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Handbook of Reliability, Availability, Maintainability and Safety in Engineering Design - Part 47

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Handbook of Reliability, Availability, Maintainability and Safety in Engineering Design - Part 47 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 443 Transition tg is prd each time a prd transition is disabled or it fires its memory variable ag is reset and its indicator re-sampling variable rg is set to 0 the firing time must be re-sampled from the same distribution when tg becomes re-enabled . Transition tg is prs when tg is disabled its associated age variable ag is not reset but maintains its constant value until tg is re-enabled whereby tg 1. At each successive enabling point ag restarts from the previously retained value. When tg fires both ag and rg are reset so that the firing time must be re-sampled at the successive enabling point 72 . The memory of tg is reset only when the transition fires. Transition tg is pri under this policy each time tg is disabled its age variable ag is reset but its indicator re-sampling variable rg remains equal to 1 and the firing time value 71 remains active so that in the next enabling period an identical firing will result. The same value is maintained over different enabling periods up to the firing of tg. Only when tg fires are both ag and rg reset and the firing time is resampled 72 . Hence also in this case the memory is lost only upon firing of tg. If the firing time is exponentially distributed both the prd and prs policies behave in the same way. However the pri policy does not have the property of no memory. Thus the marking process of an SPN with only exponentially distributed firing times is not a continuous-time Markov chain CTMC if at least a single non-exclusively enabled transition exists with assigned pri policy. If the firing time is deterministic both the prd and pri policies behave in the same way that is re-sampling a deterministic variable always provides an identical value . The memory of the global marking process is considered as the superposition of the individual memories of the transitions. In general the marking process M t underlying an SPN is not .