Why is the Remaining Useful Life Prediction Uncertain?



Published Oct 14, 2013
Shankar Sankararaman Kai Goebel


This paper discusses the significance and interpretation of uncertainty in the remaining useful life (RUL) prediction of components used in several types of engineering applications, and answers certain fundamental questions such as “Why is the RUL prediction uncertain?”, “How to interpret the uncertainty in the RUL prediction?”, and “How to compute the un- certainty in the RUL prediction?”. Prognostics and RUL pre- diction are affected by various sources of uncertainty. In or- der to make meaningful prognostics-based decision-making, it is important to analyze how these sources of uncertainty affect the remaining useful life prediction, and thereby, compute the overall uncertainty in the remaining useful life pre- diction. The classical (frequentist) and Bayesian (subjective) interpretations of uncertainty and their implications on prognostics are explained, and it is argued that the Bayesian interpretation of uncertainty is more suitable for remaining useful life prediction in the context of condition-based monitoring. Finally, it is demonstrated that the calculation of uncertainty in remaining useful life can be posed as an uncertainty propagation problem, and the practical challenges involved in computing the uncertainty in the remaining useful life prediction are discussed.

How to Cite

Sankararaman, S. ., & Goebel, K. . (2013). Why is the Remaining Useful Life Prediction Uncertain?. Annual Conference of the PHM Society, 5(1). https://doi.org/10.36001/phmconf.2013.v5i1.2263
Abstract 1015 | PDF Downloads 479



Uncertainty Quantification, Bayesian, Remaining useful Life, model-based prognosis, uncertainty propagation, interpretation

Bichon, B., Eldred, M., Swiler, L., Mahadevan, S., & McFar- land, J. (2008). Efficient global reliability analysis for nonlinear implicit performance functions. AIAA journal, 46(10), 2459–2468.
Bucher, C. G. (1988). Adaptive samplingan iterative fast monte carlo procedure. Structural Safety, 5(2), 119– 126.
Caflisch, R. E. (1998). Monte carlo and quasi-monte carlo methods. Acta numerica, 1998, 1–49.

Calvetti, D., & Somersalo, E. (2007). Introduction to bayesian scientific computing: ten lectures on subjective computing (Vol. 2). Springer New York.

Celaya, J., Saxena, A., & Goebel, K. (2012). Uncertainty representation and interpretation in model-based prognostics algorithms based on kalman filter estimation. In Proceedings of the Annual Conference of the PHM Society (pp. 23–27).

Celaya, J., Saxena, A., Kulkarni, C., Saha, S., & Goebel, K. (2012). Prognostics approach for power MOSFET un- der thermal-stress aging. In Reliability and Maintainability Symposium (RAMS), 2012 Proceedings-Annual (pp. 1–6).

Coppe, A., Haftka, R. T., Kim, N. H., & Yuan, F.-G. (2010). Uncertainty reduction of damage growth properties us- ing structural health monitoring. Journal of Aircraft, 47(6), 2030–2038.

Daigle, M., & Goebel, K. (2010). Model-based prognostics under limited sensing. In Aerospace Conference, 2010 IEEE (pp. 1–12).

Daigle, M., & Goebel, K. (2011). A model-based prognostics approach applied to pneumatic valves. International Journal of Prognostics and Health Management, 2(2).

Daigle, M., & Goebel, K. (2013). Model-based prog- nostics with concurrent damage progression pro- cesses. Systems, Man, and Cybernetics: Sys- tems, IEEE Transactions on, 43(3), 535-546. doi: 10.1109/TSMCA.2012.2207109

Daigle, M., Saxena, A., & Goebel, K. (2012). An efficient deterministic approach to model-based prediction un- certainty estimation. In Annual conference of the prog- nostics and health management society (pp. 326–335).

de Finetti, B. (1977). Theory of probability, Volumes I and II. Bull. Amer. Math. Soc. 83 (1977), 94-97, 0002–9904.

deNeufville, R. (2004). Uncertainty management for engineering systems planning and design. In Engineering systems symposium mit. Cambridge, MA..

Der Kiureghian, A., Lin, H.-Z., & Hwang, S.-J. (1987). Second-order reliability approximations. Journal of
Engineering Mechanics, 113(8), 1208–1225.

Dolinski, K. (1983). First-order second-moment approximation in reliability of structural systems: critical review and alternative approach. Structural Safety, 1(3), 211–

Engel, S. J., Gilmartin, B. J., Bongort, K., & Hess, A. (2000).Prognostics, the real issues involved with predicting life remaining. In Aerospace Conference Proceedings, 2000 IEEE (Vol. 6, pp. 457–469).

Farrar, C. R., & Lieven, N. A. (2007). Damage prognosis: the future of structural health monitoring. Philosophi- cal Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 365(1851), 623– 632.

Glynn, P. W., & Iglehart, D. L. (1989). Importance sampling for stochastic simulations. Management Science, 35(11), 1367–1392.

Gu, J., Barker, D., & Pecht, M. (2007). Uncertainty assessment of prognostics of electronics subject to random vibration. In AAAI fall symposium on artificial intelligence for prognostics (pp. 50–57).

Haldar, A., & Mahadevan, S. (2000). Probability, reliability, and statistical methods in engineering design. John Wiley & Sons, Incorporated.

Hastings, D. and McManus, H. (2004). A framework for understanding uncertainty and its mitigation and exploitation in complex systems. In Engineering Systems Symposium MIT (p. 19). Cambridge MA..

Hohenbichler, M., & Rackwitz, R. (1983). First-order con- cepts in system reliability. Structural safety, 1(3), 177– 188.

Liao, H., Zhao, W., & Guo, H. (2006). Predicting remaining useful life of an individual unit using proportional haz- ards model and logistic regression model. In Reliability and Maintainability Symposium, 2006. RAMS’06. An- nual (pp. 127–132).

Loh, W.-L. (1996). On latin hypercube sampling. The annals of statistics, 24(5), 2058–2080.

Ng, K.-C., & Abramson, B. (1990). Uncertainty management in expert systems. IEEE Expert Systems, 20.

Orchard, M., Kacprzynski, G., Goebel, K., Saha, B., & Vacht- sevanos, G. (2008, oct.). Advances in uncertainty representation and management for particle filtering applied to prognostics. In Prognostics and Health Management, 2008. PHM 2008. International Conference on (p. 1 -6). doi: 10.1109/PHM.2008.4711433

Popper, K. (1959). The propensity interpretation of probability. The British journal for the philosophy of science, 10(37), 25–42.

Saha, B., & Goebel, K. (2008). Uncertainty management for diagnostics and prognostics of batteries using Bayesian techniques. In Aerospace Conference, 2008 IEEE (pp. 1–8).

Sankararaman, S. (2012). Uncertainty quantification and integration in engineering systems (Ph.D. Dissertation). Vanderbilt University.

Sankararaman, S., Daigle, M., Saxena, A., & Goebel, K. (2013). Analytical algorithms to quantify the uncertainty in remaining useful life prediction. In Aerospace Conference, 2013 IEEE (pp. 1–11).

Sankararaman, S., & Goebel, K. (2013, Apr). Uncertainty quantification in remaining useful Life of aerospace components using state space models and inverse FORM. In Proceedings of the 15th Non-Deterministic Approaches Conference.

Sankararaman, S., Ling, Y., & Mahadevan, S. (2011). Un- certainty quantification and model validation of fatigue crack growth prediction. Engineering Fracture Mechanics, 78(7), 1487–1504.

Sankararaman, S., Ling, Y., Shantz, C., & Mahadevan, S. (2011). Uncertainty quantification in fatigue crack growth prognosis. International Journal of Prognostics and Health Management, 2(1).

Sankararaman, S., & Mahadevan, S. (2011). Likelihood- based representation of epistemic uncertainty due to sparse point data and/or interval data. Reliability En- gineering & System Safety, 96(7), 814–824.

Szabo ́, L. (2007). Objective probability-like things with and without objective indeterminism. Studies In History and Philosophy of Science Part B: Studies In History and Philosophy of Modern Physics, 38(3), 626–634.

Tang, L., Kacprzynski, G., Goebel, K., & Vachtsevanos, G. (2009, march). Methodologies for uncertainty management in prognostics. In Aerospace conference, 2009 IEEE (p. 1 -12). doi: 10.1109/AERO.2009.4839668

Van Zandt, J. R. (2001). A more robust unscented transform. In International symposium on optical science and technology (pp. 371–380).

Von Mises, R. (1981). Probability, statistics and truth. Dover Publications.
Technical Research Papers

Most read articles by the same author(s)

1 2 3 4 5 > >>