Point and Interval Estimation for a Simple Step-Stress Model with Type-II Censoring

Conditional independence of blocked ordered data

“…This block independence was a key property in the development of exact conditional inferential procedures based on different forms of censored data [see Childs et al (2003), , and Balakrishnan, Han and Iliopoulos (2008)] and also for the step-stress tests [see Balakrishnan et al (2007) and Balakrishnan, Xie and Kundu (2008)]. This conditional independence result has also been implicitly present in some other results such as recurrence relations for order statistics such as those discussed by Govindarajulu (1963) and Balakrishnan, Govindarajulu and Balasubramanian (1993).…”

Minimal repair under a step-stress test

“…For details on step-stress models, we refer to Nelson (1990), Gouno and Balakrishnan (2001), Bagdonavicius and Nikulin (2002), Gouno (2006), Balakrishnan et al (2007) and Balakrishnan (2009). We consider here the simple step-stress setup which means that there is only one change in the stress levels; however, the results can be generalized to the case of multiple stress levels as well.…”

Statistical analysis of exponential lifetimes under an adaptive Type‐II progressive censoring scheme

“…To construct exact confidence intervals of λ, we need the assumption, similar to [5], that the probability Pr(λ ≥ w|J = j) is an increasing function of λ. This assumption guarantees the invertibility of the pivotal quantities and allow us to construct exact confidence intervals of λ based on the exact distribution ofλ.…”