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Handbook of Reliability, Availability, Maintainability and Safety in Engineering Design - Part 48

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Handbook of Reliability, Availability, Maintainability and Safety in Engineering Design - Part 48 studies the combination of various methods of designing for reliability, availability, maintainability and safety, as well as the latest techniques in probability and possibility modelling, mathematical algorithmic modelling, evolutionary algorithmic modelling, symbolic logic modelling, artificial intelligence modelling, and object-oriented computer modelling, in a logically structured approach to determining the integrity of engineering design. . | 4.3 Analytic Development of Availability and Maintainability in Engineering Design 453 4.3.2.2 Designing for Availability Using Petri Net Modelling Returning to the initial quantitative example of designing for availability with the inclusion of preventive maintenance Fig. 4.24 illustrates the MRSPN representation of the system Bobbio et al. 1997 . The working state is modelled by place Pup. The generally distributed transition tf models the failure distribution of which the firing results in the system moving to place Pdown. Upon system failure the preventive maintenance activity is suspended the inhibitor arc from place Pdown to transition tclock is used to model this fact. The deterministic transition tclock models the constant inspection interval. It is competitively enabled with tf so that the one that fires first disables the other. Once tclock fires a token moves in place Pmai as well as the activity related with the preventive maintenance transition tmai starts . During the preventive maintenance phase the system is down and cannot fail by using the inhibitor arc from place Pmai to transition tf. The completion of the maintenance firing of tmai re-initialises the system in an as-good-as-new condition hence tf is assigned a prd policy. Since upon failure and repair a completed interval must elapse before the successive preventive maintenance takes place tclock also must be assigned a prd policy. As can be observed from Fig. 4.24 tf and tclock are conflicting prd transitions. a Numerical Computations for the Availability Petri Net Model Since there are no immediate transitions in the PN all the markings are tangible. Starting from an initial marking m1 the token distribution of the reachable markings represented in Fig. 4.24 assuming the following order for the places Pup Pclock down Pmai is given by mi 1 1 0 0 m2 0 1 1 0 m3 1 0 0 1 . From marking m1 both tf and tclock may fire leading to m2 and m3 respectively. From m2 only tdown can fire leading to m1 and .