When units experience some use of unknown duration for some time, one may use three-parameter…

When units experience some use of unknown duration for
some time, one may use three-parameter Weibull distribution to express its
failure time. The parameters are: the location parameter ν, the scale
parameter η, and the shape parameter β. Its reliability function is

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with β, v, η > 0 and t ≥ 0. Note that
when ν = 1 the model becomes the well-known two-parameter Weibull
distribution.

(a) What is the hazard-rate function of the
three-parameter distribution?

(b) Show the conditions of the hazard-rate function when

(i) v ≥ 1 and β ≥ 1

(ii) v ≤ 1 and β ≤ 1

(iii) β > 1

(iv) β

 

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