scholarly journals Shock models leading to G* class of lifetime distributions

2020 ◽  
Vol 9 (2) ◽  
pp. 61-66
Author(s):  
K.V. Jayamol ◽  
K. K. Jose
Keyword(s):  
Poisson Process ◽  
Damage Model ◽  
Probability Generating Function ◽  
Stochastic Ordering ◽  
Life Distribution ◽  
Lifetime Distributions ◽  
Reliability Modeling ◽  
Shock Models ◽  
Failure Distribution ◽  
Cumulative Damage Model

In this paper we study a stochastic ordering namely alternate probability generating function (a.p.g.f .... ) ordering and its properties. The life distribution H(t) of a device subject to shocks governed by a Poisson process is considered as a function of the probabilities Pk of surviving the first k shocks. Various properties of the discrete failure distribution Pk are shown to be reflected in corresponding properties of the continuous life distribution H(t). A certain cumulative damage model and various applications of these models in reliability modeling are also considered.

A useful ageing property based on the Laplace transform

1983 ◽  
Vol 20 (3) ◽  
pp. 615-626 ◽  
Author(s):  
Bengt Klefsjö
Keyword(s):  
Laplace Transform ◽  
Damage Model ◽  
Cumulative Damage ◽  
Closure Properties ◽  
Shock Models ◽  
The Laplace Transform ◽  
Life Distributions ◽  
Cumulative Damage Model ◽  
Ageing Property

The class of life distributions for which , where , and , is studied. We prove that this class is larger than the HNBUE (HNWUE) class (consisting of those life distributions for which for x ≧ 0) and present results concerning closure properties under some usual reliability operations. We also study some shock models and a certain cumulative damage model. The class of discrete life distributions for which for 0 ≦ p ≦ 1, where , is also studied.

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.

A useful ageing property based on the Laplace transform

1983 ◽  
Vol 20 (03) ◽  
pp. 615-626 ◽  
Author(s):  
Bengt Klefsjö
Keyword(s):  
Laplace Transform ◽  
Damage Model ◽  
Cumulative Damage ◽  
Closure Properties ◽  
Shock Models ◽  
The Laplace Transform ◽  
Life Distributions ◽  
Cumulative Damage Model ◽  
Ageing Property

The class of life distributions for which , where , and , is studied. We prove that this class is larger than the HNBUE (HNWUE) class (consisting of those life distributions for which for x ≧ 0) and present results concerning closure properties under some usual reliability operations. We also study some shock models and a certain cumulative damage model. The class of discrete life distributions for which for 0 ≦ p ≦ 1, where , is also studied.

Preservation of certain classes of life distributions under Poisson shock models

1994 ◽  
Vol 31 (02) ◽  
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.

scholarly journals Preservation of some partial orderings under Poisson shock models

1989 ◽  
Vol 21 (03) ◽  
pp. 713-716 ◽  
Author(s):  
Harshinder Singh ◽  
Kanchan Jain
Keyword(s):  
Poisson Process ◽  
Residual Life ◽  
Stochastic Ordering ◽  
Mean Residual Life ◽  
Survival Functions ◽  
Constant Intensity ◽  
Variable Ordering ◽  
Shock Models ◽  
Partial Orderings ◽  
Likelihood Ratio Ordering

Suppose each of the two devices is subjected to shocks occurring randomly as events in a Poisson process with constant intensity λ. Let Pk denote the probability that the first device will survive the first k shocks and let denote such a probability for the second device. Let and denote the survival functions of the first and the second device respectively. In this note we show that some partial orderings, namely likelihood ratio ordering, failure rate ordering, stochastic ordering, variable ordering and mean residual-life ordering between the shock survival probabilities and are preserved by the corresponding survival functions and .

scholarly journals Preservation of some partial orderings under Poisson shock models

1989 ◽  
Vol 21 (3) ◽  
pp. 713-716 ◽  
Author(s):  
Harshinder Singh ◽  
Kanchan Jain
Keyword(s):  
Poisson Process ◽  
Residual Life ◽  
Stochastic Ordering ◽  
Mean Residual Life ◽  
Survival Functions ◽  
Constant Intensity ◽  
Variable Ordering ◽  
Shock Models ◽  
Partial Orderings ◽  
Likelihood Ratio Ordering

Suppose each of the two devices is subjected to shocks occurring randomly as events in a Poisson process with constant intensity λ. Let Pk denote the probability that the first device will survive the first k shocks and let denote such a probability for the second device. Let and denote the survival functions of the first and the second device respectively. In this note we show that some partial orderings, namely likelihood ratio ordering, failure rate ordering, stochastic ordering, variable ordering and mean residual-life ordering between the shock survival probabilities and are preserved by the corresponding survival functions and .

On classes of life distributions based on the mean time to failure function

2021 ◽  
Vol 58 (2) ◽  
pp. 289-313
Author(s):  
Ruhul Ali Khan ◽  
Dhrubasish Bhattacharyya ◽  
Murari Mitra
Keyword(s):  
Damage Model ◽  
Replacement Policy ◽  
Time To Failure ◽  
Mean Time To Failure ◽  
Moment Convergence ◽  
Life Distributions ◽  
Cumulative Damage Model ◽  
The Mean ◽  
Age Replacement ◽  
Mean Time

AbstractThe performance and effectiveness of an age replacement policy can be assessed by its mean time to failure (MTTF) function. We develop shock model theory in different scenarios for classes of life distributions based on the MTTF function where the probabilities $\bar{P}_k$ of surviving the first k shocks are assumed to have discrete DMTTF, IMTTF and IDMTTF properties. The cumulative damage model of A-Hameed and Proschan [1] is studied in this context and analogous results are established. Weak convergence and moment convergence issues within the IDMTTF class of life distributions are explored. The preservation of the IDMTTF property under some basic reliability operations is also investigated. Finally we show that the intersection of IDMRL and IDMTTF classes contains the BFR family and establish results outlining the positions of various non-monotonic ageing classes in the hierarchy.

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