Robustness of perturbation analysis estimates for automated manufacturing systems

Perturbation Analysis (P/A) of Discrete Event Systems is a technique that enables parameter sensitivities to be determined while observing a single experiment on the system. In the context of automated manufacturing systems, P/A enables system managers to obtain answers to many "what-if" questions about their system just by observing its current operation. Thus, for a Flexible Manufacturing System (FMS), the FMS manager could obtain estimates of the effects of adding pallets/fixtures, adding carts or AGVs, changing machine cycle times, and so on, simply by observing the current FMS operations and applying the P/A algorithms to these observations. An over view of the P/A approach, along with a literature survey and discussion of the benefits of P/A over other techniques, is given in Ho et al. [1] Application to FMS, and some related implementation issues, are discussed by Suri and Dille [2]. Recently there have been many theoretical results on the consistency and convergence of P/A: an example is Suri and Zazanis [3]. A bibliography of such results can he found in [1] and [3]. One of the advantages of the P/A approach versus other analysis techniques is that it reduces the modelling assumptions, in the sense that it operates on actual data obtained from observing a system. There are two main steps involved in applying P/A: i) perturbation generation, which relates the change in a parameter to changes in "neighboring" events, and ii) perturbation propagation which relates the effects of perturbations in one event to (possibly) all other events in the system. In many cases, both these steps are determined completely by the data being observed. In some cases however, the perturbation generation step requires an assumption of the probability distribution for an observed random variable. For example, suppose a parameter of a machine is its mean time to repair (MTTR). Now suppose we are interested in knowing, what would be the effect of improving the efficiency of our repair team. so that MTTR is reduced by 10 minutes? In order for P/A to answer this, we need to know more about the relation between the parameter MTTR and the actual (observed) repair times. Thus, one of the criticisms of P/A has been that while it reduces some modelling assumptions, it still requ- ires assuming many probability distributions. This criticism, it turns out, is not entirely fair. First, we can show that for many practical cases, very little needs to be assumed about the distributions mentioned. Second, for a simple system which is analytically tractable, namely the M/G/1 queue, we can derive analytic bounds on the errors introduced even when incorrect assumptions are made. Finally, for more complex systems, we show experimental results indicating again that errors in such assumptions have small effects on the P/A estimates. All these results can be found in [4] which is being submitted for journal publication, The sum of these results is that, when used in practical systems, the P/A technique is going to be robust with respect to the assumptions made. Intuitively, this can be explained quite simply: The propagation part of the algorithm depends only on the observations, and also, the errors introduced at the generation stage tend to be small. This is but one more argument for promoting P/A as a practical analysis technique for actual automated manufacturing systems.