When analysing reliability data from a repairable system e.g. a car, a fridge, etc, reliability specialists are interested in the full life history of a system so that they may identify problems that have affected its life and apply solutions, if possible, to other new systems so that these new systems do not suffer from the same problems. The basis of reliability analysis is to understand how systems are failing by modeling their life history so that prediction of the likely future reliability of systems is possible. This is the basis of reliability growth (development) testing where systems under development are tested to find latent design and manufacturing defects so that they can be eliminated from the full‐scale production system.
The simplest way of identifying structure in the system's life history is to plot the data. Three plots are commonly used: plotting failures on a time line; plotting the failure number against cumulative time, and plotting an estimate of the intensity, the rate of occurrence of failures (ROCOF) against cumulative time. These plots appear in Ascher and Feingold [31] and Crowder
et al
. [61] among others. These plots will help to identify structure such as an increase or decrease in the interfailure times of a system over time (more commonly known as reliability growth and reliability decay); evidence of cycles in the data—these may be short or long cycles; periods of high or low reliability (again related to usage); gaps in the time stream (due to change in the reporting mechanism, management, etc) and outliers (possible abnormal operating conditions).
This review lists the intensity functions and their associated expected number of failures, which is the mean value parameter of the nonhomogeneous Poisson process (NHPP). The simplest and best known intensities, those based on mortality rates, those based on hazards of well‐known probability distributions, the software related intensities, and those based on differential equations and extensions are discussed under their appropriate classification headings.
