637We next derive the cdf of the failure time, i.e.,. From (7) and (9), we have (34) In (34), for the first expectation term, using Lemma 2 by setting , , , and then taking the expectation with respect to , we have (35) For the second expectation term, using Lemma 2 by setting , , , and taking the expectation with respect to , we have (36) This completes the proof.
ACKNOWLEDGMENTThe authors sincerely thank the Editor, Associate Editor, and anonymous reviewers for their valuable suggestions and thorough review. Their constructive comments have considerably helped in the revision of this paper.
REFERENCES[1] J. W. Sun, L. Li, and L. F. Xi, "Modified two-stage degradation model for dynamic maintenance threshold calculation considering uncertainty," A degradation path-dependent approach for remaining useful life estimation with an exact and closed-form solution," Eur.
Abstract-Activity cycle diagram (ACD), which is essentially a timed Petri net, is one of the oldest formal modeling tools for discrete-event systems, and a flexible manufacturing system (FMS) is a highly automated job shop that is used widely in mechanical and electronics industries. Previous FMS modeling studies have indicated that formal modeling of real-life (or industrial) FMSs with classical ACDs (or Petri nets) is almostimpossible. This paper presents an incremental modeling procedure for building a formal simulation model of a real-life FMS with parameterized ACD (P-ACD) that was proposed recently. The incremental modeling procedure consists of job flow modeling, job routing modeling, dispatching rule modeling, and refixture operation modeling. In this paper, a P-ACD model of a real-life FMS was constructed and an FMS simulator was implemented from the proposed P-ACD model. A simulation experiment was conducted in order to demonstrate the usefulness of the FMS simulator. and maaabdullah@kau.edu.sa). This paper has supplementary downloadable material at http://ieeexplore.ieee.org, provided by the author. This includes videos for the dedicated FMS simulator and its animation. Clip 1 (demonstration.avi) shows the dedicated FMS simulator can be used to represent a class of a FMS and simulate an instance of the FMS described by the input data. Clip 2 (animation.avi) shows the animation of a FMS, which was constructed using Proof Animation of Wolverine Software and uses the trace file converted from the simulation log generated by the dedicated FMS simulator. This material is 41.4 MB in size.Note to Practitioners-FMSs are used widely in discrete part manufacturing. Recently, the authors developed P-ACD with which a formal model of a real-life industrial FMS can be built. There are three key deliverables in this paper: an FMS simulator executing the P-ACD model of the FMS, P-ACD models of a real-life FMS, and an incremental modeling procedure for building a P-ACD model of the FMS. Thus, as a practitioner, you may: 1) use the FMS simulator posted in the authors' URL as a dedicated simulator for your FMS, if the configuration of your FMS is similar to tha...