Point and Interval Estimation for the Lifetime Distribution of a k-Unit Parallel System Based on Progressively Type-II Censored Data

This work considers point and interval estimation for the lifetime distribution of a k-unit parallel system assuming exponential distribution for the components lifetime. The parameter of the distribution is estimated by the maximum likelihood method based on samples which are progressively Type-II censored. The expression for Fisher's information is derived. Approximate confidence intervals are constructed based on the asymptotic distribution of the maximum likelihood estimator and log-transformed maximum likelihood estimator. The confidence levels of the approximate confidence intervals are examined via simulation. They turn out to be quite satisfactory. An approximate β-expectation tolerance interval for the life distribution is also discussed.