Law for Estimation ◾ 245
e triangular SLA compliance model is far superior to a plausible Gaussian
model. Typically, the Gaussian tail would exceed 100%, distort calculations, and
force us to take countermeasures such as a messy truncation. e triangular PDF is
compact and does not outstep empirical experience.
Other Statistics
e mode is obviously the peak, and hence, the following relationship is true:
Mode = c
Dispersion is strongly indicated by the base width, b − a. However, a proper
calculation of variance is according to the following equation:
Variance = (a
2
+ b
2
+ c
2
– ab – ac – bc)/18 (15.6)
An example is as follows:
Given
a = 0,
b = 10,
c = 5 (for a symmetrical triangular model),
We get
Variance = 4.17,
Standard deviation = 2.0412.
It may be noted that as c changes, the variance slightly changes.
Skew
Although the process boundaries constitute a firm base, the apex c can be moved
from the left extreme to the right extreme, as shown in the three examples in
Figure 15.5.
e first example has its peak at the lower limit and gives a triangle skewed to
the right. e second example has its peak in the middle position between the lim-
its, providing symmetry. e peak in the third example coincides with the upper
limit, giving a negative skew. ese three peaks demonstrate how the triangular
PDF can be made to be symmetrical or skewed. e peak can take an infinite
number of positions within these extremes.