2021 Annual Meeting

(345m) Fitting of Failure Models with Bathtub-Shaped Failure Rate to Data Using Optimization Algorithms

Authors

Ikonen, T. - Presenter, Aalto University
Corona, F., Aalto University
Harjunkoski, I., Hitachi ABB Power Grids
Industrial production plants may contain hundreds or even thousands of components (e.g., valves, drives, pumps, and electrical motors) that degrade over time. If the component is not replaced, the degradation eventually leads to a failure. The ongoing integration of information system at the different automation hierarchy levels and cheaper sensors enable more extensive and systematic collection of process data [1]. In this work, we focus on component lifetime data. By collecting the component lifetimes, and their operating conditions, the plant operators can make predictions of component-specific failure probabilities during the next operation window. The predictions can be used to decide appropriate component replacement times, leading to more reliable and safer operation of the plant.

An engineering component often has a bathtub-shaped failure rate, which is a combination of three simultaneous failure phenomena: a decreasing infant mortality rate, a constant random failure rate, and an increasing failure rate due to degradation. The literature of such failure models is fairly established. Many of these models are generalizations of the Weibull distribution (see, e.g., [2-10]), but may also be a derived from other probability distributions, such as the Gompertz distribution [11] or the Burr distribution [12].

In order to make predictions of the failure probabilities using these models, the model parameters need to be fitted to the lifetime data, e.g., by maximizing the log-likelihood. While some authors explicitly maximize the log-likelihood function, a commonly used approach in the literature is to find a point in the parameter space where the partial derivatives of the log-likelihood are zero. As these log-likelihood functions are non-convex, the approach may result in a local optimum or a local maximum (or even a saddle point).

In this work, we fit 10 failure models [2-11] to two widely studied datasets [13, 14] (with a bathtub-shaped failure rate) by maximizing the log-likelihood using three algorithms for non-linear optimization from the Scipy.optimize library [15]. The optimization algorithms are Nelder-Mead with adaptive parameters [16], SLSQP [17], and L-BFGS-B [18]. Each model fitting is conducted by performing optimization procedures repeatedly from 100 randomly chosen points in the parameter space. We show that better fit can be found for 12 out of 16 model-dataset pairs, for which reference parameters are available. We also discuss the performance of the optimization algorithms and give recommendations for selecting an algorithm. Finding better fittings is important as they improve the accuracy of the failure probability predictions, and thus have an impact on the decision-making of potentially costly component replacements. We demonstrate the difference in the decision-making using one of the failure model-dataset pairs [6, 13] on a data-driven selective maintenance optimization problem [19].

References
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