Abstract
In this paper, we present some sharp upper bounds on the deviations of the mean residual lifetime of progressive type II right censored order statistics from the mean residual lifetime, m(t)=E(X t )=E(X−t|X>t), for arbitrary t>0. We also describe the distributional forms for which the bounds are attained. The obtained bounds are numerically evaluated and compared with other classical rough ones. AMS subject classifications 62G30, 62E15
Highlights
The scheme of progressive type II censored sampling is an important scheme in lifetesting experiments
Suppose N units are randomly placed on a life test; at the first failure time of one of the units, a number of R1 surviving units is randomly withdrawn from the test; at the second failure time, R2 surviving units are selected at random and taken out of the experiment, and so on; at the time of the nth failure, the remaining Rn = N − R1 − . . . − Rn−1 − n objects are removed
4 Concluding remarks In this paper, we have developed the maximized evaluations of the MRL function of progressively type II right censored order statistics (PCOSs) of order statistics, measured in location and scale units of the residual life random variable Xt = (X − t|X > t) and expressed in terms of percentile points t = F−1(p), 0 < p < 1
Summary
The scheme of progressive type II censored sampling is an important scheme in lifetesting experiments. Hashemi et al (2010) have studied some properties of the residual lifetime of progressively type II right censored order statistics (PCOSs). 2 Bounds for MRL of PCOSs Let X1, · · · , Xn be the iid random variables (r.v.’s) with cdf F, pdf f , and finite first and second moments.
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