Predictions for Progressively Type-II Censored Failure Times from the Half Triangle Distribution

Abstract

This paper deals with the problem of predicting censored data in a half triangle distribution with an unknown parameter based on progressively Type-II censored samples. We derive maximum likelihood predictors and some approximate maximum likelihood predictors of censored failure times in a progressively Type-II censoring scheme. In addition, we construct the shortest-length predictive intervals for censored failure times. Finally, Monte Carlo simulations are used to assess the validity of the proposed methods.

Type-II stepwise progressive censoring

“…Moreover, assume that at the first failure time (y 1 ), s 1 surviving experimental units are removed and at the second failure time For more detail about Type-II progressive censoring readers can refer to Balakrishnan and Aggarwala (2000), Balakrishnan (2007), , Balakrishnan et al (2008, Burkschat (2008), Burkschat et al (2006), Cohen (1963), Cramer (2014), Cramer and Kamps (2001), Herd (1956). Some valuable results can also be found in Ghitany et al (2013Ghitany et al ( , 2014, Kang and Seo (2011), Krishna and Kumar (2013), Pakyari and Balakrishnan (2013), Rezapour et al (2013aRezapour et al ( , 2013b, Seo and Kang (2014). Cramer and Iliopoulos (2009) proposed an adaptive Type-II progressive censoring such that the number of removals has been involved in previous failure times and the number of previous censored items.…”