scholarly journals Improved bounds for the availability and unavailability in a fixed time interval for systems of maintained, interdependent components

1980 ◽  
Vol 12 (01) ◽  
pp. 200-221 ◽  
Author(s):  
B. Natvig
Keyword(s):  
Lower Bound ◽  
System Reliability ◽  
Nuclear Reactors ◽  
Random Variables ◽  
Fixed Time ◽  
Time Interval ◽  
Coherent System ◽  
Exact Results ◽  
Fixed Time Interval ◽  
Special Case

In this paper we arrive at a series of bounds for the availability and unavailability in the time interval I = [t A , t B ] ⊂ [0, ∞), for a coherent system of maintained, interdependent components. These generalize the minimal cut lower bound for the availability in [0, t] given in Esary and Proschan (1970) and also most bounds for the reliability at time t given in Bodin (1970) and Barlow and Proschan (1975). In the latter special case also some new improved bounds are given. The bounds arrived at are of great interest when trying to predict the performance process of the system. In particular, Lewis et al. (1978) have revealed the great need for adequate tools to treat the dependence between the random variables of interest when considering the safety of nuclear reactors. Satyanarayana and Prabhakar (1978) give a rapid algorithm for computing exact system reliability at time t. This can also be used in cases where some simpler assumptions on the dependence between the components are made. It seems, however, impossible to extend their approach to obtain exact results for the cases treated in the present paper.

scholarly journals Improved bounds for the availability and unavailability in a fixed time interval for systems of maintained, interdependent components

1980 ◽  
Vol 12 (1) ◽  
pp. 200-221 ◽  
Author(s):  
B. Natvig
Keyword(s):  
Lower Bound ◽  
System Reliability ◽  
Nuclear Reactors ◽  
Random Variables ◽  
Fixed Time ◽  
Time Interval ◽  
Coherent System ◽  
Exact Results ◽  
Fixed Time Interval ◽  
Special Case

In this paper we arrive at a series of bounds for the availability and unavailability in the time interval I = [tA, tB] ⊂ [0, ∞), for a coherent system of maintained, interdependent components. These generalize the minimal cut lower bound for the availability in [0, t] given in Esary and Proschan (1970) and also most bounds for the reliability at time t given in Bodin (1970) and Barlow and Proschan (1975). In the latter special case also some new improved bounds are given. The bounds arrived at are of great interest when trying to predict the performance process of the system. In particular, Lewis et al. (1978) have revealed the great need for adequate tools to treat the dependence between the random variables of interest when considering the safety of nuclear reactors.Satyanarayana and Prabhakar (1978) give a rapid algorithm for computing exact system reliability at time t. This can also be used in cases where some simpler assumptions on the dependence between the components are made. It seems, however, impossible to extend their approach to obtain exact results for the cases treated in the present paper.

scholarly journals Continuous limits of linear and nonlinear quantum walks

2019 ◽  
Vol 32 (04) ◽  
pp. 2050008 ◽  
Author(s):  
Masaya Maeda ◽  
Akito Suzuki
Keyword(s):  
Quantum Walk ◽  
Fixed Time ◽  
Quantum Walks ◽  
Continuous Limit ◽  
Time Interval ◽  
Fixed Time Interval ◽  
Nonlinear Dirac Equation ◽  
Nonlinear Quantum ◽  
Special Case ◽  
Linear Quantum

In this paper, we consider the continuous limit of a nonlinear quantum walk (NLQW) that incorporates a linear quantum walk as a special case. In particular, we rigorously prove that the walker (solution) of the NLQW on a lattice [Formula: see text] uniformly converges (in Sobolev space [Formula: see text]) to the solution to a nonlinear Dirac equation (NLD) on a fixed time interval as [Formula: see text]. Here, to compare the walker defined on [Formula: see text] and the solution to the NLD defined on [Formula: see text], we use Shannon interpolation.

scholarly journals The association in time of a Markov process with application to multistate reliability theory

1985 ◽  
Vol 22 (2) ◽  
pp. 473-479 ◽  
Author(s):  
Nils Lid Hjort ◽  
Bent Natvig ◽  
Espen Funnemark
Keyword(s):  
Markov Process ◽  
Fixed Time ◽  
Reliability Theory ◽  
Time Interval ◽  
Sufficient Condition ◽  
Independent Components ◽  
Fixed Time Interval ◽  
Binary Case ◽  
Special Case

A series of bounds for the availability and unavailability in a fixed time interval, I, for a system of maintained, interdependent components are given in Natvig (1980) in the traditional binary case, and in Funnemark and Natvig (1985) in the multistate case. For the special case of independent components the only assumption needed to arrive at these bounds is that the marginal performance process of each component is associated in I. When these processes are Markovian and binary, a sufficient condition for this to hold is given by Esary and Proschan (1970). In the present paper we generalize this condition to the multistate case, and give an equivalent and much more convenient condition in terms of the transition intensities.

scholarly journals The association in time of a Markov process with application to multistate reliability theory

1985 ◽  
Vol 22 (02) ◽  
pp. 473-479 ◽  
Author(s):  
Nils Lid Hjort ◽  
Bent Natvig ◽  
Espen Funnemark
Keyword(s):  
Markov Process ◽  
Fixed Time ◽  
Reliability Theory ◽  
Time Interval ◽  
Sufficient Condition ◽  
Independent Components ◽  
Fixed Time Interval ◽  
Binary Case ◽  
Special Case

A series of bounds for the availability and unavailability in a fixed time interval, I, for a system of maintained, interdependent components are given in Natvig (1980) in the traditional binary case, and in Funnemark and Natvig (1985) in the multistate case. For the special case of independent components the only assumption needed to arrive at these bounds is that the marginal performance process of each component is associated in I. When these processes are Markovian and binary, a sufficient condition for this to hold is given by Esary and Proschan (1970). In the present paper we generalize this condition to the multistate case, and give an equivalent and much more convenient condition in terms of the transition intensities.

A PROPOSED FORMULA FOR HORIZONTAL REVENUE ALLOCATION IN NIGERIA

2012 ◽  
Vol 29 (06) ◽  
pp. 1250033
Author(s):  
VIRTUE U. EKHOSUEHI ◽  
AUGUSTINE A. OSAGIEDE
Keyword(s):  
Optimal Control ◽  
Federal Government ◽  
Optimal Control Theory ◽  
Fixed Time ◽  
Tax Revenue ◽  
Time Interval ◽  
Fixed Time Interval ◽  
Hypothetical Data ◽  
Revenue Allocation ◽  
The Individual

In this study, we have applied optimal control theory to determine the optimum value of tax revenues accruing to a state given the range of budgeted expenditure on enforcing tax laws and awareness creation on the payment of the correct tax. This is achieved by maximizing the state's net tax revenue over a fixed time interval subject to certain constraints. By assuming that the satisfaction derived by the Federal Government of Nigeria on the ability of the individual states to generate tax revenue which is as near as the optimum tax revenue (via the state's control problem) is described by the logarithmic form of the Cobb–Douglas utility function, a formula for horizontal revenue allocation in Nigeria in its raw form is derived. Afterwards, we illustrate the use of the proposed horizontal revenue allocation formula using hypothetical data.

The evolution and measurement of a population of pairs

1995 ◽  
Vol 32 (04) ◽  
pp. 1048-1062 ◽  
Author(s):  
Eric Jakeman ◽  
Sean Phayre ◽  
Eric Renshaw
Keyword(s):  
Fixed Time ◽  
Statistical Properties ◽  
Time Interval ◽  
Fixed Time Interval ◽  
Analytical Results

The statistical properties of a population of immigrant pairs of individuals subject to loss through emigration are calculated. Exact analytical results are obtained which exhibit characteristic even–odd effects. The population is monitored externally by counting the number of emigrants leaving in a fixed time interval. The integrated statistics for this process are evaluated and it is shown that under certain conditions only even numbers of individuals will be observed.

scholarly journals Maximizing the Expected Duration of Owning a Relatively Best Object in a Poisson Process with Rankable Observations

2009 ◽  
Vol 46 (02) ◽  
pp. 402-414
Author(s):  
Aiko Kurushima ◽  
Katsunori Ano
Keyword(s):  
Poisson Process ◽  
Stopping Time ◽  
Fixed Time ◽  
Time Interval ◽  
Prior Density ◽  
Deterministic Equation ◽  
Fixed Time Interval ◽  
Unknown Number ◽  
Random Intensity ◽  
Time Selection

Suppose that an unknown number of objects arrive sequentially according to a Poisson process with random intensity λ on some fixed time interval [0,T]. We assume a gamma prior density G λ(r, 1/a) for λ. Furthermore, we suppose that all arriving objects can be ranked uniquely among all preceding arrivals. Exactly one object can be selected. Our aim is to find a stopping time (selection time) which maximizes the time during which the selected object will stay relatively best. Our main result is the following. It is optimal to select the ith object that is relatively best and arrives at some time s i (r) onwards. The value of s i (r) can be obtained for each r and i as the unique root of a deterministic equation.

Sign in / Sign up

Export Citation Format

Share Document