ABSTRACT
Up to now we have discussed simulations in which the random variables under consideration, either as the inputs to a model or as the outputs from the simulation, were not only independent but also univariate. Examples include independent replications of a response time at a computer terminal, a waiting time in a queue, or the time to failure of an individual component. However, it may be necessary or desirable to consider joint (bivariate) properties of a system—for example, not only the response time at a computer terminal but also the number of people signed on to the computer at the time of response. Similarly, the times to failure of several components may be related, if for no other reason than that they could fail because of a common shock to the system. An interesting and striking example of this common-mode type of failure was the near crash of an L1011 airliner in Florida in 1983, when all three engines failed because of a mistake in maintenance. Also in Chapter 9 we studied various methods for assessing the variability of estimates of a characteristic θ from a sample X 1, …, Xj , …, Xm . In particular, we studied individual (or marginal) properties of the jackknife estimate and the bootstrap estimate of the standard deviation of estimates of θ. However, these two standard deviation estimates probably will be correlated with each other. This correlation may be of interest when comparing jackknife and bootstrap estimates, and it can be assessed using the techniques given in this chapter.
