Reliability distributions are actually designed to fit regions of the bathtub curve shown in Figure 9.1. An overview of key reliability statistics is provided in Special Topics A to aid the reader.
For example, the Weibull distribution is basically a power law over time (see Special Topics A.4.2). If we were to invent a distribution based on wear-out for example, we might use a failure rate λ(t) proportional to time raised to a power >1. For example, wear-out on a particular device may fit a power law with time squared as (Figure 9.2)
This is essentially a Weibull failure rate, although the actual Weibull failure rate is written in a more sophisticated way as (see Special Topics A.4.2):
This is still a power law and, in this case, β would equate to 3. Note α is the characteristic life. Many reliability engineers ...