Abstract A Markov approach has been used to perform RAM (Reliability, Availability and Maintainability) analysis for a parallel system consisting of two non-identical units. Preventive maintenance is incorporated to reduce the risk of unexpected failures. One unit does not fail during maintenance and is fully restored. The analysis is based on the Chapman–Kolmogorov equations, which are solved using the Laplace transform method with Mathematica version 12.30. The failure and repair rates of the units are assumed to be constant, implying that the times follow a negative exponential distribution. A cost-benefit analysis has also been carried out using specific values for the failure and repair rates. Sensitivity analysis is conducted to examine the influence of system parameters on performance measures, with results presented through tables and graphical illustrations. Furthermore, a cost-benefit analysis is performed to evaluate the economic viability of the system under different operational scenarios. To highlight the practical relevance of the study, real-world applications have been discussed, particularly focusing on the functioning of Automated Teller Machines (ATMs) and Green Channel counters in banks.
Yadav et al. (2026) studied this question.