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A: Monte Carlo simulation applies powerful tools towards finding accurate solutions to complex problems that analytical approaches cannot solve. Practical problems are usually very complicated. To apply analytical methods to complicated problems, one has to simplify them by making assumptions that are only “somewhat” reasonable. By doing so, however, the solutions often deviate too greatly from reality to be truly useful. Worse, the problems may be so complicated that there is no reasonable way to simplify the situation enough so as to apply an analytical approach. In both these cases, Monte Carlo simulation is the right way to go.
A: Monte Carlo simulation is based on an accurate description of the underlying context of a maintenance situation. Consequently it leads to a more effective CBM policy (data interpretation method or model). By “effective” I mean a policy that addresses the specified objectives of the CBM program in the asset’s current operating context.
A: By providing a more accurate estimation of system remaining useful life.
A: By simulating the distribution of the system’s remaining useful life based on:
A: Cumulative hazard is the integral of the hazard function from the system starting time to the current time. It approximates a system’s “state of health” at the current time.
A: Cumulative damage conservation is an analysis approach that recognizes and accounts for an equipment’s current operating conditions as well as its past operation (profile) in order to more accurately estimate the conditional failure distribution. It is assumed that cumulative damage (cumulative hazard) is conserved at each covariate jump. For example, an analysis of a gas turbine operating at a relatively high level of stress, say on heavy fuel oil, and which is subsequently switched over to the less damaging natural gas form of fuel, remembers, the past operating profile. Many such complex factors may be integrated into the analysis for estimating the conditional failure distribution and hence residual life.
A: Clockwork Solutions Inc. has developed an especially flexible software application, SPAR, for the prediction and management of the performance and life cycle costs of complex systems via Monte Carlo simulation.
A: Covariates are monitored and/or operational variables. Covariate behavior models are mathematical and statistical models that describe the behavior of covariates.We need to use covariate behavior models to predict future operation profiles that are required in the calculation of remaining useful life.
A: On one hand, PHM relates both the working age and covariates to the risk of system failure. It is, in this way, an advanced technique for describing the failure mechanism underlying a CBM policy. On the other hand, Monte Carlo simulation is capable of accurately describing complicated physical assets and their operating contexts. The combination of PHM and MC enables better life predictions.
A: Model validation is a common concern of CBM practitioners. Ideally, if we have enough data available, we can divide it into two groups: the training data group, and test data group. The training data group is used to build the model. The proposed decision model is then validated using the test data group. The techniques and tools available in the PHM and MC packages provide for model verification and validation in this way. Ultimately, the extent to which the monitored variables, operating profile, and failure authentication accurately reflect failure mechanisms, determines the validity of the model.
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