Reliability modelling of performance functions containing correlated basic variables, with application to construction project risk management

[摘要] ENGLISH ABSTRACT:Correlation mechanisms describing systematic variations and common sensitivities are criticalcontributors to uncertainty in quantitative functions modelling project performance in termsof probabilistic or basic variables. Current reliability methods transform dependent vectors toan equivalent set of independent standard normal variates. A simple method is developed fordealing with correlation in the original variable space.An algebraic description of the direction cosine (or alpha) for performance functions underconditions of dependence is formally derived and numerically validated. The resultantGeneral First Order Second Moment (GFOSM) method for correlated basic variables isshown to be equivalent to the orthogonal transformation method. Geometric and physicalinterpretations of the general direction cosine are developed, with alpha found to beequivalent to the correlation between a basic variable and performance function.Corresponding inequalities and normalizing conditions are also developed for alpha.Expressions for a number of applications utilising the general dependent form for thedirection cosine are derived and demonstrated. The current definition of the direction cosineas an importance factor is validated for dependent conditions, and conditions establishedunder which this descriptor is no longer adequate. Expressions are derived to measure thesignificance of a variable in terms of stochastic importance and function sensitivity, toestablish reliability index sensitivity to the omission of non-critical items, quantifyingvariable elasticity and an elasticity index. The general FOSM method for correlated basicvariables is applied to system analysis to generate modal correlation coefficients betweenfailure modes.The general direction cosine is stable for multivariate linear functions and functions of limitedcurvature across a range of reliabilities and correlation levels. This characteristic furthersimplifies the process by providing for deterministic reliability modelling of performancefunctions containing dependent variables, avoiding the solution of the more complex jointdensity function.The extension of the current theory and the treatment of performance functions in the originalvector space develop invaluable insight into the correlation mechanisms driving risk andreliability. This will assist project managers to better understand areas that can affect projectperformance, to focus management attention, develop mitigation strategies and to allocateresources for the optimal management of project risk.

[发布机构] Stellenbosch University