ABSTRACT
The initial presentation in this chapter on normal distributions will focus on failure rate, but can be simply applied to all other applications involving normal distributions. When T, time to failure, has a normal distribution with mean μ and variance σ, its probability distribution function (pdf) is given by
f t t t( ) = - -æ è ç
ö ø ÷
é
ë ê ê
ù
û ú ú
- ¥ < < ¥1 2
1 2
ps m
s exp ; (9.1)
The graph of f(t) is the familiar bell-shaped curve shown in Figure 9.1.1,2
There are two points at which the curve in Figure 9.1 changes shape in the normal curve. The curve changes at the first point, from being concave with respect to the horizontal axis, to being convex at the first point. At the second point, it again changes to concavity. These are known as points of inflection. Interestingly, the points of inflection are located at an interval σ from the mean, that is, at x ± s, or 68% of the area under the curve symmetrically displaced from the mean.
