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.

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.

Shock models with underlying birth process

1975 ◽  
Vol 12 (1) ◽  
pp. 18-28 ◽  
Author(s):  
M. S. A-Hameed ◽  
F. Proschan
Keyword(s):  
Failure Rate ◽  
Life Distribution ◽  
Birth Process ◽  
Increasing Failure Rate ◽  
Shock Models ◽  
Life Distributions ◽  
New Better Than Used ◽  
Better Than

This paper extends results of Esary, Marshall and Proschan (1973) and A-Hameed and Proschan (1973). We consider the life distribution of a device subject to a sequence of shocks occurring randomly in time according to a nonstationary pure birth process: given k shocks have occurred in [0, t], the probability of a shock occurring in (t, t + Δ] is λ kλ (t)Δ + o (Δ). We show that various fundamental classes of life distributions (such as those with increasing failure rate, or those with the ‘new better than used' property, etc.) are obtained under appropriate assumptions on λ k, λ (t), and on the probability of surviving a given number of shocks.

Shock models with underlying birth process

1975 ◽  
Vol 12 (01) ◽  
pp. 18-28 ◽  
Author(s):  
M. S. A-Hameed ◽  
F. Proschan
Keyword(s):  
Failure Rate ◽  
Life Distribution ◽  
Birth Process ◽  
Increasing Failure Rate ◽  
Shock Models ◽  
Life Distributions ◽  
New Better Than Used ◽  
Better Than

This paper extends results of Esary, Marshall and Proschan (1973) and A-Hameed and Proschan (1973). We consider the life distribution of a device subject to a sequence of shocks occurring randomly in time according to a nonstationary pure birth process: given k shocks have occurred in [0, t], the probability of a shock occurring in (t, t + Δ] is λ kλ (t)Δ + o (Δ). We show that various fundamental classes of life distributions (such as those with increasing failure rate, or those with the ‘new better than used' property, etc.) are obtained under appropriate assumptions on λ k, λ (t), and on the probability of surviving a given number of shocks.

Shock models leading to increasing failure rate and decreasing mean residual life survival

1982 ◽  
Vol 19 (01) ◽  
pp. 158-166 ◽  
Author(s):  
Malay Ghosh ◽  
Nader Ebrahimi
Keyword(s):  
Poisson Process ◽  
Failure Rate ◽  
Residual Life ◽  
Mean Residual Life ◽  
Increasing Failure Rate ◽  
Shock Models

Shock models leading to various univariate and bivariate increasing failure rate (IFR) and decreasing mean residual life (DMRL) distributions are discussed. For proving the IFR properties, shocks are not necessarily assumed to be governed by a Poisson process.

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.

scholarly journals The new better than used failure rate class of life distribution

1988 ◽  
Vol 20 (1) ◽  
pp. 237-240 ◽  
Author(s):  
A. M. Abouammoh ◽  
A. N. Ahmed
Keyword(s):  
Failure Rate ◽  
Life Distribution ◽  
Shock Models ◽  
Rate Class ◽  
Life Distributions ◽  
Dual Class ◽  
New Better Than Used ◽  
Ageing Distribution ◽  
Better Than

A new concept of ageing distribution, namely new better than used in failure rate (NBUFR), is introduced. Different properties of the NBUFR class and its dual class are presented. Its relations to other classes of life distributions are investigated. Finally, NBUFR survival under shock models is discussed.

Preservation of certain classes of life distributions under Poisson shock models

1994 ◽  
Vol 31 (2) ◽  
pp. 458-465 ◽  
Author(s):  
Enrico Fagiuoli ◽  
Franco Pellerey
Keyword(s):  
Poisson Process ◽  
Sufficient Conditions ◽  
Life Distribution ◽  
Shock Models ◽  
Life Distributions

Recently defined classes of life distributions are considered, and some relationships among them are proposed. The life distribution H of a device subject to shocks occurring randomly according to a Poisson process is also considered, and sufficient conditions for H to belong to these classes are discussed.

Partial orderings under cumulative damage shock models

1993 ◽  
Vol 25 (04) ◽  
pp. 939-946 ◽  
Author(s):  
Franco Pellerey
Keyword(s):  
Likelihood Ratio ◽  
Sufficient Conditions ◽  
Cumulative Damage ◽  
Discrete Distributions ◽  
Counting Processes ◽  
Likelihood Ratio Order ◽  
Common Shocks ◽  
Shock Models ◽  
Partial Orderings ◽  
The Mean

Two devices are subjected to common shocks arriving according to two identical counting processes. Let and denote the probability of surviving k shocks for the first and the second device, respectively. We find conditions on the discrete distributions and in order to obtain the failure rate order (FR), the likelihood ratio order (LR) and the mean residual order (MR) between the random lifetimes of the two devices. We also obtain sufficient conditions under which the above mentioned relations between the discrete distributions are verified in some cumulative damage shock models.

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