Exact
inference for progressively
type-I
censored exponential failure data
N. Balakrishnan, D.Han and G. Iliopoulos
For
reasons of time constraint and cost reduction, censoring is commonly employed
in practice, especially in reliability engineering. Among various censoring
schemes, progressive type-I right censoring provides not only the practical
advantage of known termination time but also greater flexibility to the
experimenter in the design stage by allowing for the removal of test units at
non-terminal time points. In this article, we consider a progressively type-I
censored life-test under the assumption that the lifetime of each test unit is
exponentially distributed. For small to moderate sample sizes, a practical
modification is proposed to the censoring scheme in order to guarantee a
feasible life-test under progressive type-I censoring. Under this setup, we
obtain the maximum likelihood estimator (MLE) of the unknown mean parameter and
derive the exact sampling distribution of the MLE under the condition that its
existence is ensured. Using the exact distribution of the MLE as well as its
asymptotic distribution and the parametric bootstrap method, we then discuss
the construction of confidence intervals for the mean parameter and their
performance is assessed through Monte Carlo simulations. Finally, an example is
presented in order to illustrate all the methods of inference discussed here.
Key words and phrases: Conditional
inference; exponential distribution; maximum likelihood estimation; progressive
type-I censoring; stochastic monotonicity