scholarly journals Hazard Rate Properties of a General Counting Process Stopped at an Independent Random Time

2011 ◽  
Vol 48 (1) ◽  
pp. 56-67 ◽  
Author(s):  
F. G. Badia
Keyword(s):  
Failure Rate ◽  
Hazard Rate ◽  
Counting Process ◽  
Sufficient Conditions ◽  
Random Time ◽  
Renewal Processes ◽  
Increasing Failure Rate ◽  
Reversed Hazard Rate ◽  
Decreasing Reversed Hazard Rate

In this work we provide sufficient conditions under which a general counting process stopped at a random time independent from the process belongs to the reliability decreasing reversed hazard rate (DRHR) or increasing failure rate (IFR) class. We also give some applications of these results in generalized renewal and trend renewal processes stopped at a random time.

scholarly journals Hazard Rate Properties of a General Counting Process Stopped at an Independent Random Time

2011 ◽  
Vol 48 (01) ◽  
pp. 56-67 ◽  
Author(s):  
F. G. Badia
Keyword(s):  
Failure Rate ◽  
Hazard Rate ◽  
Counting Process ◽  
Sufficient Conditions ◽  
Random Time ◽  
Renewal Processes ◽  
Increasing Failure Rate ◽  
Reversed Hazard Rate ◽  
Decreasing Reversed Hazard Rate

In this work we provide sufficient conditions under which a general counting process stopped at a random time independent from the process belongs to the reliability decreasing reversed hazard rate (DRHR) or increasing failure rate (IFR) class. We also give some applications of these results in generalized renewal and trend renewal processes stopped at a random time.

scholarly journals On increasing-failure-rate random variables

2005 ◽  
Vol 42 (03) ◽  
pp. 797-809 ◽  
Author(s):  
Sheldon M. Ross ◽  
J. George Shanthikumar ◽  
Zegang Zhu
Keyword(s):  
Markov Chain ◽  
Failure Rate ◽  
Renewal Process ◽  
Counting Process ◽  
Random Number ◽  
Sufficient Conditions ◽  
Random Variables ◽  
Random Variable ◽  
Increasing Failure Rate ◽  
Random Threshold

We provide sufficient conditions for the following types of random variable to have the increasing-failure-rate (IFR) property: sums of a random number of random variables; the time at which a Markov chain crosses a random threshold; the time until a random number of events have occurred in an inhomogeneous Poisson process; and the number of events of a renewal process, and of a general counting process, that have occurred by a randomly distributed time.

scholarly journals On increasing-failure-rate random variables

2005 ◽  
Vol 42 (3) ◽  
pp. 797-809 ◽  
Author(s):  
Sheldon M. Ross ◽  
J. George Shanthikumar ◽  
Zegang Zhu
Keyword(s):  
Markov Chain ◽  
Failure Rate ◽  
Renewal Process ◽  
Counting Process ◽  
Random Number ◽  
Sufficient Conditions ◽  
Random Variables ◽  
Random Variable ◽  
Increasing Failure Rate ◽  
Random Threshold

We provide sufficient conditions for the following types of random variable to have the increasing-failure-rate (IFR) property: sums of a random number of random variables; the time at which a Markov chain crosses a random threshold; the time until a random number of events have occurred in an inhomogeneous Poisson process; and the number of events of a renewal process, and of a general counting process, that have occurred by a randomly distributed time.

Failure distributions of shock models

1980 ◽  
Vol 17 (03) ◽  
pp. 745-752 ◽  
Author(s):  
Gary Gottlieb
Keyword(s):  
Failure Rate ◽  
Sufficient Conditions ◽  
Cumulative Damage ◽  
Shock Model ◽  
Life Distribution ◽  
Increasing Failure Rate ◽  
Shock Models ◽  
Damage Process

A single device shock model is studied. The device is subject to some damage process. Under the assumption that as the cumulative damage increases, the probability that any additional damage will cause failure increases, we find sufficient conditions on the shocking process so that the life distribution will be increasing failure rate.

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.

COMPARISONS OF SAMPLE RANGES ARISING FROM MULTIPLE-OUTLIER MODELS: IN MEMORY OF MOSHE SHAKED

2017 ◽  
Vol 33 (1) ◽  
pp. 28-49
Author(s):  
Narayanaswamy Balakrishnan ◽  
Jianbin Chen ◽  
Yiying Zhang ◽  
Peng Zhao
Keyword(s):  
Hazard Rate ◽  
Stochastic Order ◽  
Sufficient Conditions ◽  
Hazard Rates ◽  
Proportional Hazard ◽  
Stochastic Comparisons ◽  
Hazard Rate Order ◽  
Numerical Examples ◽  
Reversed Hazard Rate ◽  
Usual Stochastic Order

In this paper, we discuss the ordering properties of sample ranges arising from multiple-outlier exponential and proportional hazard rate (PHR) models. The purpose of this paper is twofold. First, sufficient conditions on the parameter vectors are provided for the reversed hazard rate order and the usual stochastic order between the sample ranges arising from multiple-outlier exponential models with common sample size. Next, stochastic comparisons are separately carried out for sample ranges arising from multiple-outlier exponential and PHR models with different sample sizes as well as different hazard rates. Some numerical examples are also presented to illustrate the results established here.

On the Closure of Aging Classes Under the Formation of Coherent Structures

2021 ◽  
pp. 2140002
Author(s):  
Ioannis S. Triantafyllou
Keyword(s):  
Failure Rate ◽  
Coherent Structures ◽  
Sufficient Conditions ◽  
Failure Criteria ◽  
Closure Property ◽  
Coherent Systems ◽  
Increasing Failure Rate ◽  
Independent And Identically Distributed

In this paper, we study the closure property of the Increasing Failure Rate (IFR) class under the formation of coherent systems. Sufficient conditions for the nonpreservation of the IFR attribute for reliability structures consisting of [Formula: see text] independent and identically distributed ([Formula: see text] components are provided. More precisely, we deal with the IFR preservation (or nonpreservation) under the formation of structures with two common failure criteria by the aid of their signature vectors.

scholarly journals The DFR Property for Counting Processes Stopped at an Independent Random Time

2015 ◽  
Vol 52 (02) ◽  
pp. 574-585 ◽  
Author(s):  
F. G. Badía ◽  
C. Sangüesa
Keyword(s):  
Failure Rate ◽  
Sufficient Conditions ◽  
Random Time ◽  
Queueing Models ◽  
Counting Processes ◽  
Arrival Times ◽  
Interarrival Times ◽  
Decreasing Failure Rate ◽  
Number Of Customers

In this paper we consider general counting processes stopped at a random timeT, independent of the process. Provided thatThas the decreasing failure rate (DFR) property, we present sufficient conditions on the arrival times so that the number of events occurring beforeTpreserves the DFR property ofT. In particular, when the interarrival times are independent, we consider applications concerning the DFR property of the stationary number of customers waiting in queue for specific queueing models.

Multivariate conditional hazard rates and the MIFRA and MIFR properties

1988 ◽  
Vol 25 (01) ◽  
pp. 150-168 ◽  
Author(s):  
Moshe Shaked ◽  
J. George Shanthikumar
Keyword(s):  
Failure Rate ◽  
Sufficient Conditions ◽  
Load Sharing ◽  
Hazard Rates ◽  
Reliability Model ◽  
Increasing Failure Rate ◽  
Imperfect Repair ◽  
The Relationship

If T = (T 1, · ··, Tn ) is a vector of random lifetimes then its distribution can be determined by a set λof multivariate conditional hazard rates. In this paper, sufficient conditions on λare found which imply that T is Block–Savits MIFRA (multivariate increasing failure rate average) or Savits MIFR (multivariate increasing failure rate). Applications for a multivariate reliability model of Ross and for load-sharing models are given. The relationship between Shaked and Shanthikumar model of multivariate imperfect repair and the MIFRA property is also discussed.

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