Roger Flage & Terje Aven
EXPRESSING AND COMMUNICATING UNCERTAINTY IN RELATION TO QUANTITATIVE RISK ANALYSIS
A quantitative risk analysis (QRA) should provide a broad, informative and balanced picture of risk, in order to support decisions. To achieve this, a proper treatment of uncertainty is a prerequisite. Most approaches to treatment of uncertainty in QRA seem to be based on the thinking that uncertainty relates to the calculated probabilities and expected values. This causes difficulties when it comes to communicating what the analysis results mean, and could easily lead to weakened conclusions if large uncertainties are involved. An alternative approach is to hold uncertainty, not probability, as a main component of risk, and regard probabilities purely as epistemic-based expressions of uncertainty. In the paper the latter view is taken, and we describe what should be the main components of a risk description when following this approach. We also indicate how this approach relates to decision-making. An important issue addressed is how to communicate the shortcomings and limitations of probabilities and expected values. Sensitivity analysis plays a key role in this regard. Examples are included to illustrate ideas and findings.

A. Blokus-Roszkowska, K. Kołowrocki
MODELLING ENVIRONMENT AND INFRASTRUCTURE OF SHIPYARD TRANSPORTATION SYSTEMS AND PROCESSES
In the paper an analytical model of port transportation systems environment and infrastructure influence on their operation processes is constructed and presented in an example of shipyard rope transportation systems in Naval Shipyard in Gdynia. A general semi-markov model of a system operation process is proposed and the methods of its parameters statistical identification are presented. Further, the shipyard rope transportation system and the ship rope elevator operation processes are analyzed and their operation states are defined. A preliminary collection of statistical data necessary to the ship transportation systems’ operation processes identification is included.

P. Baraldi, E. Zio, M. Compare
IMPORTANCE MEASURES IN PRESENCE OF UNCERTAINTIES
This paper presents a work on the study of importance measures in presence of uncertainties originating from the lack of knowledge and information on the system (epistemic uncertainties). A criterion is proposed for ranking the risk contributors in presence of uncertainties described by probability density functions.

L. Gucma, M. Schoeneich
MONTE CARLO METHOD OF SHIP’S UNDERKEEL CLEARANCE EVALUATION FOR SAFETY OF FERRY APPROACHING TO YSTAD PORT DETERMINATION
The paper is concerned with the analysis of simulation research results of newly design Piast ferry entering to modernized Ystad Port. The ship simulation model is described. After execution of real time simulations the Monte Carlo method of underkeel clearance evaluation is applied to asses the probability of ferry touching the bottom. The results could be used in risk assessment of ships entering to the ports.

L. Gucma
METHODS OF SHIP-BRIDGE COLLISION SAFETY EVALUATION
The paper presents methods and models used nowadays for risk assessment of ship-bridge collisions.

R. Guo, D. Guo
DEAR THEORY IN SYSTEM DYNAMIC ANALYSIS
In this paper, we introduce our newly created DEAR (an abbreviation of Differential Equation Associated Regression) theory, which merges differential equation theory, regression theory and random fuzzy variable theory into a new rigorous small sample based inferential theoretical foundation. We first explain the underlying idea of DEAR modelling, its classification, and then the M-estimation of DEAR model. Furthermore, we explore the applicability of DEAR theory in the analysis in system dynamics, for example, repairable system analysis,
quality dynamics analysis, stock market analysis, and ecosystem analysis, etc.

 

S. Guze
RELIABILITY ANALYSIS OF TWO-STATE SERIES-CONSECUTIVE “M OUT OF K: F” SYSTEMS
A non-stationary approach to reliability analysis of two-state series and consecutive “m out of k: F” systems is presented. Further, the series-consecutive “m out of k: F” system is defined and the recurrent formulae for its reliability function evaluation are proposed. Moreover, the application of the proposed formulae to reliability evaluation of the radar system composed of two-state components is illustrated.

B. Kwiatuszewska-Sarnecka, K. Kołowrocki, J. Soszyńska
MODELLING OF OPERATIONAL PROCESSES OF BULK CARGO TRANSPORTATION SYSTEM
A general analytical model of industrial systems infrastructure influence on their operation processes is constructed. Next, as its particular case a detailed model of port infrastructure influence on port transportation systems operation processes is obtained to apply and test it to selected transportation systems used in Gdynia Port.

D. Montoro-Cazorla
SHOCK MODELS UNDER POLICY N
We present the life distribution of a device subject to shocks governed by phase-type distributions. The probability of failures after shocks follows discrete phase-type distribution. Lifetimes between shocks are affected by the number of cumulated shocks and they follow continuous phase-type distributions. The device can support a maximum of N shocks. We calculate the distribution of the lifetime of the device and illustrate the calculations by means of a numerical application. Computational aspects are introduced. This model extends
other previously considered in the literature.
 

 

Joanna Soszynska
ASYMPTOTIC APPROACH TO RELIABILITY EVALUATION OF LARGE “M OUT OF L”-SERIES SYSTEM IN VARIABLE OPERATION CONDITIONS
The semi-markov model of the system operation process is proposed and its selected parameters are defined. There are found reliability and risk characteristics of the multi-state “m out of l”-series system. Next, the joint model of the semi-markov system operation process and the considered multi-state system reliability and risk is constructed. The asymptotic approach to reliability and risk evaluation of this system in its operation process is proposed as well.

C. Tanguy
ASYMPTOTIC DEPENDENCE OF AVERAGE FAILURE RATE AND MTTF FOR A RECURSIVE, MESHED NETWORK ARCHITECTURE
The paper is concerned with the exact and asymptotic calculations of the availability, average failure rate and MTTF (Mean Time To Failure) for a recursive, meshed architecture proposed by Beichelt and Spross. It shows that the asymptotic size dependences of average failure rate and MTTF are different, but not inverse of each other, as is unfortunately assumed too frequently. Besides, the asymptotic limit is reached for rather small networks.

D Valis
CONTRIBUTION TO FAILURE DESCRIPTION
In our lives we meet many events which have very diverse causes, mechanisms of development and consequences. We frequently work with the events´ description besides other assessments in safety/risk assessment. In pure technical applications these events are related with the failure occurrence of equipment, a device, a system or an item. The theory speaks about failure itself, its mechanisms, circumstances of occurrence, etc. but at the same time we need appropriate terminology to describe these conditions. Our basic approaches into observing, dealing and handling failure may fall into two groups. We either talk about a probabilistic approach or about a deterministic (logic) approach. As we need to get some information about a failure we need to find it or transfer it from different sources. This contribution can be a complex problem for the term “failure” and its related characteristics. In the paper there are mentioned functions of an object and their description, classification of failures, main characteristics of failure, possible causes of failure, mechanisms of failure and consequences of failure and also other contributions related with failure very closely.

 

D. Valis
CONTRIBUTION TO AVAILABILITY ASSESSMENT OF COMPLEX SYSTEMS
As we use complex systems with one shot items in many technical applications we need to know basic characteristics of such system. Performance, safety and other are as much important as dependability measures. In real applications we have to take into account a related distribution of an observed variable. In terms of complex systems with one shot items it is a discrete random variable related to one shot item. The whole system and its failures (unexpected and inadvertent events) may have two typical types of distributions and their
characteristics. We either consider a continuous variable (such as time, mileage, etc.) or a counting variable (such as number of cycles, sequences, etc.) regarding to a failure occurrence. As the one shot items is supposed to back up the main system function the total reliability of the system should be higher than. The main issue regarding the system using one shot items in their construction is to determine the probability of the task (mission) success. The paper presents both theoretical approach and practical example of the solution.

Mateusz Zajac, Tymoteusz Budny
ON DETERMINATION OF SOME CHARACTERISTICS OF SEMI-MARKOV PROCESS FOR DIFFERENT DISTRIBUTIONS OF TRANSIENT PROBABILITIES
There is a model of transport system presented in the paper. The possible semi - Markov process definitions are included. The system is defined by semi – Markov processes, while functions distributions are assumed. There are attempts to assess factors for other than exponential functions distributions. The paper consist discussion on Weibull and Gamma distribution in semi – Markov calculations. It appears that some forms of distribution functions makes computations extremely difficult.

Xuejing Zhao, Mitra Fouladirad, Christophe Bérenguer, Laurent Bordes
MAINTENANCE POLICY FOR DETERIORATING SYSTEM WITH EXPLANATORY VARIABLES
This paper discusses the problem of the optimization of maintenance threshold and inspection period for a continuously deteriorating system with the influence of covariates. The deterioration is modeled by an increasing stochastic process. The process of covariates is assumed to be a temporally homogeneous finite-state Markov chain. A model similar to the proportional hazards model is used to represent the influence of the covariates. Parametric estimators of the unknown parameters are obtained by using Least Square Method. The optimal
maintenance threshold and the optimal inspection interval are derived to minimize the expected average cost. Comparisons of the expected average costs under different conditions of covariates and different maintenance policies are given by numerical results of Monte Carlo simulation.

J. Okulewicz, T. Salamonowicz
PREVENTIVE MAINTENANCE WITH IMPERFECT REPAIRS OF A SYSTEM WITH REDUNDANT OBJECTS
An object ability to realise tasks may be restored by repairing only failed components. This is called imperfect repair as the object is not as good as new after such a repair. Preventive replacement is an example of imperfect repair as well. The advantage of such maintenance is that it enables controlling a reliability level of a system. Sets of objects’ components which should be replaced are derived on a basis of statistical diagnosing with use of data about components failures. The acceptable level of a failure risk while executing transportation tasks has been taken as a criterion of choosing elements to be replaced. An algorithm of selecting components for preventive replacement has been developed. It was shown that a level of a system reliability can be controlled by changing an order of a quantile function in coordination and a number of redundant objects. A computer simulation model of the system was used to illustrate derived dependencies.

Jakub Nedbalek
RBF NETWORKS FOR FUNCTION APPROXIMATION IN DYNAMIC MODELLING
The paper demonstrates the comparison of Monte Carlo simulation algorithm with neural network enhancement in the reliability case study. With regard to process dynamics, we attempt to evaluate the tank system unreliability related to the initiative input parameters setting. The neural network is used in equation coefficients calculation, which is executed in each transient state. Due to the neural networks, for some of the initial component settings we can achieve the results of computation faster than in classical way of coefficients calculating and substituting into the equation.

M.F. Milazzo, G. Maschio, G. Uguccioni
FREQUENCY ASSESSMENT OF LOSS OF CONTAINMENT INCLUDING THE EFFECTS OF MEASURES OF RISK PREVENTION

This paper presents a method for the quantification of the effects of measures of risk prevention of the frequency for rupture of pipework. Some methodologies, given in the literature for this purpose, assume that each plant under analysis is characterized by the same combinations of causes of failure and prevention mechanisms but this assumption is not always true. The approach suggested here is based on the methodology proposed in 1999 by Papazoglou for the quantification of the effects of organizational and managerial factors. Taking advantage of this methodology the objective of the assessment of the influence of measures of risk prevention in pipework has
been achieved through the definition of the links between the causes of failure and the measures adopted by the company in order to prevent and/or to mitigate them.

Krzysztof Kolowrocki, Joanna Soszynska
MODELLING ENVIRONMENT AND INFRASTRUCTURE INFLUENCE ON RELIABILITYAND OPERATION PROCESSES OF PORT OIL TRANSPORTATION SYSTEM
In the paper a probabilistic model of industrial systems environment and infrastructure influence on their operation processes is proposed. Semi-markov processes are used to construct a general model of complex industrial systems’ operation processes. Main characteristics of this model are determined as well. In particular case, for a port oil transportation system, its operation states are defined, the relationships between them are fixed and particular model of its operation process is constructed and its main characteristics are determined. Further, the joint model of the system operation process and the system reliability is defined sand applied to the reliability evaluation of the port oil transportation system.