Exponential Distribution

This is probably the most important distribution in reliability work and is used almost exclusively for reliability prediction of electronic equipment. It describes the situation wherein the hazard rate is constant which can be shown to be generated by a Poisson process. This distribution is valuable if properly used. It has the advantages of:

  1. single, easily estimated parameter (λ)
  2. mathematically very tractable
  3. fairly wide applicability
  4. is additive  that is, the sum of a number of independent exponentially distributed variables is exponentially distributed.

Some particular applications of this model include:

  1. items whose failure rate does not change significantly with age.
  2. complex and repairable equipment without excessive amounts of redundancy.
  3. equipment for which the early failures or “infant mortalities” have been eliminated by “burning in” the equipment for some reasonable time period.

The failure density function is

for t > 0, where λ is the hazard (failure) rate, and the reliability function is

the mean life (θ) = 1/λ, and, for repairable equipment the MTBF = θ = 1/λ .

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