# Stochastic Comparisons of Lifetimes of Two Series and Parallel Systems with Location-Scale Family Distributed Components having Archimedean Copulas

@article{Kundu2017StochasticCO, title={Stochastic Comparisons of Lifetimes of Two Series and Parallel Systems with Location-Scale Family Distributed Components having Archimedean Copulas}, author={Amarjit Kundu and Shovan Chowdhury}, journal={arXiv: Statistics Theory}, year={2017} }

In this paper, we compare the lifetimes of two series and two parallel systems stochastically where the lifetime of each component follows location-scale (LS) family of distributions. The comparison is carried out under two scenarios: one, that the components of the systems have a dependent structure sharing Archimedean copula and two, that the components are independently distributed. It is shown that the systems with components in series or parallel sharing Archimedean copula with more… Expand

#### References

SHOWING 1-10 OF 32 REFERENCES

Comparisons of series and parallel systems with components sharing the same copula

- Mathematics
- 2010

The paper is devoted to study stochastic comparisons of series and parallel systems with vectors of component lifetimes sharing the same copula. We show that, under some conditions on the common… Expand

Stochastic comparison of lifetimes of two (n-k+1)-out-of-n systems with heterogeneous dependent components

- Computer Science, Mathematics
- J. Multivar. Anal.
- 2014

The results of Ma (1997), which compare lifetimes of two (n-k+1)-out-of-n systems with heterogeneous dependent populations and homogeneousdependent populations, for samples with dependent components are generalized. Expand

On stochastic comparisons of maximum order statistics from the location-scale family of distributions

- Mathematics, Computer Science
- J. Multivar. Anal.
- 2017

We consider the location-scale family of distributions, which contains many standard lifetime distributions. We give conditions under which the largest order statistic of a set of random variables… Expand

Stochastic comparisons of order statistics in the scale model

- Mathematics
- 2011

Abstract Independent random variables X λ 1 , … , X λ n are said to belong to the scale family of distributions if X λ i ∼ F ( λ i x ) , for i=1,…,n, where F is an absolutely continuous distribution… Expand

New results on comparisons of parallel systems with heterogeneous gamma components

- Mathematics
- 2011

This paper discusses ordering properties of lifetimes of parallel systems with two independent heterogeneous gamma components in terms of dispersive and star orders. It is proved, among others, that… Expand

Relative Ageing of Series and Parallel Systems With Statistically Independent and Heterogeneous Component Lifetimes

- Mathematics, Computer Science
- IEEE Transactions on Reliability
- 2016

The system with homogeneous componentlifetimes is proved to age relatively faster than that with component lifetimes following the proportional hazard rates (reversed hazard rates) model in terms of the reversed hazard rate (hazard rate). Expand

Stochastic comparisons of parallel systems of heterogeneous exponential components

- Mathematics
- 1997

Abstract Let X1, …, Xn be independent exponential random variables with Xi having hazard rate λi, i = 1, …, n. Let λ = (λ1, …, λn). Let Y1, …, Yn be a random sample of size n from an exponential… Expand

Stochastic comparisons on sample extremes of dependent and heterogenous observations

- Mathematics
- 2016

Stochastic comparison on order statistics from heterogeneous-dependent observations has been paid lots of attention recently. This paper devotes to investigating the ordering properties of order… Expand

SOME RESULTS ON THE RELATIVE AGEING OF TWO LIFE DISTRIBUTIONS

- Mathematics
- 1994

Kalashnikov and Rachev (1986) have proposed a partial ordering of life distributions which is equivalent to an increasing hazard ratio, when the ratio exists. This model can represent the phenomenon… Expand

Ordering results for the smallest and largest order statistics from independent heterogeneous exponential–Weibull random variables

- Mathematics
- 2016

ABSTRACT In this paper, we discuss stochastic comparisons of the smallest and largest order statistics from independent heterogeneous exponential–Weibull random variables. Let be independent random… Expand