Some statistical distributions

  • A. D. S. Carter


A number of statistical distributions are used time and time again in reliability work, and need to be discussed particularly from that point of view before examining field evidence. Perhaps the one used most extensively is the negative exponential distribution. We have already seen in section 4.4 how it can represent the variation of reliability with time for infinitely rough loading. In addition any period of constant failure rate can be represented by this distribution. We shall therefore follow our brief study of the ubiquitous normal distribution with the negative exponential. However, it can be limited in application, particularly for mechanical products. Many real distributions do not quite correspond to the negative exponential, and significant errors could arise by forcing them into this mould. We therefore need something more flexible. The Weibull distribution fills this requirement rather well, better indeed than might be hoped for, because additionally it can be made to approximate very closely to the normal distribution. It is again very valuable for the same reason quoted in the case of the negative exponential distribution: many real distributions which bear superficial resemblance to the normal distribution are in fact sufficiently different as to exclude its use. Since it can ‘stand in’ for both the negative exponential and the normal distributions besides representing many other real ones, the Weibull distribution is very popular with reliability workers. It has a number of drawbacks as we shall see, but clearly merits close attention, and hence we shall follow our study of the negative exponential distribution by a study of the Weibull distribution.


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© A. D. S. Carter 1986

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  • A. D. S. Carter

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