This paper deals with the problems of computational and structural complexity in designing maximally permissive liveness-enforcing supervisors for a class of Petri nets called Systems of Simple Sequential Processes with Resources (S 3 PR) without ξ-resources. The supervisor consists of two parts: the first part proposes an algorithm to extract a desired emptied strict minimal siphon (SMS) from a given emptied siphon based on loop resource subsets. This is faster than the existing ones. The second part proposes a siphon-based deadlock prevention policy, which can obtain a maximally permissive liveness-enforcing supervisor with reduced structural complexity and no weighted monitors, owing to the contribution of the first part, which can compute a desired SMS such that one with the smallest number of resource places is selected first for control. Several flexible manufacturing systems are used to show the proposed method and its superior performance over the previous ones.
Existing policies for deadlock control are mainly based on siphons due to their ability to indicate deadlocks, and can be used as a powerful tool to deal with deadlock situations in flexible manufacturing systems. In order to avoid deadlocks, researchers often add monitors to control siphons. This may result in redundant monitors, unnecessary cost, and restriction of the behavior permissiveness. For example, for a system of sequential systems with shared resources (S4R), the existing deadlock control policies based on max, max′ or max′′‐controlled siphons tend to overly restrict the behavior of a controlled system. To ensure maximal permissive behavior of controlled systems, a new concept of siphon controllability named W‐control is defined and then a sufficient and necessary condition under which a WS3PR is live if all its siphons are W‐controlled. Examples are given to demonstrate them.
On the basis of the principle of degradation mechanism invariance, a Wiener degradation process with random drift parameter is used to model the data collected from the constant stress accelerated degradation test. Small-sample statistical inference method for this model is proposed. On the basis of Fisher's method, a test statistic is proposed to test if there is unit-to-unit variability in the population. For reliability inference, the quantities of interest are the quantile function, the reliability function, and the mean time to failure at the designed stress level. Because it is challenging to obtain exact confidence intervals (CIs) for these quantities, a regression type of model is used to construct pivotal quantities, and we develop generalized confidence intervals (GCIs) procedure for those quantities of interest. Generalized prediction interval for future degradation value at designed stress level is also discussed. A Monte Carlo simulation study is used to demonstrate the benefits of our procedures. Through simulation comparison, it is found that the coverage proportions of the proposed GCIs are better than that of the Wald CIs and GCIs have good properties even when there are only a small number of test samples available. Finally, a real example is used to illustrate the developed procedures.
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