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DIN/VDI Standards Committee Acoustics, Noise Control and Vibration Engineering

Overview

A reliability block diagram (RBD) is a pictorial representation of the successful functioning of a system. It shows the logical connection of the (functional) components (represented by blocks) required for the successful operation of the system (hereinafter referred to as "system success"). Consequently, a RBD is equivalent to a logical equation of Boolean variables and the probability calculations are primarily related to constant values of the success/failure probabilities of a block. There are many different analytical methods available for reliability analysis, of which the reliability block diagram (RBD) is one. Consequently, before deciding to use the RBD, the analyst should investigate the purpose of each technique and its individual or combined applicability for assessing the availability, survival probability, failure frequency and other measures of reliability of a given system or component. The results obtainable from each method, the data required for performing the analysis, the complexity of the analysis and other factors identified in this standard should also be taken into consideration. Assuming that the blocks in the RBD behave independently of each other and that the order in which failures occur is not important, the calculations can be extended to time-dependent probability calculations that include both unrepaired and repaired blocks (for example, blocks representing unrepaired or repaired components). In this case, three reliability steps related to the successful functioning of the system shall be considered: the survival probability itself, RS(t), but also the availability, AS(t), and the failure frequency wS(t). While the calculations of AS(t) and wS(t) for systems with repaired components can be carried out relatively easily, the calculation of RS(t) is subject to systemic dependencies that cannot be taken into account within the mathematical framework of RBD. Nevertheless, approximations of RS(t) are available in certain cases. The RBD technique is linked to fault tree analysis and Markov techniques: - the underlying mathematics is the same for RBD and fault tree (FT): While RBD focuses on system success, FT focuses on system failure. It is always possible to transfer a RBD into an FT and vice versa. From a mathematical point of view, RBD and FT models share dual logical expressions. Consequently, the mathematical developments and restrictions are similar in both cases. - If the availability, Ai(t), of a block can be computed using an individual Markov process independently of the other blocks, this availability, Ai(t), can be used as input for computations related to a RBD including this block. This approach, in which the RBD provides the logical structure and the individual Markov processes provide the numerical values of the availability of the blocks, is referred to as "RBD-driven Markov processes". For systems where the order of failures shall be considered, or where the repaired blocks do not behave independently, or where the survival probability of the system, RS(t), cannot be calculated by analytical methods, Monte Carlo simulation or other modeling techniques, such as dynamic RBD, Markov or Petri net techniques, may be more appropriate. The responsible committee is DKE/K 132 "Zuverlässigkeit" ("Reliability") of the DKE (German Commission for Electrical, Electronic and Information Technologies) at DIN and VDE.

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Responsible national committee

DKE/K 132 - Zuverlässigkeit