Chapter 4
Reliability Theory
Daniel Krpelík, Frank P. A. Coolen, and Louis J. M. Aslett
Abstract Devices are of little use to us if they do not function properly, but whether
they will function or not is subjected to uncertainty. Reliability theory studies the
failure laws, i.e. constructs models and reasons with the chance that a device is
functioning. Once we have obtained such models, we can take the reliability aspects
into account during the design process.
This chapter introduces basics of mathematical reliability theory with emphasis
on how can the reliability depend on design parameters.
Keywords Reliability · Survival analysis · System reliability · Design for
reliability
4.1 Reliability and Risk
Causality is an essential principle which aids us to cope with the complexity of the
world and, at least approximately, and to predict possible consequences of various
actions. Nevertheless, since our understanding of the world comes from idealised
models with limited scope of applicability, the derived predictions will usually
deviate from the observed reality. As a result, we are generally not able to predict
future events with absolute certainty. That is why we need to generalise our methods
of reasoning to release ourselves from the shackles of binary logic and to include
statements about possibilities and their various degrees of credibility, which allows
us to rigorously address notions of “likeliness”, “chance” and “probability”.
D. Krpelík ()
Department of Mathematical Sciences, Durham University, Durham, UK
Department of Applied Mathematics, VŠB - Technical University of Ostrava, Ostrava, Czechia
e-mail: daniel.krpelik@durham.ac.uk
F. P. A. Coolen · L. J. M. Aslett
Durham University, Durham, UK
© Springer Nature Switzerland AG 2021
M. Vasile (ed.), Optimization Under Uncertainty with Applications to Aerospace
Engineering, https://doi.org/10.1007/978-3-030-60166-9_4
111
Reliability Theory
Daniel Krpelík, Frank P. A. Coolen, and Louis J. M. Aslett
Abstract Devices are of little use to us if they do not function properly, but whether
they will function or not is subjected to uncertainty. Reliability theory studies the
failure laws, i.e. constructs models and reasons with the chance that a device is
functioning. Once we have obtained such models, we can take the reliability aspects
into account during the design process.
This chapter introduces basics of mathematical reliability theory with emphasis
on how can the reliability depend on design parameters.
Keywords Reliability · Survival analysis · System reliability · Design for
reliability
4.1 Reliability and Risk
Causality is an essential principle which aids us to cope with the complexity of the
world and, at least approximately, and to predict possible consequences of various
actions. Nevertheless, since our understanding of the world comes from idealised
models with limited scope of applicability, the derived predictions will usually
deviate from the observed reality. As a result, we are generally not able to predict
future events with absolute certainty. That is why we need to generalise our methods
of reasoning to release ourselves from the shackles of binary logic and to include
statements about possibilities and their various degrees of credibility, which allows
us to rigorously address notions of “likeliness”, “chance” and “probability”.
D. Krpelík ()
Department of Mathematical Sciences, Durham University, Durham, UK
Department of Applied Mathematics, VŠB - Technical University of Ostrava, Ostrava, Czechia
e-mail: daniel.krpelik@durham.ac.uk
F. P. A. Coolen · L. J. M. Aslett
Durham University, Durham, UK
© Springer Nature Switzerland AG 2021
M. Vasile (ed.), Optimization Under Uncertainty with Applications to Aerospace
Engineering, https://doi.org/10.1007/978-3-030-60166-9_4
111