Reliability from Theory to Practice: Model Limitations
Jorge Perciado - Asset Management Specialist at Work Management Solutions
Mathematical models, by which a system behaviour and outcomes can be represented and evaluated, are one of the main tools for directing management decisions in engineering applications. However, in the field of Reliability Engineering, mathematical precision and statistical method availability are limited by inherent levels of system variability and failure uncertainty . The use of probabilistic and statistical mathematical methods is useful for providing significative insights and forecasts into system behaviour and outcomes. Therefore, understanding model limitations is of critical importance to obtain meaningful data that lead to well-founded asset management decisions.
When choosing a reliability model, factors such as experience, scientific laws, failure history, and previous data from well-supported sources, are generally considered . Nevertheless, they do not necessarily reflect reality as well as deterministic engineering or physics-based formulae. Reliability models are simplified abstractions of reality due to the complexity of real-world systems, which are composed of many interrelated components. Thus, several assumptions are usually made in engineering for a system within defined boundaries, allowing the development and study of complex systems [3, 4].
The intrinsic variations in repairable systems must also be considered when employing mathematical models, as they generate differences between the model and real-life situations . Besides manufacturing and environmental variation, reliability variation is primarily influenced by people during the whole life cycle of a certain asset (designers, test engineers, manufacturers, suppliers, maintainers and users). Another source of variation is the effect of time on the system and its components. Change may occur over time, so the data and models generated at one time may be inadequate at other times [2, 3]. Moreover, as far as reliability is concerned, the most important variations usually occur in the tails of the probability density function, where there is inevitably less or no data. In these cases, the data are more uncertain and conventional statistic models can be misleading .
Besides intrinsic system variation, mathematical models as applied to reliability engineering, have other limitations. Variables in reliability engineering systems might interact with each other, causing combined effects different from their individual variation . Moreover, it is also very important to check the quality and veracity of data used in the model, otherwise, even the most robust and complex fuzzy Monte Carlo simulation will yield incorrect data. The statistical models to represent different situations must be chosen carefully because they may differ in their variables, constraints and methodologies. Any change or assumption applied to the model may drastically alter the fitting of the model. In fact, statistics already provide techniques to choose the best distribution and data models, which involve “goodness of fit” testing [1, 4]. These statistical tools should be combined with an understanding of the science, engineering and failure history of the assets. There is also a social limitation in the training of both engineers and statisticians. While most engineering training and education cover mainly deterministic engineering and mathematics, few statisticians are capable to understand the practical aspects and complexity of engineering problems . The gap between engineering practice and statistics leads to inappropriate analysis and conclusions from reliability results, which generates a general scepticism of statistical methods amongst engineers.
Despite their limitations, statistical methods provide a guide or indication of the behaviour and future outputs of a system. The use of mathematical models in reliability require human experience as well as a deep understanding of real scientific and engineering knowledge. Instead of asking only for a final reliability number or forecast, asset management professionals should assess results in light of the methodology, assumptions and boundaries of the models when making decisions.
1. Birolini, A., Reliability Engineering: Theory and Practice. 2013: Springer Berlin Heidelberg.
2. Richardson, B.C., Limitations on the use of mathematical models in transportation policy analysis. 1979, University Microfilms International, Ann Arbor, Mich.
3. Blischke, W.R. and D.P. Murthy, Reliability: modelling, prediction, and optimization. Vol. 767. 2011: John Wiley & Sons.
4. O'Connor, P. and A. Kleyner, Practical Reliability Engineering. 2012: Wiley