Thesis (PhD)--Stellenbosch University, 2002. / ENGLISH ABSTRACT: Correlation mechanisms describing systematic variations and common sensitivities are critical
contributors to uncertainty in quantitative functions modelling project performance in terms
of probabilistic or basic variables. Current reliability methods transform dependent vectors to
an equivalent set of independent standard normal variates. A simple method is developed for
dealing with correlation in the original variable space.
An algebraic description of the direction cosine (or alpha) for performance functions under
conditions of dependence is formally derived and numerically validated. The resultant
General First Order Second Moment (GFOSM) method for correlated basic variables is
shown to be equivalent to the orthogonal transformation method. Geometric and physical
interpretations of the general direction cosine are developed, with alpha found to be
equivalent 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 the
direction cosine are derived and demonstrated. The current definition of the direction cosine
as an importance factor is validated for dependent conditions, and conditions established
under which this descriptor is no longer adequate. Expressions are derived to measure the
significance of a variable in terms of stochastic importance and function sensitivity, to
establish reliability index sensitivity to the omission of non-critical items, quantifying
variable elasticity and an elasticity index. The general FOSM method for correlated basic
variables is applied to system analysis to generate modal correlation coefficients between
failure modes.
The general direction cosine is stable for multivariate linear functions and functions of limited
curvature across a range of reliabilities and correlation levels. This characteristic further
simplifies the process by providing for deterministic reliability modelling of performance
functions containing dependent variables, avoiding the solution of the more complex joint
density function.
The extension of the current theory and the treatment of performance functions in the original
vector space develop invaluable insight into the correlation mechanisms driving risk and
reliability. This will assist project managers to better understand areas that can affect project
performance, to focus management attention, develop mitigation strategies and to allocate
resources for the optimal management of project risk. / AFRIKAANSE OPSOMMING: Korrelasie meganismes wat sistematiese afwykings en gemeenskaplike sensitiwiteite
veroorsaak, is kritieke bydraers tot onsekerheid in kwantitatiewe funksies wat projek prestasie
modelleer m terme van probabilistiese of basiese veranderlikes. Huidige
betroubaarheidsmetodes transformeer afhanklike vektore tot 'n ekwivalente stel van standaard
normaalonafhanklike veranderlikes. '0 Eenvoudige metode is ontwikkelom die effekte van
korrelasie in die oorspronklike vektorspasie te hanteer.
'n Algebraise beskrywing van die rigtingseosines (genoem alfa) vir prestasiefunksies onder
omstandighede van afhanklikheid is formeel afgelei en numeries gevalideer. Dit is bewys dat
die resulterende Algemene Eerste Orde Tweede Moment metode vir gekorreleerde basiese
veranderlikes ekwivalent is aan die tradisionele Ortogonale Transformasie metode.
Geometriese en fisiese interpretasies vir die algemene rigtingscosinus is ontwikkel, met
bewys dat alfa ekwivalent is aan die korrelasie tussen 'n basiese veranderlike en die
prestasiefunksie. Ooreenstemmende ongelykhede en normaliserings-kondisies is ook vir alfa
ontwikkel.
Uitdrukkings vir 'n aantal toepassings wat gebruik maak van die algemene afhanklike vorm
van die rigtingscosinus is afgelei en gedemonstreer. Die huidige definisie van die
rigtingscosinus as 'n belangrikheidsfaktor is gevalideer vir kondisies van afhanklikheid en
omstandighede is uitgewys wanneer dit onvoldoende is. Uitdrukkings is afgelei om
stochastiese belangrikheid te meet asook funksie sensitiwiteit, die sensitiwiteit van die
betroubaarheidsindeks tot die weglating van nie kritiese veranderlikes, sowel as die
kwantifisering van elastisiteit en die elastisiteitsindeks. Die Algemene Eerste Orde Tweede
Moment metode vir gekorreleerde' veranderlikes is toegepas op sisteem analise om die
korrelasie tussen falingsmodes te genereer.
Die algemene rigtingscosinus is stabiel vir liniêre funksies en funksies met 'n beperkte
kromming oor 'n reeks betroubaarheidswaardes en korrelasie vlakke. Hierdie kenmerk
vereenvoudig die metode verder deur voorsiening te maak vir deterministiese
betroubaarheidsmodellering van prestasie funksies met afhanklike veranderlikes, deur die
oplossing van die meer komplekse gesamentlike-digtheidsfunksies te vermy.
Die uitbreiding van die huidige teorie en die hantering van prestasie funksies in die
oorspronklike vektor spasie ontwikkel waardevolle insig in die korrelasie meganismes wat
risiko en betroubaarheid oorheers. Hierdie insig sal projekbestuurders in staat stelom kritieke
gebiede wat projek prestasie kan affekteer beter te verstaan, om hulle aandag daarop te fokus,
om teenmaatreël-strategieë te ontwikkel en hulpbronne toe te ken vir die optimale bestuur van
projek risiko.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:sun/oai:scholar.sun.ac.za:10019.1/53030 |
| Date | 12 1900 |
| Creators | Ker-Fox, Gregory Mark |
| Contributors | Retief, J. V., Stellenbosch University. Faculty of Engineering. Dept. of Civil Engineering. |
| Publisher | Stellenbosch : Stellenbosch University |
| Source Sets | South African National ETD Portal |
| Language | en_ZA |
| Detected Language | Unknown |
| Type | Thesis |
| Format | 168 p. |
| Rights | Stellenbosch University |
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