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Handbook of Reliability, Availability, Maintainability and Safety in Engineering Design - Part 46 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 433 Fig. 4.16 Flowchart of the Monte Carlo simulation procedure Law et al. 1991 The Monte Carlo simulation approach generates statistical estimates of the system output based on the given distributions of the inputs and error models. This gives more information than does the extreme condition approach by which only the best and worst performance are estimated. Because the statistical approach is based on Monte Carlo simulation it often requires a large number of simulations. More effective sampling techniques such as the Latin hypercube and fractional factorial design can be used to reduce the amount of simulations Hicks 1993 . The Monte Carlo simulation procedure is as follows Law et al. 1991 i Generate H samples of x1 and x2 as simulation inputs based on distribution functions. ii For the given x1 calculate the distribution parameters of the internal uncertainty 81 x1 for simulation model I and generate N samples of the internal uncertainty 81 for simulation model I based on the distribution function. iii Evaluate the corresponding outputy F1 x1 81 x1 for simulation model I. iv For each y calculate the distribution parameters of the internal uncertainty e2 x2y of simulation model II and generate M samples of the internal uncertainty 82 based on the distribution function. v Evaluate the corresponding output z F2 x2 82 x2 for simulation model II. vi Calculate the mean value p.z the standard deviation c z or the c.d.f. and p.d.f. of z based on H x M x N samples of z. 434 4 Availability and Maintainability in Engineering Design d Mitigating the Effect of Uncertainty To assist designers to make reliable design decisions under uncertainties the proposed techniques of propagating the effect of uncertainties is integrated with the multidisciplinary optimisation approach based on the principles of robust design i.e. by extending the quality engineering concept to the mitigation of the .
