Statistics for Maintenance Modelling: Repairable Systems

# Fitting a NHPP Model and Estimating Parameters Using Lambda 2(t)¤

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When (t) = 2(t) = , substituting (ti) by 2(ti) in the log-likelihood, ln L = ln (ti) - (t) dt, we have:

ln L = ln () - dt

= n(ln + ln ) + ( - 1) ln ti -

Differentiating the log-likelihood with respect to and and setting the derivatives to zero, we have:

ln L = n-1 - = 0

ln L = n-1 + n ln + ti - ln (t0) = 0

Solving the above equations simultaneously we have the closed form maximum likelihood estimators for and as:

= and = .