Estimating Remaining Useful Life Using Actuarial Methods



Eric Bechhoefer Rune Schlanbusch Tor Inge Waag


In many instances, condition monitoring equipment has not been installed on machinery. Yet, operators still need guidance as to when to perform maintenance that is better than what is offered by the equipment manufacturers. For these systems, running hours, counts, or some other measure of usage may be available. This data, along with failure rate data, can provide an expected time to failure, and the estimated remaining useful life. The failure rate (even small sample size) is used to estimate the shape and scale parameters for the Weibull distribution. Then the conditional expectation of the truncated survival function of the Weibull is used to estimate the time to failure. This is an actuarial technique to solve the conditional survival function problem of: given that the equipment has survived to time x, what is that probability of the equipment surviving to time x + y. The inverse cumulative distribution of the truncated survival function can then be used to estimate the remaining useful life, that is: a time when the conditional likelihood of failure is small, such as 10%. The 90% confidence of the shape and scale parameters is then used to give a bound on the remaining useful life. This method is then tested on a real world bearing dataset.

How to Cite

Bechhoefer, E., Schlanbusch, R. ., & Inge Waag, T. . (2015). Estimating Remaining Useful Life Using Actuarial Methods. Annual Conference of the PHM Society, 7(1).
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Weibull distribution, Conditional Probability, RUL, survival function

Abernaethy, R. (1996), The New Weibull Handbook. Gulf Publishing, Houston, Tx.

Bechhoefer, E., He, D. (2012). A Process for Data Driven Prognostics. MFPT Proceeding.

Cohen, A. (1965). Maximum Likelihood Estimation in the Weibull Distribution based on Complete and Censored Samples. Technometrics, Vol. 7, No 4, 1965.

London, D., (1997). Survival Models and Their Estimation. ACTEX Publishing Winsted, CT.
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