Statistics for Maintenance Modelling: Repairable Systems

# Estimating the Maximum Likelihood Parameters from Lambda 1(t)¤

Differentiating the log-likelihood with respect to 0 and 1 and setting the derivatives to zero:

ln L = n - = 0

ln L = ti - = 0

After some algebra, 0 may be expressed explicitly in terms of 1, that is:

= and finally we have:

ti + n1-1 nt0(1 - )-1 = 0

From this equation we can find 1 and therefore 0 = ln (n 1( - 1)-1). The programme involved in solving this equation is modest. A simple interactive search or repeated bisection will suffice.