Reliability Analysis of Multi-state Systems with Heterogeneous Multi-state Elements Dmitrij Birjukov National Taras Shevchenko University of Kyiv Faculty of Cybernetics

Multi-state system example and definition Example. Let’s consider communication network that provide message passing. The information security achieved via information encoding. In the case of encoding unit(subsystem) failure, the network will still perform message passing, but with the lower level of security. So this system has at least 3 states. Definition. Systems that characterized by different levels of performance are known as multi-state systems (MSS). Another examples of MSS are power systems and computer systems, where the elements’ performance is characterized by generating capacity and data processing speed respectively. Most of reliability analysis and optimization models assume that system consists of binary-state components, where the states are functioning and failure. Binary-state reliability models don't allow to describe adequately: MSS operation processes, remaining resources, system state evolution, reasons of system failures and mechanisms of their prevention.

Report overview The aim of this work is to provide decision making framework for reliable MSS design. This report represents the following results: reliability model of multi-state system with heterogeneous multi- state elements; redundancy optimization problem for multi-state elements (where redundant elements are identical or non-identical).

Multi-state systems reliability models overview MSS reliability assessment based on (1) extension of the Boolean models to the multi-valued case, (2) stochastic processes (mainly Markov and semi-Markov) approach, (3) universal generating function approach. The main difficulty in the MSS reliability analysis is the “dimension damnation” since each system element can have many different states (not only two states as the binary-state system). This makes the known approaches overworked and time consuming, because the number of system states increases dramatically with the increase in the number of system elements. However, mentioned method were applied to simple models, such as the series, parallel systems (so called simple-structured systems models). In practice, technical systems are more complex, they include huge number of elements, that perform different tasks.

Multi-state systems reliability models overview Main restrictions of known multi-state reliability models are the following: state sets of elements consist states with same meaning (therefore each element have same number of identical states); state sets of elements are ordered (partially-ordered); system consists of elements with same functionality. The reliability evaluation is strongly required on the stage of system engineering design. To evaluate MSS reliability in the case of complex technical systems special mathematical approach and software are needed.

Multi-state system with heterogeneous elements (1)

Multi-state system with heterogeneous elements (2)

Multi-state system with heterogeneous elements (3)

Multi-state system with heterogeneous elements (4)

Multi-state system with heterogeneous elements (5)

Multi-state system with heterogeneous elements (6)

Multi-state system reliability and efficiency indexes (1)

Multi-state system reliability and efficiency indexes (2)

Multi-state System reliability and efficiency indexes (3)

Redundancy allocation of multi-state elements

MSSHE redundancy optimization problem

Conclusions When considering the system composed from heterogeneous elements (of different intending) known multi-state system reliability models can't be implemented. This paper presents a novel approach to multi-state complex- structured system reliability analysis. It provides decision making framework for reliable MSS design.