Gradient Estimation for Multicomponent Maintenance Systems with Age-Replacement Policy

Abstract

We consider multicomponent maintenance systems with an F -failure group age-replacement policy: it keeps failed components idling until F components are failed and then replaces all failed components together with the nonfailed components whose age has passed the critical threshold age n for components of type n. With each maintenance action, costs are associated. We derive various unbiased gradient estimators based on the measure-valued differentiation approach for the gradient of the average cost. Each estimator has its own domain of applicability. We also compare the performance of our gradient estimators when applied to stochastic optimization with other general gradient-free methods.

Optimal Control of a Partially Observable Failing System with Costly Multivariate Observations

“…Some recent and classical survey articles on maintenance optimization can be found be Refs. [7,33,34] Other noteworthy recent contributions are: Dayanik and Gurler, [11] Dogramaci and Fraiman, [12] Heidergott and Farenhorst-Yuan, [15] Kurt and Kharoufeh, [23] Makis and Jiang, [27] and Ulukus et al, [32] among others. In addition to the theoretical work done in this area, maintenance models have been successfully applied in many real world applications including furnace erosion prediction using the state-space model, [8] transmission fault detection using the proportional hazards model, [26] and helicopter gearbox state assessment using the hidden Markov model.…”

Gradient estimation for smooth stopping criteria

“…Alternatively, a variant of the score function method, called the push-out score function, has been developed for this kind of threshold optimization in inventory models; see [35], as well as [36] for an early reference. For a perturbation analysis of a maintenance model where θ triggers (preventive) maintenance of system components whose age exceeds θ , we refer to [19,16]. Finally, for applications to financial models, where θ is the value of a barrier in some option model, we refer to [15,31,17,21].…”

Forecasting remaining useful life: Interpretable deep learning approach via variational Bayesian inferences

“…Maintenance of physical equipment, machinery, systems and even complete infrastructure represents an essential process for ensuring successful operation. It helps minimizing downtime of technical equipment [1], eliminate the risk thereof [2], or prolong the life of systems [3]. Maintenance is often enforced by external factors, such as regulations or quality management [4].…”

“…For instance, the International Air Transport Association (IATA) reported that maintenance costs of 49 major airlines increased by over 3 percent from 2012 to 2016, finally totaling $15.57 billion annually. 1 Decision support in maintenance can be loosely categorized according to two different objectives depending on whether they serve a corrective or preemptive purpose. 2 The former takes place after the failure of machinery with the goal of restoring its operations back to normal.…”

“…Machine learning models are subject to an inherent drawback: they frequently operate in a blackbox fashion [10,11,12], which, when providing decision support, directly impedes potential insights into the underlying rules behind their decision-making. However, interpretability is demanded for a 1 International Air Transport Association (IATA). Airline maintenance cost executive commentary.…”