Mechanical Reliability

The third stage was the development of a theory of mechanical reliability, which grew naturally out of the study of mechanical systems subject to uncertainties. Traditionally, reliability has been studied using probabilistic tools, focussing on the question: what is the probability of mission accomplishment? However, many of the uncertainties in mechanical systems – geometrical imperfections, time-varying loads, material properties – arise due to unfamiliar environments, new materials or new uses of existing technology. Probability distributions can describe these uncertainties, but verifying a probability distribution may be arduous, and the subsequent analysis can also be very difficult. The disparity between what is known and what needs to be known is an information-gap, and by this time, the info-gap methodology for modelling and managing uncertainty was well developed, and ready to be extended to the field of reliability. The designer needs to choose between design alternatives in order to confidently satisfy performance specifications. The basic info-gap robustness question is: how wrong can the models and data be, and the design in question will still satisfy the performance requirements? A design which performs adequately over a large range of error is preferred over a design which performs adequately only if the design-base knowledge is nearly correct. Large robustness suggests more confidence in the design. In this way the info-gap robustness leads to a prioritization of the design options. Furthermore, this can be done without knowing a probability distribution.

(Ben-Haim, 1996)
Y. Ben-Haim, 1996, Robust Reliability in the Mechanical Sciences, Springer-Verlag, ISBN 3-540-61058-8.


Robust reliability is a new non-probabilistic theory of reliability of mechanical systems. It is based on convex information-gap models of uncertainty which express the gap between what is known and what needs to be known. Robust reliability is particularly suited to the types of fragmentary information characteristic of mechanical systems and structures.
The book is designed as an upper-level undergraduate or first-year graduate text of robust reliability of mechanical systems. It gives the student or engineer a working knowledge of robust reliability which will enable him to analyse the reliability of mechanical systems. Each chapter is introduced with a brief conceptual survey of the main ideas, which are then developed through examples. Problems at the end of each chapter give the reader the opportunity to strengthen his understanding.

Chapter 1: Preview of Robust Reliability
Chapter 2: Convexity and Uncertainty
Chapter 3: Robust Reliability of Static Systems
Chapter 4: Robust Reliability of Time-Varying Systems
Chapter 5: Fault Diagnosis, System Identification and Reliability Testing
Chapter 6: Reliability of Mathematical Models
Chapter 7: Convex and Probabilistic Models of Uncertainty
Chapter 8: Robust Reliability and the Poisson Process
Chapter 9: Last But Not Final

From Reviews of Robust Reliability in the Mechanical Sciences

“The book may be well recommended to all scientists, practicing engineers and students who are interested in reliability of mechanical systems.” Prof. L.Fryba, Czech Academy of Sciences. From Journal of Sound and Vibration.
“[A] particularly strong feature of the book is its extensive discussion of the motivation for developing robust reliability as a powerful alternative to the classical reliability theory.” Prof. George J. Klir, Binghamton University — SUNY. From International Journal of General Systems.

“Ben-Haim’s stimulating and elegantly written book should make it possible to develop pilot applications for testing and assessment by potential users — designers, code writers, insurers, and regulatory agencies. Given the incontestable limitations of other approaches, the approach developed by Ben-Haim should, in my opinion, be given thoughtful and informed consideration as a possibly useful complementary tool for investigating selected structural reliability problems.” Dr. Emil Simiu, NIST Fellow, National Institute of Standards and Technology. From Structural Safety.

“Robust reliability methods are very useful for problems in which little information is available … [which] is the case with many real life problems. Therefore, every reliability engineer should have these methods handy in his toolbox.” Prof. E. Nikolaides, Virginia Polytechnic Institute. From Structural Optimization.

Have you confronted design or planning problems for which standard methods are cumbersome or inadequate? Perhaps info-gap theory can help. Contact me at