Type-I censored sequential k-out-of-n systems

Type-I censored sequential order statistics are introduced and their distribution is examined. In the case of underlying exponential distributions, the conditional joint and marginal distributions of the normalized spacings given the number of observed failure times are obtained. Furthermore, the conditional distribution of the maximum likelihood estimator of a scale parameter based on a Type-I censored sample of sequential order statistics from exponential distributions is derived. A monotonicity property and limits of the survival function of this estimator with respect to the scale parameter are shown. These properties are important for the construction of an exact confidence interval for the scale parameter.