The simplest way to describe a component’s reliability is in terms of its failure rate. The failure of a component can be decreasing, constant, or increasing with time. If the failure rate is constant, then the reliability of the component is described by the exponential distribution. The only parameter required for the exponential distribution is the failure rate (λ) or MTBF (1 / λ). The units for the failure rate multiplier is specified under General in the System file properties. For more information, see General System File Properties

The exponential distribution can be viewed as a special case of the Weibull distribution, where the shape factor (β) is known to equal 1 (WeiBayes Beta=1). When the failure rate for a component is constant, then its reliability is best described by the Weibull or exponential distribution. A constant failure rate leads to the memoryless property, which states that the remaining life of a used component is independent of its current age, thereby declaring that a used component as good as a new component. (The Weibull distribution is memoryless only when the value equals 1.) Because the exponential distribution assumes that there is no infant mortality or wear-out period, the field data must be carefully tested to ensure that such assumptions are valid. For the exponential distribution, the MTTF is the reciprocal of the failure rate.

Calculations

The probability density function, f(t), and the survival function, that is reliability, R(t) = 1 − F(t), with respect to time t, follows for computing exponential distributions. The exponential distribution is a special instance of the Weibull distribution with β = 1 and η = 1 /λ = MTTF. The equation for computing exponential distributions is:

Where:

t ≥ 0 and η > .1.

In this case, λ is the constant occurrence (failure rate) parameter of the distribution.