Semi-Markov shock models with additive damage

1986 ◽  
Vol 18 (3) ◽  
pp. 772-790 ◽  
Author(s):  
M. J. M. Posner ◽  
D. Zuckerman
Keyword(s):  
Sufficient Conditions ◽  
Control Limit ◽  
Shock Model ◽  
Markov Modelling ◽  
Shock Models ◽  
Replacement Model ◽  
Computational Aspects ◽  
Replacement Problem

We examine a replacement model for a semi-Markov shock model with additive damage. Sufficient conditions are given for the optimality of control limit policies. The paper generalizes and unifies previous research in the area.In addition, we investigate in detail the practical modelling and computational aspects of the replacement problem using a semi-Markov modelling structure.

Semi-Markov shock models with additive damage

1986 ◽  
Vol 18 (03) ◽  
pp. 772-790
Author(s):  
M. J. M. Posner ◽  
D. Zuckerman
Keyword(s):  
Sufficient Conditions ◽  
Control Limit ◽  
Shock Model ◽  
Markov Modelling ◽  
Shock Models ◽  
Replacement Model ◽  
Computational Aspects ◽  
Replacement Problem

We examine a replacement model for a semi-Markov shock model with additive damage. Sufficient conditions are given for the optimality of control limit policies. The paper generalizes and unifies previous research in the area. In addition, we investigate in detail the practical modelling and computational aspects of the replacement problem using a semi-Markov modelling structure.

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.

A Generalized Age-Replacement Model

1992 ◽  
Vol 6 (4) ◽  
pp. 525-541 ◽  
Author(s):  
Stephan G. Vanneste
Keyword(s):  
Optimization Procedure ◽  
Control Limit ◽  
Maintenance Policy ◽  
Unimodal Function ◽  
Replacement Model ◽  
Markov Decision ◽  
Optimal Maintenance ◽  
Age Replacement ◽  
Replacement Problem ◽  
Optimal Maintenance Policy

Four practically important extensions of the classical age-replacement problem are analyzed using Markov decision theory: (1) opportunity maintenance, (2) imperfect repair, (3) non-zero repair times, and (4) Markov degradation of the working unit. For this general model, we show that the optimal maintenance policy is of the control limit type and that the average costs are a unimodal function of the control limit. An efficient optimization procedure is provided to find the optimal policy and its average costs. The analysis extends and unifies existing results.

Failure distributions of shock models

1980 ◽  
Vol 17 (3) ◽  
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.

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.

Determining the control limit policy in a replacement model with linear restoration

1991 ◽  
Vol 10 (6) ◽  
pp. 335-341 ◽  
Author(s):  
David Perry ◽  
M.J.M. Posner
Keyword(s):  
Control Limit ◽  
Replacement Model

Reliability assessment of system under a generalized cumulative shock model

2019 ◽  
Vol 234 (1) ◽  
pp. 129-137 ◽  
Author(s):  
Min Gong ◽  
Serkan Eryilmaz ◽  
Min Xie
Keyword(s):  
Reliability Assessment ◽  
Shock Model ◽  
External Shocks ◽  
Phase Type Distribution ◽  
Internal Factors ◽  
Reliability Characteristics ◽  
Shock Models ◽  
The One ◽  
Random Shocks ◽  
Real Practice

Reliability assessment of system suffering from random shocks is attracting a great deal of attention in recent years. Excluding internal factors such as aging and wear-out, external shocks which lead to sudden changes in the system operation environment are also important causes of system failure. Therefore, efficiently modeling the reliability of such system is an important applied problem. A variety of shock models are developed to model the inter-arrival time between shocks and magnitude of shocks. In a cumulative shock model, the system fails when the cumulative magnitude of damage caused by shocks exceed a threshold. Nevertheless, in the existing literatures, only the magnitude is taken into consideration, while the source of shocks is usually neglected. Using the same distribution to model the magnitude of shocks from different sources is too critical in real practice. To this end, considering a system subject to random shocks from various sources with different probabilities, we develop a generalized cumulative shock model in this article. We use phase-type distribution to model the variables, which is highly versatile to be used for modeling quantitative features of random phenomenon. We will discuss the reliability characteristics of such system in some detail and give some clear expressions under the one-dimensional case. Numerical example for illustration is also provided along with a summary.

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.

General shock models associated with correlated renewal sequences

1983 ◽  
Vol 20 (3) ◽  
pp. 600-614 ◽  
Author(s):  
J. G. Shanthikumar ◽  
U. Sumita
Keyword(s):  
Limit Theorem ◽  
Renewal Process ◽  
Threshold Level ◽  
Numerical Results ◽  
Shock Model ◽  
Failure Times ◽  
Clearing System ◽  
Shock Models ◽  
Subsequent Interval

In this paper we define and analyze a general shock model associated with a correlated pair (Xn, Yn) of renewal sequences, where the system fails when the magnitude of a shock exceeds (or falls below) a prespecified threshold level. Two models, depending on whether the nth shock Xn is correlated to the length Yn of the interval since the last shock, or to the length Yn of the subsequent interval until the next shock, are considered. The transform results, an exponential limit theorem, and properties of the associated renewal process of the failure times are obtained. An application in a stochastic clearing system with numerical results is also given.

Sign in / Sign up

Export Citation Format

Share Document