## Common-Mode Failure ------------------- Common mode failure refers to events that are not statistically independent. Failures in multiple parts of a system may be caused by a single fault, particularly random failures due to environmental conditions or aging. An example is an electronic system wherein a fault in a power supply stops supplying power to a whole line, causing failures in multiple subsystems hooked to that line. This is particularly important in safety-critical systems using multiple redundant channels. If the probability of failure in one subsystem is $p$, then it would be expected that an $N$ channel system would have a probability of failure of $p^{N}$. However, in practice, the probability of failure is much higher because they are not statistically independent; for example, external factors such as ionizing radiation or electromagnetic interference (EMI) may affect all the channels equally. The principle of redundancy states that, when events of failure of a component are statistically independent, the probabilities of their joint occurrence multiply. Thus, for instance, if the probability of failure of a component of a system is one in one thousand per year, the probability of the joint failure of two of them is one in one million per year, provided that the two events are statistically independent. This principle favors the strategy of the redundancy of components, which we discuss when we talk about [[Fault-Tolerant Design Techniques|fault-tolerant design techniques]].