scholarly journals Directional approach to gradual cover: the continuous case

2020 ◽  
Author(s):  
Tammy Drezner ◽  
Zvi Drezner ◽  
Pawel Kalczynski
Keyword(s):  
Continuous Case ◽  
Gradual Cover

scholarly journals The number of failed components in a coherent working system when the lifetimes are discretely distributed

Metrika ◽  
2021 ◽  
Author(s):  
Krzysztof Jasiński
Keyword(s):  
Random Variables ◽  
Continuous Case ◽  
Coherent System ◽  
Coherent Systems ◽  
Discrete Random Variables ◽  
Independent And Identically Distributed

AbstractIn this paper, we study the number of failed components of a coherent system. We consider the case when the component lifetimes are discrete random variables that may be dependent and non-identically distributed. Firstly, we compute the probability that there are exactly i, $$i=0,\ldots ,n-k,$$ i = 0 , … , n - k , failures in a k-out-of-n system under the condition that it is operating at time t. Next, we extend this result to other coherent systems. In addition, we show that, in the most popular model of independent and identically distributed component lifetimes, the obtained probability corresponds to the respective one derived in the continuous case and existing in the literature.

scholarly journals Effectiveness of a Flexible and Continuous Case Management Program for Suicide Attempters

2020 ◽  
Vol 17 (7) ◽  
pp. 2599
Author(s):  
Min-Hyuk Kim ◽  
Jinhee Lee ◽  
Hyunjean Noh ◽  
Jin-Pyo Hong ◽  
Hyun Kim ◽  
...  
Keyword(s):  
Case Management ◽  
Teaching Hospital ◽  
Suicide Attempts ◽  
Management Program ◽  
Continuous Case ◽  
Case Management Program ◽  
Suicide Attempters ◽  
Flexible Approach ◽  
Risk Of Death ◽  
Management Group

The purpose of this study was to investigate the effect of continuous case management with a flexible approach on the prevention of suicide by suicide reattempt in a real clinical setting. The subjects in this study were 526 suicide attempters who visited emergency rooms in a teaching hospital in South Korea. Subjects were provided a continuous case management program with a flexible approach according to the severity of their suicide risk and needs. During the entire observation period (from 182 days to 855 days, mean = 572 ± 254), 18 patients (3.7%) died by suicide reattempt: Eight patients (2.27%) in the case management group and 10 patients (7.35%) in the no-case management group. The Cox regression analysis showed that the case management group had a 75% lower risk of death from suicide attempts than the no-case management group (HR = 0.34, 95% CI = 0.13–0.87). This result was shown to be more robust after adjusting for confounding factors such as gender, age, psychiatric treatment, suicide attempts, and family history of suicide (adjusted HR = 0.27, 95% CI = 0.09–0.83). This study was conducted in a single teaching hospital and not a randomized controlled one. A flexible and continuous case management program for suicide attempters is effective for preventing death by suicide reattempts.

On the regularity of one-sided fractional maximal functions

2018 ◽  
Vol 68 (5) ◽  
pp. 1097-1112 ◽  
Author(s):  
Feng Liu
Keyword(s):  
Bounded Variation ◽  
Maximal Functions ◽  
Continuous Case ◽  
Discrete Case ◽  
Maximal Operators ◽  
Functions Of Bounded Variation ◽  
Sharp Bounds ◽  
Regularity Properties ◽  
Natural Extensions ◽  
The One

Abstract In this paper we investigate the regularity properties of one-sided fractional maximal functions, both in continuous case and in discrete case. We prove that the one-sided fractional maximal operators $ \mathcal{M}_{\beta}^{+} $ and $ \mathcal{M}_{\beta}^{-} $ map $ W^{1,p}(\mathbb{R}) $ into $ W^{1,q}(\mathbb{R}) $ with 1 <p <∞, 0≤β<1/p and q=p/(1-pβ), boundedly and continuously. In addition, we also obtain the sharp bounds and continuity for the discrete one-sided fractional maximal operators $ M_{\beta}^{+} $ and $ M_{\beta}^{-} $ from $ \ell^{1}(\mathbb{Z}) $ to $ {\rm BV}(\mathbb{Z}) $. Here $ {\rm BV}(\mathbb{Z}) $ denotes the set of all functions of bounded variation defined on ℤ. The results we obtained represent significant and natural extensions of what was known previously.

REDEFINING FAILURE RATE FUNCTION FOR DISCRETE DISTRIBUTIONS

2002 ◽  
Vol 09 (03) ◽  
pp. 275-285 ◽  
Author(s):  
M. XIE ◽  
O. GAUDOIN ◽  
C. BRACQUEMOND
Keyword(s):  
Failure Rate ◽  
Rate Function ◽  
Monotonicity Property ◽  
Discrete Distributions ◽  
The Other ◽  
Continuous Case ◽  
Discrete Version ◽  
Series System ◽  
Failure Rate Function ◽  
Definition Of

For discrete distribution with reliability function R(k), k = 1, 2,…,[R(k - 1) - R(k)]/R(k - 1) has been used as the definition of the failure rate function in the literature. However, this is different from that of the continuous case. This discrete version has the interpretation of a probability while it is known that a failure rate is not a probability in the continuous case. This discrete failure rate is bounded, and hence cannot be convex, e.g., it cannot grow linearly. It is not additive for series system while the additivity for series system is a common understanding in practice. In the paper, another definition of discrete failure rate function as In[R(k - 1)/R(k)] is introduced, and the above-mentioned problems are resolved. On the other hand, it is shown that the two failure rate definitions have the same monotonicity property. That is, if one is increasing/decreasing, the other is also increasing/decreasing. For other aging concepts, the new failure rate definition is more appropriate. The failure rate functions according to this definition are given for a number of useful discrete reliability functions.

scholarly journals Controllability and observability of linear impulsive adjoint dynamic system on time scale

2020 ◽  
Vol 51 (3) ◽  
pp. 201-217
Author(s):  
Nusrat Yasmin ◽  
Safia Mirza ◽  
Awais Younus ◽  
Asif Mansoor
Keyword(s):  
Dynamic System ◽  
Time Scales ◽  
Time Scale ◽  
Continuous Case ◽  
Time Varying ◽  
Controllability And Observability

This paper deals with the controllability, observability of the solution of time-varying system on time scales. We obtain new results about controllability and observability and generalize to a time scale some known properties about stability from the continuous case.

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