Pure jump shock models in reliability

1986 ◽  
Vol 18 (02) ◽  
pp. 423-440 ◽  
Author(s):  
James W. Drosen
Keyword(s):  
Markov Process ◽  
Failure Rate ◽  
Failure Time ◽  
Jump Markov Process ◽  
Damage Level ◽  
Random Threshold ◽  
Shock Models ◽  
Environmental Shocks

There are many examples of a device suffering damage from random environmental shocks. We model the damage level of such a device as a pure jump Markov process, where the incremental damage caused by a shock depends both on the magnitude of the shock and on the damage level just before the shock. We also look at the time until failure of the device, which occurs when the damage level exceeds a random threshold. The distribution of the failure time and the failure rate are examined, and conditions for the failure rate to be increasing or to have an increasing average are found.

Pure jump shock models in reliability

1986 ◽  
Vol 18 (2) ◽  
pp. 423-440 ◽  
Author(s):  
James W. Drosen
Keyword(s):  
Markov Process ◽  
Failure Rate ◽  
Failure Time ◽  
Jump Markov Process ◽  
Damage Level ◽  
Random Threshold ◽  
Shock Models ◽  
Environmental Shocks

There are many examples of a device suffering damage from random environmental shocks. We model the damage level of such a device as a pure jump Markov process, where the incremental damage caused by a shock depends both on the magnitude of the shock and on the damage level just before the shock. We also look at the time until failure of the device, which occurs when the damage level exceeds a random threshold. The distribution of the failure time and the failure rate are examined, and conditions for the failure rate to be increasing or to have an increasing average are found.

Optimal replacement for self-repairing shock models by general failure rate

1984 ◽  
Vol 21 (1) ◽  
pp. 108-119 ◽  
Author(s):  
Gary Gottlieb ◽  
Benny Levikson
Keyword(s):  
Markov Process ◽  
Failure Rate ◽  
Lower Cost ◽  
Cumulative Damage ◽  
Control Limit ◽  
Replacement Policy ◽  
Time Of Arrival ◽  
Optimal Replacement ◽  
Shock Models ◽  
Optimal Replacement Policy

A device is subject to a series of shocks which cause damage and eventually failure will occur at the time of arrival of one of the shocks. In between the shocks, the device is partially repaired as the cumulative damage decreases as some Markov process. The device must be replaced upon failure at some cost but it can also be replaced before failure at a lower cost. We consider the general case where the failure rate need not be increasing and replacement can be made at any time. The form of the optimal replacement policy is found and fairly general conditions are given for which a control limit policy is optimal.

Optimal replacement with semi-Markov shock models

1976 ◽  
Vol 13 (01) ◽  
pp. 108-117 ◽  
Author(s):  
Richard M. Feldman
Keyword(s):  
Markov Process ◽  
Cumulative Damage ◽  
Control Limit ◽  
Damage Level ◽  
Fixed Level ◽  
Optimal Replacement ◽  
Shock Models ◽  
Semi Markov Process ◽  
Damage Process ◽  
Replacement Rule

Consider a system that is subject to a sequence of randomly occurring shocks; each shock causes some damage of random magnitude to the system. Any of the shocks might cause the system to fail, and the probability of such a failure is a function of the sum of the magnitudes of damage caused from all previous shocks. The purpose of this paper is to derive the optimal replacement rule for such a system whose cumulative damage process is a semi-Markov process. This allows for both the time between shocks and the damage due to the next shock to be dependent on the present cumulative damage level. Only policies within the class of control-limit policies will be considered; namely, policies with which no action is taken if the damage is below a fixed level, and a replacement is made if the damage is above that. An example will be given illustrating the use of the optimal replacement rule.

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.

Optimal replacement with semi-Markov shock models

1976 ◽  
Vol 13 (1) ◽  
pp. 108-117 ◽  
Author(s):  
Richard M. Feldman
Keyword(s):  
Markov Process ◽  
Cumulative Damage ◽  
Control Limit ◽  
Damage Level ◽  
Fixed Level ◽  
Optimal Replacement ◽  
Shock Models ◽  
Semi Markov Process ◽  
Damage Process ◽  
Replacement Rule

Consider a system that is subject to a sequence of randomly occurring shocks; each shock causes some damage of random magnitude to the system. Any of the shocks might cause the system to fail, and the probability of such a failure is a function of the sum of the magnitudes of damage caused from all previous shocks.The purpose of this paper is to derive the optimal replacement rule for such a system whose cumulative damage process is a semi-Markov process. This allows for both the time between shocks and the damage due to the next shock to be dependent on the present cumulative damage level.Only policies within the class of control-limit policies will be considered; namely, policies with which no action is taken if the damage is below a fixed level, and a replacement is made if the damage is above that.An example will be given illustrating the use of the optimal replacement rule.

Optimal replacement for self-repairing shock models by general failure rate

1984 ◽  
Vol 16 (1) ◽  
pp. 15-15
Author(s):  
Gary Gotilieb ◽  
Benny Levikson
Keyword(s):  
Markov Process ◽  
Failure Rate ◽  
Lower Cost ◽  
Cumulative Damage ◽  
Control Limit ◽  
Replacement Policy ◽  
Time Of Arrival ◽  
Optimal Replacement ◽  
Shock Models ◽  
Optimal Replacement Policy

A device is subject to a series of shocks which cause damage and eventually failure will occur at the time of arrival of one of the shocks. In between the shocks, the device is partially repaired as the cumulative damage decreases as some Markov process. The device must be replaced upon failure at some cost but it also can be replaced before failure at a lower cost. We consider the general case where the failure rate need not be increasing and replacement can be made at any time. The form of the optimal replacement policy is found and fairly general conditions are given for which a control limit policy is optimal.

Optimal replacement for self-repairing shock models by general failure rate

1984 ◽  
Vol 21 (01) ◽  
pp. 108-119
Author(s):  
Gary Gottlieb ◽  
Benny Levikson
Keyword(s):  
Markov Process ◽  
Failure Rate ◽  
Lower Cost ◽  
Cumulative Damage ◽  
Control Limit ◽  
Replacement Policy ◽  
Time Of Arrival ◽  
Optimal Replacement ◽  
Shock Models ◽  
Optimal Replacement Policy

A device is subject to a series of shocks which cause damage and eventually failure will occur at the time of arrival of one of the shocks. In between the shocks, the device is partially repaired as the cumulative damage decreases as some Markov process. The device must be replaced upon failure at some cost but it can also be replaced before failure at a lower cost. We consider the general case where the failure rate need not be increasing and replacement can be made at any time. The form of the optimal replacement policy is found and fairly general conditions are given for which a control limit policy is optimal.

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 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.

Sign in / Sign up

Export Citation Format

Share Document