Abstract
Reliability is naturally one of the most important properties of processing systems, still there is no general method that is capable of simultaneously considering the reliability during the design procedure. Consequently, the optimality of the decisions in process design cannot be guaranteed. The main reason of the lack of general method is that the process design and the reliability engineering are based on different types of mathematical modelling tools. While process design traditionally considered as mixed-integer optimization, reliability engineering is based on probability theory, therefore, a general modelling tool is required that can conveniently cover these two areas. In the present work, it has been shown that the formerly developed combinatorial approach to process network synthesis, the so-called P-graph framework, can conveniently cover and integrate these two areas. The method for reliability analysis of processing systems is general and can effectively analyze complex, highly interconnected networks. Furthermore, the reliability analysis method given here can be embedded to process design tools. A formerly unavailable formula, the system reliability formula has also been defined for processing networks. The focus of the present work is on structures of processing systems, all statements and algorithms are general and proved. The solutions of challenging real problems are also given.
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Abbreviations
- n :
-
Number of operating units
- \(p_i\) :
-
Reliability of a unit
- \(\varvec{p}\) :
-
Reliability vector
- \(x_i\) :
-
Functionality of a unit (binary)
- X :
-
State of a system (binary vector)
- U :
-
Set of structurally operational subnetworks
- \(\hat{r}\) :
-
Reliability of the system
- P :
-
Set of products in a PNS problem
- R :
-
Set of raw materials in a PNS problem
- O :
-
Set of operating units in a PNS problem
- \([y_0,y_1]\) :
-
Directed path on graph
- L :
-
Set of combinatorially feasible subnetworks
- \(\varPsi \) :
-
Operability function of a system
- \(\varOmega \) :
-
Set of all subnetworks of the network
- \(\wp \) :
-
Power set
- P(U):
-
Probability of event U
- PNS:
-
Process network synthesis
- MIP:
-
Mixed integer programming
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Kovacs, Z., Orosz, A. & Friedler, F. Synthesis algorithms for the reliability analysis of processing systems. Cent Eur J Oper Res 27, 573–595 (2019). https://doi.org/10.1007/s10100-018-0577-0
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DOI: https://doi.org/10.1007/s10100-018-0577-0