A Note on Some Functional Relationships Involving the Mean Inactivity Time Order

2009 ◽  
Vol 58 (1) ◽  
pp. 172-178 ◽  
Author(s):  
E.-M. Ortega
Keyword(s):  
Functional Relationships ◽  
Inactivity Time ◽  
Time Order ◽  
Mean Inactivity Time ◽  
The Mean

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.

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

Testing Behavior of the Mean Inactivity Time

2018 ◽  
Vol 46 (6) ◽  
pp. 20160611
Author(s):  
M. Kayid ◽  
S. Izadkhah
Keyword(s):  
Inactivity Time ◽  
Mean Inactivity Time ◽  
The Mean

scholarly journals Increasing Mean Inactivity Time Ordering: A Quantile Approach

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
M. Kayid ◽  
S. Izadkhah ◽  
A. Alfifi
Keyword(s):  
Stochastic Order ◽  
Sufficient Conditions ◽  
Parallel Systems ◽  
The Other ◽  
Stochastic Orders ◽  
General Family ◽  
Order Relations ◽  
Inactivity Time ◽  
Time Order ◽  
Mean Inactivity Time

We study further the quantile mean inactivity time order. Relations between the proposed stochastic order and the other transform stochastic orders are obtained. Besides, sufficient conditions for the stochastic order are provided. Then, preservation of the order under monotone transformations, series, and parallel systems and mixtures of a general family of semiparametric distributions is studied. Examples are also given to illustrate the results.

scholarly journals A New Lifetime Distribution: Properties, Copulas, Applications, and Different Classical Estimation Methods

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-18
Author(s):  
Naif Alotaibi
Keyword(s):  
Least Square ◽  
Estimation Methods ◽  
Mean Deviation ◽  
Mean Residual Life ◽  
Least Square Estimation ◽  
New Model ◽  
Inactivity Time ◽  
Mean Inactivity Time ◽  
The Mean ◽  
Anderson Darling

A new continuous version of the inverse flexible Weibull model is proposed and studied. Some of its properties such as quantile function, moments and generating functions, incomplete moments, mean deviation, Lorenz and Bonferroni curves, the mean residual life function, the mean inactivity time, and the strong mean inactivity time are derived. The failure rate of the new model can be “increasing-constant,” “bathtub-constant,” “bathtub,” “constant,” “J-HRF,” “upside down bathtub,” “increasing,” “upside down-increasing-constant,” and “upside down.” Different copulas are used for deriving many bivariate and multivariate type extensions. Different non-Bayesian well-known estimation methods under uncensored scheme are considered and discussed such as the maximum likelihood estimation, Anderson Darling estimation, ordinary least square estimation, Cramér-von-Mises estimation, weighted least square estimation, and right tail Anderson Darling estimation methods. Simulation studies are performed for comparing these estimation methods. Finally, two real datasets are analyzed to illustrate the importance of the new model.

FURTHER RESULTS INVOLVING THE MIT ORDER AND THE IMIT CLASS

2005 ◽  
Vol 19 (3) ◽  
pp. 377-395 ◽  
Author(s):  
I. A. Ahmad ◽  
M. Kayid ◽  
F. Pellerey
Keyword(s):  
Reliability Theory ◽  
Convex Order ◽  
Lifetime Distributions ◽  
Increasing Convex Order ◽  
Shock Models ◽  
Inactivity Time ◽  
Mean Inactivity Time ◽  
Time Class ◽  
Right Spread Order ◽  
The Mean

The purpose of this article is to study several preservation properties of the mean inactivity time order under the reliability operations of convolution, mixture, and shock models. In that context, the increasing mean inactivity time class of lifetime distributions is characterized by means of right spread order and increasing convex order. Some applications in reliability theory are described. Finally, a new test of such a class is discussed.

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