Logarithmic distributions in reliability analysis

Abstract

Real-life systems are complex, with many independent parameters which can affect the system. Their behaviour can therefore be very variable. This is especially true of the more involved processes which occur in reliability and degradation processes. However, there are some characteristics which are observed which can be understood simply because they are characteristic of complex systems. These include distributions that are very often logarithmic rather than uniform, log–normal failure distributions and 1/ f noise. A wide variety of diverse examples is given to illustrate the common occurrence of such observations together with the underlying unifying themes. There are several basic reasons for the origin of logarithmic distributions. One is that they arise from multiplicative processes. Another is that although basic science is often introduced as linear, with non-linear effects added as a correction, complex systems are often inherently non-linear. This produces multiplicative effects, such as harmonic generation and fractal behaviour.