A system with n independent components which works if and only if a least
k of its n components work is called a k-out-of-n system. For exponentially distributed
component lifetimes, we obtain point and interval estimators for the scale parameter
of the component lifetime distribution of a k-out-of-n system when the system failure
time is observed only. In particular, we prove that the maximum likelihood estimator
(MLE) of the scale parameter based on progressively Type-II censored system lifetimes
is unique. Further, we propose a fixed-point iteration procedure to compute the MLE for
k-out-of-n systems data. In addition, we illustrate that the Newton–Raphson method
does not converge for any initial value. Finally, exact confidence intervals for the scale
parameter are constructed based on progressively Type-II censored system lifetimes.

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