Likelihood inference for the component lifetime distribution based on progressively censored parallel systems data

ABSTRACT

Point and interval estimators for the scale parameter of the component lifetime distribution of a k-component parallel system are obtained when the component lifetimes are assumed to be independently and identically exponentially distributed. We prove that the maximum likelihood estimator of the scale parameter based on progressively Type-II censored system lifetimes is unique and can be obtained by a fixed-point iteration procedure. In particular, we illustrate that the Newton–Raphson method does not converge for any initial value. Furthermore, exact confidence intervals are constructed by a transformation using normalized spacings and other component lifetime distributions including Weibull distribution are discussed.

KEYWORDS:

• Progressive Type-II censoring
• MLE
• fixed-point iteration
• exact confidence intervals
• exponential distribution
• Weibull distribution
• parallel system

Acknowledgments

We are grateful to two anonymous reviewers and an associate editor for suggestions which led to an improved version of the manuscript.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCiD

E. Cramer http://orcid.org/0000-0001-8354-5425