This log-likelihood function is composed of three summation portions:

or

(7)

where:

*Fe*is the number of groups of times-to-failure data points*Ni*is the number of times-to-failure in the*i*th time-to-failure data group*μ*is the Gumbel shape parameter (unknown a priori, the first of two parameters to be found)*σ*is the Gumbel scale parameter (unknown a priori, the second of two parameters to be found)*Ti*is the time of the*i*th group of time-to-failure data*S*is the number of groups of suspension data pointsis the number of suspensions in

*i*th group of suspension data pointsis the time of the

*i*th suspension data group*FI*is the number of interval failure data groupsis the number of intervals in

*i*th group of data intervalsis the beginning of the

*i*th interval- and is the ending of the
*i*th interval

For the purposes of MLE, left censored data will be considered to be intervals with

The solution of the maximum log-likelihood function is found by solving for (, ) so that:

See
Also:

Appendix C: Distribution Log-Likelihood Equations

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