  In this paper, we construct a bound copula, which can reach both Frechet's
lower and upper bounds for perfect positive and negative dependence cases.
Since it covers a wide range of dependency and simple for computational
purposes, it can be very useful. We then develop a new perturbed copula using
the lower and upper bounds of Frechet copula and show that it satisfies all
properties of a copula. In some cases, it is very difficult to get results such
as distribution functions and the expected values in explicit form by using
copulas such as Archemedes, Guassian, $t$-copula. Thus, we can use these new
copulas. For both copulas, we derive the strength of measures of the dependency
such as Spearman's rho, Kendall's tau, Blomqvist's beta and Gini's gamma, and
the coefficients of the tail dependency. As an application, we use the bound
copula to analyze the dependency between two service times to evaluate the mean
waiting time and the mean service time when customers launch two replicas of
each task on two parallel servers using the cancel-on-finish policy. We assume
that the inter-arrival time is exponential and the service time is general.
