cluding confidence tests, hypothesis tests, and statistical control charts
While the chi-square test is perhaps the most frequently referenced goodness-

of-fit technique in general-application statistical textbooks, its popularity in aca-
demic circles indeed may be due to its simplicity: Authors can easily describe and
demonstrate the test without the need for computer software. In practice, how-
ever, data are analyzed almost exclusively using computer software, allowing the
use of more sophisticated techniques that are better suited for most applications,
particularly in testing continuous distributions. Two of these techniques are the
Kolmogorov-Smirnov (K-S) test and the Anderson-Darling test. Both these tech-
niques may be used to compare the fit of assumed distributions to sample data.
For the most part, probability plots offer only visual confirmation of goodness
of fit of the data to the assumed distribution. A common method to interpret
the probability plots predates computerization of the technique. In days past,
one simply would lay a fat pencil on the graph, and if the data were obscured