scholarly journals On the HNBUE property in a class of correlated cumulative shock models

1995 ◽  
Vol 27 (4) ◽  
pp. 1186-1188 ◽  
Author(s):  
Rafael Pérez-Ocón ◽  
M. Luz Gámiz-Pérez
Keyword(s):  
Failure Time ◽  
System Failure ◽  
Shock Model ◽  
Correct Proof ◽  
Shock Models

Conditions for a correlated cumulative shock model under which the system failure time is HNBUE are given. It is shown that the proof of a theorem given by Sumita and Shanthikumar (1985) relative to this property is not correct and a correct proof of the theorem is given.

scholarly journals On the HNBUE property in a class of correlated cumulative shock models

1995 ◽  
Vol 27 (04) ◽  
pp. 1186-1188
Author(s):  
Rafael Pérez-Ocón ◽  
M. Luz Gámiz-Pérez
Keyword(s):  
Failure Time ◽  
System Failure ◽  
Shock Model ◽  
Correct Proof ◽  
Shock Models

Conditions for a correlated cumulative shock model under which the system failure time is HNBUE are given. It is shown that the proof of a theorem given by Sumita and Shanthikumar (1985) relative to this property is not correct and a correct proof of the theorem is given.

Distribution properties of the system failure time in a general shock model

1984 ◽  
Vol 16 (2) ◽  
pp. 363-377 ◽  
Author(s):  
J. G. Shanthikumar ◽  
Ushio Sumita
Keyword(s):  
Failure Time ◽  
Sufficient Conditions ◽  
System Failure ◽  
Shock Model ◽  
Completely Monotone ◽  
Shock Models ◽  
Subsequent Interval ◽  
New Better Than Used ◽  
Better Than

In this paper we study some distribution properties of the system failure time in general shock models associated with correlated renewal sequences (Xn, Yn) . Two models, depending on whether the magnitude of the nth shock Xn is correlated to the length Yn of the interval since the last shock, or to the length of the subsequent interval to the next shock, are considered. Sufficient conditions under which the system failure time is completely monotone, new better than used, new better than used in expectation, and harmonic new better than used in expectation are given for these two models.

Distribution properties of the system failure time in a general shock model

1984 ◽  
Vol 16 (02) ◽  
pp. 363-377 ◽  
Author(s):  
J. G. Shanthikumar ◽  
Ushio Sumita
Keyword(s):  
Failure Time ◽  
Sufficient Conditions ◽  
System Failure ◽  
Shock Model ◽  
Completely Monotone ◽  
Shock Models ◽  
Subsequent Interval ◽  
New Better Than Used ◽  
Better Than

In this paper we study some distribution properties of the system failure time in general shock models associated with correlated renewal sequences (X n, Y n) . Two models, depending on whether the magnitude of the nth shock X n is correlated to the length Y n of the interval since the last shock, or to the length of the subsequent interval to the next shock, are considered. Sufficient conditions under which the system failure time is completely monotone, new better than used, new better than used in expectation, and harmonic new better than used in expectation are given for these two models.

A class of correlated cumulative shock models

1985 ◽  
Vol 17 (2) ◽  
pp. 347-366 ◽  
Author(s):  
Ushio Sumita ◽  
J. George Shanthikumar
Keyword(s):  
Failure Time ◽  
Asymptotic Properties ◽  
Sufficient Conditions ◽  
Random Variables ◽  
System Failure ◽  
Shock Models ◽  
The Times ◽  
New Better Than Used ◽  
Better Than

In this paper we define and analyze a class of cumulative shock models associated with a bivariate sequence {Xn, Yn}∞n=0 of correlated random variables. The {Xn} denote the sizes of the shocks and the {Yn} denote the times between successive shocks. The system fails when the cumulative magnitude of the shocks exceeds a prespecified level z. Two models, depending on whether the size of the nth shock is correlated with the length of the interval since the last shock or with the length of the succeeding interval until the next shock, are considered. Various transform results and asymptotic properties of the system failure time are obtained. Further, sufficient conditions are established under which system failure time is new better than used, new better than used in expectation, and harmonic new better than used in expectation.

A class of correlated cumulative shock models

1985 ◽  
Vol 17 (02) ◽  
pp. 347-366 ◽  
Author(s):  
Ushio Sumita ◽  
J. George Shanthikumar
Keyword(s):  
Failure Time ◽  
Asymptotic Properties ◽  
Sufficient Conditions ◽  
Random Variables ◽  
System Failure ◽  
Shock Models ◽  
The Times ◽  
New Better Than Used ◽  
Better Than

In this paper we define and analyze a class of cumulative shock models associated with a bivariate sequence {Xn , Yn }∞ n =0 of correlated random variables. The {Xn } denote the sizes of the shocks and the {Yn } denote the times between successive shocks. The system fails when the cumulative magnitude of the shocks exceeds a prespecified level z. Two models, depending on whether the size of the nth shock is correlated with the length of the interval since the last shock or with the length of the succeeding interval until the next shock, are considered. Various transform results and asymptotic properties of the system failure time are obtained. Further, sufficient conditions are established under which system failure time is new better than used, new better than used in expectation, and harmonic new better than used in expectation.

SOME RESULTS ON A NEW CLASS OF SHOCK MODELS

2010 ◽  
Vol 27 (04) ◽  
pp. 503-515
Author(s):  
ALAGAR RANGAN ◽  
AYŞE TANSU
Keyword(s):  
Failure Time ◽  
System Failure ◽  
First Passage ◽  
New Class ◽  
Optimal Replacement ◽  
Random Threshold ◽  
Shock Models ◽  
Special Cases ◽  
Replacement Problem ◽  
First Passage Problem

Traditional shock models view system failure time as a first passage problem. Yeh Lam proposed a new class of models called δ-shock models in which failure was dependent on the frequency of shocks. The present work generalizes Yeh Lam's results for renewal shock arrivals and random threshold. Several special cases and an optimal replacement problem are also discussed.

EVALUATION OF THE RELIABILITY OF COMPLEX TECHNICAL RECONFIGURATION SYSTEMS BY STATISTICAL MODELING METHOD

2019 ◽  
pp. 84-88
Author(s):  
A.Yu. Kulakov
Keyword(s):  
Normal Distribution ◽  
Statistical Modeling ◽  
Quantitative Estimate ◽  
Failure Time ◽  
Modeling Method ◽  
System Failure ◽  
Similar System ◽  
Orbit Control ◽  
Reliability Characteristics ◽  
Complex Technical System

Goal. Assess the reliability of a complex technical system with periodic reconfiguration and compare the results obtained a similar system, but without reconfiguration. Materials and methods. In this article uses the method of statistical modeling (Monte Carlo) to assess the reliability of complex system. We using the normal and exponential distribution of failure time for modeling failures of system elements. Reconfiguration algorithm is the algorithm proposed for the attitude and orbit control system of spacecraft. Results. A computer program has been developed for assessing reliability on the basis of a statistical modeling method, which makes it possible to evaluate systems of varying complexity with exponential and normal distribution, as well as with and without periodic reconfiguration. A quantitative estimate of the reliability as a function of the probability of system failure is obtained. Conclusion. It has been demonstrated that a system with reconfiguration has the best reliability characteristics, both in the case of exponential and normal distribution of failures.

A general shock model for a reliability system

2000 ◽  
Vol 37 (04) ◽  
pp. 925-935 ◽  
Author(s):  
Georgios Skoulakis
Keyword(s):  
Distribution Function ◽  
Point Process ◽  
Renewal Process ◽  
General System ◽  
System Structure ◽  
Random Numbers ◽  
System Failure ◽  
Shock Model ◽  
Stieltjes Transform ◽  
Special Cases

We study a reliability system subject to shocks generated by a renewal point process. When a shock occurs, components fail independently of each other with equal probabilities that are random numbers drawn from a distribution that may differ from shock to shock. We first consider the case of a parallel system and derive closed expressions for the Laplace-Stieltjes transform and the expectation of the time to system failure and for its density in the case that the distribution function of the renewal process possesses a density. We then treat a more general system structure, which has some very important special cases, such as k-out-of-n:F systems, and derive analogous formulae.

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.

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