Proceedings of the

The 33rd European Safety and Reliability Conference (ESREL 2023)
3 – 8 September 2023, Southampton, UK

Confidence Intervals for RUL: A New Approach based on Time Transformation and Reliability Theory

Pierre Dersin1 and Roberto Rocchetta2

1Division of Operations & Maintenance Engineering, Luleå University of Technology, Sweden.

2Department for Environment Constructions and Design, Intelligent Energy Systems Group, University of Applied Science and Arts of Southern Switzerland, SUPSI-ISAAC, Switzerland.


This work describes a new analytical approach to derive confidence intervals on Remaining Useful Life (RUL) estimators. The new method applies a time transformation to make the Mean Residual Life (MRL) a linearly decreasing function of the transformed time. Then, explicit confidence bounds for the RUL are derived in the linear MRL case and mapped back to the physical space with the inverse time transformation. A reliability assessment problem of Light-emitting diodes (LEDs) that have undergone accelerated degradation tests, and for which confidence bound and RUL must be provided, demonstrates the new approach. LEDs fail when the luminous flux depreciation exceeds a maximum threshold and the time to failure corresponds to the first hitting time. In this case, Weibull distributed first hitting time is a realistic assumption, which allows the above time transformation method to be carried out explicitly. It is then shown that, if an alternative model (a Gamma distribution, with an appropriate shape factor) had been adopted instead, the results would be quite close to those obtained initially. The key parameter is the slope of the MRL in the transformed time; that parameter can be explicitly related to the shape factor of the Weibull or Gamma distribution. Comprised between 0 and 1, it is used to build the confidence interval; the larger its value (the steeper the slope, i.e., the faster the degradation), the lower the variance of the RUL is, and the narrower the confidence interval. Similar results can be obtained with a Wiener or a Gamma process, which suggests a distributional robustness of this approach. We believe this time transformation approach to be advantageous when the computational efficiency and robustness of the RUL estimation are of primary importance. It also provides useful insights into the dynamics of RUL, which are linked to the ageing characteristics.

Keywords: RUL, Time transformation, Confidence interval, Mean residual life, LED, Degradation.

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