Multicomponent lifetime distributions in the presence of ageing

2000 ◽  
Vol 37 (2) ◽  
pp. 521-533 ◽  
Author(s):  
Juanjuan Fan ◽  
S. G. Ghurye ◽  
Richard A. Levine
Keyword(s):  
Poisson Process ◽  
Parameter Space ◽  
Exponential Function ◽  
Multicomponent System ◽  
Compound Poisson Process ◽  
Shock Model ◽  
Multicomponent Systems ◽  
Survival Functions ◽  
Lifetime Distributions ◽  
Life Distributions

Lifetime distributions for multicomponent systems are developed through the interplay of ageing and stress shocks to the system. The ageing process is explicitly modeled by an exponential function with rate affected by the magnitude of stresses from a compound Poisson process shock model. Applications of these life distributions and associated failure rates towards the study of multicomponent system survival are discussed. In particular, we illustrate the behavior of these survival functions in relevant subsets of the parameter space.

Multicomponent lifetime distributions in the presence of ageing

2000 ◽  
Vol 37 (02) ◽  
pp. 521-533 ◽  
Author(s):  
Juanjuan Fan ◽  
S. G. Ghurye ◽  
Richard A. Levine
Keyword(s):  
Poisson Process ◽  
Parameter Space ◽  
Exponential Function ◽  
Multicomponent System ◽  
Compound Poisson Process ◽  
Shock Model ◽  
Multicomponent Systems ◽  
Survival Functions ◽  
Lifetime Distributions ◽  
Life Distributions

Lifetime distributions for multicomponent systems are developed through the interplay of ageing and stress shocks to the system. The ageing process is explicitly modeled by an exponential function with rate affected by the magnitude of stresses from a compound Poisson process shock model. Applications of these life distributions and associated failure rates towards the study of multicomponent system survival are discussed. In particular, we illustrate the behavior of these survival functions in relevant subsets of the parameter space.

Approximations for the single-product production-inventory problem with compound Poisson demand and service-level constraints

1984 ◽  
Vol 16 (2) ◽  
pp. 378-401 ◽  
Author(s):  
A. G. De kok ◽  
H. C. Tijms ◽  
F. A. Van der Duyn Schouten
Keyword(s):  
Poisson Process ◽  
Compound Poisson Process ◽  
Service Level ◽  
Inventory Level ◽  
Inventory Problem ◽  
Single Product ◽  
Compound Poisson ◽  
Poisson Demand ◽  
Production Inventory ◽  
Random Fluctuations

We consider a production-inventory problem in which the production rate can be continuously controlled in order to cope with random fluctuations in the demand. The demand process for a single product is a compound Poisson process. Excess demand is backlogged. Two production rates are available and the inventory level is continuously controlled by a switch-over rule characterized by two critical numbers. In accordance with common practice, we consider service measures such as the average number of stockouts per unit time and the fraction of demand to be met directly from stock on hand. The purpose of the paper is to derive practically useful approximations for the switch-over levels of the control rule such that a pre-specified value of the service level is achieved.

scholarly journals On dynamic mutual information for bivariate lifetimes

2015 ◽  
Vol 47 (4) ◽  
pp. 1157-1174 ◽  
Author(s):  
Jafar Ahmadi ◽  
Antonio Di Crescenzo ◽  
Maria Longobardi
Keyword(s):  
Mutual Information ◽  
Order Statistics ◽  
Random Sample ◽  
Exponential Model ◽  
Multicomponent Systems ◽  
Distribution Free ◽  
Lifetime Distributions ◽  
Different Ages ◽  
Special Case ◽  
Residual Lifetimes

We consider dynamic versions of the mutual information of lifetime distributions, with a focus on past lifetimes, residual lifetimes, and mixed lifetimes evaluated at different instants. This allows us to study multicomponent systems, by measuring the dependence in conditional lifetimes of two components having possibly different ages. We provide some bounds, and investigate the mutual information of residual lifetimes within the time-transformed exponential model (under both the assumptions of unbounded and truncated lifetimes). Moreover, with reference to the order statistics of a random sample, we evaluate explicitly the mutual information between the minimum and the maximum, conditional on inspection at different times, and show that it is distribution-free in a special case. Finally, we develop a copula-based approach aiming to express the dynamic mutual information for past and residual bivariate lifetimes in an alternative way.

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