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For a repairable k-out-of-n:G system
with a history-dependent critical state, this paper derives the
availability, the mean up time and the mean down time in one renewal
cycle when the system goes into the steady state. A comparison
between this system and a repairable k-out-of-n:G system
without a history-dependent critical state is conducted as well.
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This paper studies the limit theorems for the
weighted sums of Markov chains in bi-infinite environments and
obtains some sufficient conditions for the strong convergence of the
weighted sums.
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Based on the fact that branching processes
in random environments are Markovian chains in random environments,
transience and recurrence of the states are discussed and some
properties of the extinction probability are obtained.
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In this paper, we consider the perturbed
double compound Poisson risk process under constant interest force.
Exponential type upper bounds are obtained for the ultimate ruin
probability of this risk model by the way of martingale. For
infinite time and finite time survival probabilities, we obtain the
respective integro-differential equations. When the premiums are
exponentially distributed, some differential equations are derived
for infinite time survival probability.
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The proportional odds model plays an
important role in analyzing survival data. This note develops its
properties including some results on stochastic comparisons and
ageing properties. Results obtained here complement and extend some
related results in Kirmani and Gupta (2001).
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Among those papers discussing statistical
analysis of competing failure data, most of them assume independence
for failure modes. In this paper we use copula as the dependence
link function to assess competing risk models in accelerated life
testing. We compare via simulation the results of lifetime when the
failure modes are dependent with those when the failure modes are
independent, and apply our approach to a real data set in the
literature.
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A periodic maintenance policy for a
degenerate production system in which the products are sold with
free minimal repair warranty is considered. The degenerate process
of the system is characterized by three states: in-control state,
out-of control state and failure state. The amount of time that the
process stays in in-control state and out-of-control state are both
assumed to be exponentially distributed. The production system is
overhauled at fixed time t or at failure, whichever occurs first.
The optimal periodic overhaul time minimizing the expected
cost per item per cycle is analytically discussed, and three special
cases show the property of the optimal value . In addition,
sensitivity analysis and numerical examples concerning model
parameters are carried out to illuminate the effects of the model
parameters on the optimal periodic overhaul policy.
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This paper discusses the pricing of total
return swap which is one of the credit derivatives. As the total
return swap contracts are exposed to both interest rate risk and
default risk, this paper characterizes the interest rate risk
through HJM model. Intensity model and hybrid model are used to
characterize the default risk and to derive the corresponding
pricing formula for two cases when the default time and interest
rate are independent or correlated, respectively. Monte Carlo
simulation method is used here to derive the numerical solution of
the pricing problem.
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In this paper, we studied the mean
life ratio estimate between two populations, independently following
one parameter exponential distribution in a type-I censoring life
test. Under some conditions, we showed that the ratio estimate is
asymptotically normally distributed. Based on the asymptotic
normality, we also established its confidence interval. By a
simulation study, we illustrated the validation of the ratio
estimate.
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Berkson measurement error regression model
has a wide range of applications in the areas of industry,
agriculture, epidemiology, economics, and so on. This paper deals
with a multivariate ultrastructural Berkson measurement error
regression model, and presents consistent estimators for model
parameters. The asymptotic distributions for the estimators are
derived, and an application to a simple ultrastructural Berkson
measurement error regression model is given. A real example and
simulation results are provided for the illustration of the method
proposed in this paper.
