Some Concepts and Theorems of Uncertain Random Process

As a mixture of randomness and uncertainty, uncertain random variable is a measurable function from a probability space to a collection of uncertain variables. This paper will propose an uncertain random process as a generalization of both stochastic process and uncertain process. Special types of uncertain random process such as independent and stationary increment uncertain random process and uncertain random renewal process will also be discussed

Operational Decision Making under Uncertainty: Inferential, Sequential, and Adversarial Approaches

Modern security threats are characterized by a stochastic, dynamic, partially observable, and ambiguous operational environment. This dissertation addresses such complex security threats using operations research techniques for decision making under uncertainty in operations planning, analysis, and assessment. First, this research develops a new method for robust queue inference with partially observable, stochastic arrival and departure times, motivated by cybersecurity and terrorism applications. In the dynamic setting, this work develops a new variant of Markov decision processes and an algorithm for robust information collection in dynamic, partially observable and ambiguous environments, with an application to a cybersecurity detection problem. In the adversarial setting, this work presents a new application of counterfactual regret minimization and robust optimization to a multi-domain cyber and air defense problem in a partially observable environment

Analytical Properties of Credibilistic Expectation Functions

The expectation function of fuzzy variable is an important and widely used criterion in fuzzy optimization, and sound properties on the expectation function may help in model analysis and solution algorithm design for the fuzzy optimization problems. The present paper deals with some analytical properties of credibilistic expectation functions of fuzzy variables that lie in three aspects. First, some continuity theorems on the continuity and semicontinuity conditions are proved for the expectation functions. Second, a differentiation formula of the expectation function is derived which tells that, under certain conditions, the derivative of the fuzzy expectation function with respect to the parameter equals the expectation of the derivative of the fuzzy function with respect to the parameter. Finally, a law of large numbers for fuzzy variable sequences is obtained leveraging on the Chebyshev Inequality of fuzzy variables. Some examples are provided to verify the results obtained

Regression analysis of caterpillar 793D haul truck engine failure data and through-life diagnostic information using the proportional hazards model

Thesis (MScEng)--Stellenbosch University, 2012.ENGLISH ABSTRACT: Physical Asset Management (PAM) is becoming a greater concern for companies in industry today. The widely accepted British Standards Institutes’ specification for optimized management of physical assets and infrastructure is PAS55. According to PAS55, PAM is the “systematic and co-ordinated activities and practices through which an organization optimally manages its physical assets, and their associated performance, risks and expenditures over their life cycle for the purpose of achieving its organizational strategic plan”. One key performance area of PAM is Asset Care Plans (ACP). These plans are maintenance strategies which improve or ensure acceptable asset reliability and performance during its useful life. Maintenance strategies such as Condition Based Maintenance (CBM) acts upon Condition Monitoring (CM) data, disregarding the previous failure histories of an asset. Other maintenance strategies, such as Usage Based Maintenance (UBM), is based on previous failure histories, and does not consider CM data. Regression models make use of both CM data and previous failure histories to develop a model which represents the underlying failure behaviour of the asset under study. These models can be of high value in ACP development due to the fact that Residual Useful Life (RUL) can be estimated and/or the long term life cycle cost can be optimized. The objective of this thesis was to model historical failure data and CM data well enough so that RUL or optimized preventive maintenance instant estimations can be made. These estimates were used in decision models to develop maintenance schedules, i.e. ACPs. Several regression models were evaluated to determine the most suitable model to achieve the objectives of this thesis. The model found to be most suitable for this research project was the Proportional Hazards Model (PHM). A comprehensive investigation on the PHM was undertaken focussing on the mathematics and the practical implementation thereof. Data obtained from the South African mining industry was modelled with the Weibull PHM. It was found that the developed model produced estimates which were accurate representations of reality. These findings provide an exciting basis for the development of futureWeibull PHMs that could result in huge maintenance cost savings and reduced failure occurrences.AFRIKAANSE OPSOMMING: Fisiese Bate Bestuur (FBB) is besig om ’n groter bekommernis vir maatskappye in die bedryf te word. Die Britse Standaarde Instituut se spesifikasie vir optimale bestuur van fisiese bates en infrastruktuur is PAS55. Volgens PAS55 is FBB die “sistematiese en gekoördineerde aktiwiteite en praktyke wat deur ’n organisasie optimaal sy fisiese bates, hul verwante prestasie, risiko’s en uitgawes vir die doel van die bereiking van sy organisatoriese strategiese plan beheer oor hul volle lewensiklus te bestuur”. Een Sleutel Fokus Area (SFA) van FBB is Bate Versorgings Plan (BVP) ontwikkeling. Hierdie is onderhouds strategieë wat bate betroubaarheid verbeter of verseker tydens die volle bruikbare lewe van die bate. Een onderhoud strategie is Toestands Gebasseeerde Onderhoud (TGO) wat besluite baseer op Toestand Monitering (TM) informasie maar neem nie die vorige falingsgeskiedenis van die bate in ag nie. Ander onderhoud strategieë soos Gebruik Gebasseerde Onderhoud (GGO) is gebaseer op historiese falingsdata maar neem nie TM inligting in ag nie. Regressiemodelle neem beide TM data en historiese falings geskiedenis data in ag ten einde die onderliggende falings gedrag van die gegewe bate te verteenwoordig. Hierdie modelle kan baie nuttig wees vir BVP ontwikkeling te danke aan die feit dat Bruikbare Oorblywende Lewe (BOL) geskat kan word en/of die langtermyn lewenssilus koste geoptimeer kan word. Die doelwit van hierdie tesis was om historiese falingsdata en TT data goed genoeg te modelleer sodat BOL of optimale langtermyn lewensiklus kostes bepaal kan word om opgeneem te word in BVP ontwikkeling. Hierdie bepalings word dan gebruik in besluitnemings modelle wat gebruik kan word om onderhoud skedules op te stel, d.w.s. om ’n BVP te ontwikkel. Verskeie regressiemodelle was geëvalueer om die regte model te vind waarmee die doel van hierdie tesis te bereik kan word. Die mees geskikte model vir die navorsingsprojek was die Proporsionele Gevaarkoers Model (PGM). ’n Omvattende ondersoek oor die PGM is onderneem wat fokus op die wiskunde en die praktiese implementering daarvan. Data is van die Suid-Afrikaanse mynbedryf verkry en is gemodelleer met behulp van die Weibull PGM. Dit was bevind dat die ontwikkelde model resultate geproduseer het wat ’n akkurate verteenwoordinging van realiteit is. Hierdie bevindinge bied ’n opwindende basis vir die ontwikkeling van toekomstige Weibull Proporsionele Gevaarkoers Modelle wat kan lei tot groot onderhoudskoste besparings en minder onverwagte falings