CHARACTERIZATIONS OF THE RHR AND MIT ORDERINGS AND THE DRHR AND IMIT CLASSES OF LIFE DISTRIBUTIONS

2005 ◽  
Vol 19 (4) ◽  
pp. 447-461 ◽  
Author(s):  
I. A. Ahmad ◽  
M. Kayid
Keyword(s):  
Hazard Rate ◽  
Stochastic Comparison ◽  
Hazard Rate Order ◽  
Reversed Hazard Rate ◽  
Inactivity Time ◽  
Time Order ◽  
Mean Inactivity Time ◽  
Life Distributions ◽  
The Mean ◽  
Decreasing Reversed Hazard Rate

Two well-known orders that have been introduced and studied in reliability theory are defined via stochastic comparison of inactivity time: the reversed hazard rate order and the mean inactivity time order. In this article, some characterization results of those orders are given. We prove that, under suitable conditions, the reversed hazard rate order is equivalent to the mean inactivity time order. We also provide new characterizations of the decreasing reversed hazard rate (increasing mean inactivity time) classes based on variability orderings of the inactivity time of k-out-of-n system given that the time of the (n − k + 1)st failure occurs at or sometimes before time t ≥ 0. Similar conclusions based on the inactivity time of the component that fails first are presented as well. Finally, some useful inequalities and relations for weighted distributions related to reversed hazard rate (mean inactivity time) functions are obtained.

Classification of Distributions Based on Reversed Hazard Rate

2005 ◽  
Vol 56 (1-4) ◽  
pp. 231-250 ◽  
Author(s):  
Nimai Kumar Chandra ◽  
Dilip Roy
Keyword(s):  
Hazard Rate ◽  
Special Role ◽  
Reversed Hazard Rate ◽  
Probability Bound ◽  
Inactivity Time ◽  
Mean Inactivity Time ◽  
Life Distributions ◽  
The Mean

Summary Growing importance of reversed hazard rate (RHR) and inactivity time, as measures of the life distributions, can be noticed from the recent literature on survival and reliability analysis. Keeping in mind tilis special role of RHR and the mean inactivity time, we have made an attempt to define different classes of distributions and study their implicative relationships. A probability bound has also been proposed for the increasing RHR class of distributions.

MONOTONICITY PROPERTIES OF RESIDUAL LIFETIMES OF PARALLEL SYSTEMS AND INACTIVITY TIMES OF SERIES SYSTEMS WITH HETEROGENEOUS COMPONENTS

2011 ◽  
Vol 26 (1) ◽  
pp. 61-75 ◽  
Author(s):  
Weiyong Ding ◽  
Xiaohu Li ◽  
Narayanaswamy Balakrishnan
Keyword(s):  
Hazard Rate ◽  
Parallel Systems ◽  
Stochastic Comparison ◽  
Hazard Rate Order ◽  
Reversed Hazard Rate ◽  
Monotonicity Properties ◽  
Series Systems ◽  
Residual Lifetimes

Here, we discuss the stochastic comparison of residual lifetimes of parallel systems and inactivity times of series systems by means of the reversed hazard rate order when the components of the systems are independent but not necessarily identically distributed. We also establish some monotonicity properties of such residual lifetimes of parallel systems and inactivity times of series systems. These results extend some of the recent results in this direction due to Zhao, Li, and Balakrishnan [21], Kochar and Xu [12], and Saledi and Asadi [16].

Development on the mean inactivity time order with applications

2017 ◽  
Vol 45 (5) ◽  
pp. 525-529 ◽  
Author(s):  
M. Kayid ◽  
S. Izadkhah ◽  
S. Alshami
Keyword(s):  
Inactivity Time ◽  
Time Order ◽  
Mean Inactivity Time ◽  
The Mean

ON THE QUASI-STATIONARY DISTRIBUTION OF SIS MODELS

2016 ◽  
Vol 30 (4) ◽  
pp. 622-639 ◽  
Author(s):  
Gaofeng Da ◽  
Maochao Xu ◽  
Shouhuai Xu
Keyword(s):  
Stationary Distribution ◽  
Upper Bound ◽  
Hazard Rate ◽  
State Of The Art ◽  
Upper Bounds ◽  
Hazard Rate Order ◽  
Reversed Hazard Rate ◽  
Novel Method ◽  
Better Than ◽  
Quasi Stationary Distribution

In this paper, we propose a novel method for constructing upper bounds of the quasi-stationary distribution of SIS processes. Using this method, we obtain an upper bound that is better than the state-of-the-art upper bound. Moreover, we prove that the fixed point map Φ [7] actually preserves the equilibrium reversed hazard rate order under a certain condition. This allows us to further improve the upper bound. Some numerical results are presented to illustrate the results.

scholarly journals On the Convolution of Heterogeneous Bernoulli Random Variables

2011 ◽  
Vol 48 (3) ◽  
pp. 877-884 ◽  
Author(s):  
Maochao Xu ◽  
N. Balakrishnan
Keyword(s):  
Likelihood Ratio ◽  
Hazard Rate ◽  
Random Variables ◽  
Likelihood Ratio Order ◽  
Hazard Rate Order ◽  
Reversed Hazard Rate ◽  
Bernoulli Random Variables

In this paper, some ordering properties of convolutions of heterogeneous Bernoulli random variables are discussed. It is shown that, under some suitable conditions, the likelihood ratio order and the reversed hazard rate order hold between convolutions of two heterogeneous Bernoulli sequences. The results established here extend and strengthen the previous results of Pledger and Proschan (1971) and Boland, Singh and Cukic (2002).

SOME RESULTS ON REVERSED HAZARD RATE

2001 ◽  
Vol 15 (1) ◽  
pp. 95-102 ◽  
Author(s):  
Nimai Kumar Chandra ◽  
Dilip Roy
Keyword(s):  
Reliability Analysis ◽  
Stochastic Modeling ◽  
Hazard Rate ◽  
Reversed Hazard Rate ◽  
Inactivity Time

In view of the growing importance of reversed hazard rate (RHR) in reliability analysis and stochastic modeling, we have considered different implicative relationships with respect to the monotonic behavior of RHR. In that context, a few characterizing properties have also been presented based on expected inactivity time.

On Relative Reversed Hazard Rate Order

2014 ◽  
Vol 44 (2) ◽  
pp. 300-308 ◽  
Author(s):  
Majid Rezaei ◽  
Behzad Gholizadeh ◽  
Salman Izadkhah
Keyword(s):  
Hazard Rate ◽  
Hazard Rate Order ◽  
Reversed Hazard Rate
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