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Open AccessArticle

Optimization of Condition Monitoring Decision Making by the Criterion of Minimum Entropy

by Ahmed Raza 1 and Vladimir Ulansky 2,3,*
1
Projects and Maintenance Section, The Private Department of the President of the United Arab Emirates, Abu Dhabi 000372, UAE
2
Research and Development Department, Mathematical Modelling & Research Holding Limited, London W1W 7LT, UK
3
Department of Electronics, Robotics, Monitoring Technology, and IoT, National Aviation University, 03058 Kyiv, Ukraine
*
Author to whom correspondence should be addressed.
Entropy 2019, 21(12), 1193; https://doi.org/10.3390/e21121193
Received: 12 October 2019 / Revised: 17 November 2019 / Accepted: 30 November 2019 / Published: 4 December 2019
(This article belongs to the Section Multidisciplinary Applications)
Condition-based maintenance (CBM) is a promising technique for a wide variety of deteriorating systems. Condition-based maintenance’s effectiveness largely depends on the quality of condition monitoring. The majority of CBM mathematical models consider perfect inspections, in which the system condition is assumed to be determined error-free. This article presents a mathematical model of CBM with imperfect condition monitoring conducted at discrete times. Mathematical expressions were derived for evaluating the probabilities of correct and incorrect decisions when monitoring the system condition at a scheduled time. Further, these probabilities were incorporated into the equation of the Shannon entropy. The problem of determining the optimal preventive maintenance threshold at each inspection time by the criterion of the minimum of Shannon entropy was formulated. For the first time, the article showed that Shannon’s entropy is a convex function of the preventive maintenance threshold for each moment of condition monitoring. It was also shown that the probabilities of correct and incorrect decisions depend on the time and parameters of the degradation model. Numerical calculations show that the proposed approach to determining the optimal preventive maintenance threshold can significantly reduce uncertainty when deciding on the condition of the monitoring object.
Keywords: condition monitoring; false-positive; false-negative; Shannon entropy; preventive maintenance threshold; minimum entropy condition monitoring; false-positive; false-negative; Shannon entropy; preventive maintenance threshold; minimum entropy
MDPI and ACS Style

Raza, A.; Ulansky, V. Optimization of Condition Monitoring Decision Making by the Criterion of Minimum Entropy. Entropy 2019, 21, 1193.

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