Application of an M-out-of-N redundancy architecture is a well-known measure for improving the reliability of safety systems. Most scientific papers addressing the reliability assessment of such systems consider a conventional homogeneous M-out-of-N redundancy architecture that is performed for identical channels. However, often in practice, an M-out-of-N redundancy architecture does not have identical channels. Reliability assessment of such heterogeneous systems (electrical/electronic and mechanical) with nonidentical channels and a combination of constant and nonconstant failure rates is considered in this paper. Such type of M-out-of-N redundancy architecture is introduced in this research as "asymmetrical redundancy". It can be used for enhancing the reliability of old mechanical systems or for reducing mutual influence of channels and increase of diagnostic coverage. This paper also presents a new "window-based Markov method" for PFDavg (average probability of failure on demand) and PFH (average frequency of dangerous failures) calculation for systems with an asymmetrical redundancy architecture and compares the results with those obtained by using the steady-state semi-Markov method and Monte-Carlo simulation. The applicability of the developed method is demonstrated in a simple case study.

Reliability of transport equipment plays a crucial role in providing safety for passengers. Safety systems of transport equipment perform safety functions with assigned safety integrity levels (SIL). If the reliability of a safety system is not sufficient, it has to be improved till the required level. This can be done by improving maintenance, enhancement of diagnostics or by applying redundancy. To conclude that reliability value is sufficient (or not), it is necessary to calculate its value before and after reliability improvement. Such calculations can be done analytically or by a simulation approach. Usually simulation approach is time consuming for a large number of simulations. Small number of simulations leads to an error in the results. Therefore analytical methods are often welcomed by both – scientists and practitioners. This thesis investigates analytical methods of reliability calculation focusing on systems with degradation. Analytical formulas of reliability calculation have limitations for systems with degradation due to non-constant failure rates (in this thesis they are modelled by Weibull distribution). These limitations have been shown in the example of a braking system of moving walks in Chapter 3: analytical methods are mainly applicable only to systems with constant failure rates especially in the case of redundant systems.

Most analytical formulas developed for the PFD and PFH calculation assume a constant failure rate. This assumption does not necessarily hold for system components that are affected by wear. This article presents methods of analytical calculations of PFD and PFH for an M-out-of-N redundancy architecture with nonconstant failure rates and demonstrates its application in a simple case study. The method for PFD calculation is based on the ratio between cumulative distribution functions and includes forecasting of PFD values with a possibility of update of failure rate function. The approach for the PFH calculation is based on simplified formulas and the definition of PFH. In both methods, a Weibull distribution is used for characteristics of the system behavior. The PFD and PFH values are obtained for low, moderate and high degradation effects and compared with the results of exact calculations. Presented analytical formulas are a useful contribution to the reliability assessment of M-out-of-N systems.