{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,14]],"date-time":"2026-08-14T04:29:44Z","timestamp":1786681784020,"version":"build-2736575974"},"reference-count":37,"publisher":"MDPI AG","issue":"16","license":[{"start":{"date-parts":[[2026,8,12]],"date-time":"2026-08-12T00:00:00Z","timestamp":1786492800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"COMAC Innovation Research Program","award":["CIRP202314001"],"award-info":[{"award-number":["CIRP202314001"]}]},{"award":["CIRP202314001"],"award-info":[{"award-number":["CIRP202314001"]}],"id":[{"id":"https:\/\/ror.org\/03y6ba359","id-type":"ROR","asserted-by":"publisher"}]},{"name":"Aeronautical Science Foundation of China","award":["2024M060038001"],"award-info":[{"award-number":["2024M060038001"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Up\/down counters are ubiquitous in the alarm and fault-confirmation logic of electro-mechanical systems. In aircraft, several electro-mechanical modules provide position feedback for flight control; the Linear Variable Differential Transformer (LVDT) is a representative one, converting mechanical displacement into an electrical signal whose reliable monitoring is critical to flight safety. As such counters are deployed in ever more complex systems and more uncertain environments, rising safety requirements render their heuristic tuning unreliable. To address this challenge, this paper proposes a quantitative, reliability-oriented procedure for counter-based monitors, which replaces heuristic parameter tuning. Both healthy and faulty signal distributions are estimated by Kernel Density Estimation (KDE), so the framework handles non-Gaussian noise and FMEA-weighted failure modes. The threshold-and-counter logic is modeled as a finite-horizon absorbing Discrete-Time Markov Chain (DTMC), which yields the false-confirmation probability, missed-detection probability, and detection delay over a bounded horizon instead of long-run rates. Thresholds and counter parameters are then synthesized offline, leaving a lightweight online monitor that needs only threshold comparison and integer counter updates. We evaluate the method on an LVDT sum-voltage monitor using real aircraft healthy measurements and Simulink-based fault injection with 45 detectable modes, assessing the synthesized monitor on 558,001 real measured samples and an FMEA-driven fault population. Results show that, among the compared confirmation logics, our workflow yields a counter that meets the 10\u22129 false-confirmation target and the 10\u22126 missed-detection target while attaining the lowest detection delay.<\/jats:p>","DOI":"10.3390\/s26165115","type":"journal-article","created":{"date-parts":[[2026,8,12]],"date-time":"2026-08-12T12:53:48Z","timestamp":1786539228000},"page":"5115","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Finite-Horizon Reliability-Oriented Synthesis of Cumulative Up\/Down-Counter Fault-Confirmation Monitors"],"prefix":"10.3390","volume":"26","author":[{"ORCID":"https:\/\/orcid.org\/0009-0005-3730-6112","authenticated-orcid":false,"given":"Xiaoting","family":"Yuan","sequence":"first","affiliation":[{"name":"Shanghai Aircraft Design and Research Institute, Shanghai 201210, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0002-3484-241X","authenticated-orcid":false,"given":"Xiaotong","family":"Feng","sequence":"additional","affiliation":[{"name":"Department of Integrated Circuits Science and Engineering, Beihang University, Beijing 100191, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0006-6750-2058","authenticated-orcid":false,"given":"Ming","family":"Cheng","sequence":"additional","affiliation":[{"name":"Department of Environment, Chemistry and Materials, University of Bologna, 40130 Bologna, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2006-408X","authenticated-orcid":false,"given":"Peng","family":"Wang","sequence":"additional","affiliation":[{"name":"Department of Integrated Circuits Science and Engineering, Beihang University, Beijing 100191, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,8,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"645","DOI":"10.3182\/20090630-4-ES-2003.00107","article-title":"An introduction to alarm analysis and design","volume":"42","author":"Izadi","year":"2009","journal-title":"IFAC Proc. Vol."},{"key":"ref_2","unstructured":"(2016). Management of Alarm Systems for the Process Industries (Standard No. ANSI\/ISA-18.2). Technical Report."},{"key":"ref_3","unstructured":"EEMUA (2013). Alarm Systems: A Guide to Design, Management and Procurement, Engineering Equipment and Materials Users Association. Technical Report."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Wang, J., Hu, W., and Chen, T. (2024). Intelligent Industrial Alarm Systems: Advanced Analysis and Design Methods, Springer.","DOI":"10.1007\/978-981-97-6516-4"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1318","DOI":"10.1016\/j.jprocont.2011.06.019","article-title":"On expected detection delays for alarm systems with deadbands and delay-timers","volume":"21","author":"Adnan","year":"2011","journal-title":"J. Process Control"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"296","DOI":"10.1109\/TASE.2011.2176490","article-title":"Performance Assessment and Design for Univariate Alarm Systems Based on FAR, MAR, and AAD","volume":"9","author":"Xu","year":"2012","journal-title":"IEEE Trans. Autom. Sci. Eng."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"96","DOI":"10.1016\/j.conengprac.2017.10.016","article-title":"Analysis and Design of Time-Deadbands for Univariate Alarm Systems","volume":"71","author":"Afzal","year":"2018","journal-title":"Control Eng. Pract."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"382","DOI":"10.1016\/j.jprocont.2012.12.013","article-title":"Study of generalized delay-timers in alarm configuration","volume":"23","author":"Adnan","year":"2013","journal-title":"J. Process Control"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"669","DOI":"10.1016\/j.ifacol.2015.09.045","article-title":"Design and analysis of improved alarm delay-timers","volume":"48","author":"Zang","year":"2015","journal-title":"IFAC-PapersOnLine"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1002\/aic.15860","article-title":"Design and assessment of delay timer alarm systems for nonlinear chemical processes","volume":"64","author":"Tulsyan","year":"2018","journal-title":"AIChE J."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"11295","DOI":"10.1021\/acs.iecr.9b00014","article-title":"Univariate model-based deadband alarm design for nonlinear processes","volume":"58","author":"Tulsyan","year":"2019","journal-title":"Ind. Eng. Chem. Res."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"106113","DOI":"10.1016\/j.conengprac.2024.106113","article-title":"Selection of alarm deadbands and delay timers with their connections based on risk indicators for removing nuisance alarms","volume":"153","author":"Zhang","year":"2024","journal-title":"Control Eng. Pract."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"112073","DOI":"10.1016\/j.automatica.2024.112073","article-title":"Performance Analysis for Stochastic Anomaly Detectors with On\/Off-Delay Timers","volume":"173","author":"Zhou","year":"2025","journal-title":"Automatica"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"877","DOI":"10.1016\/j.psep.2022.12.036","article-title":"Performance Analysis of Up\/Down Counters in Alarm Design","volume":"170","author":"Raei","year":"2023","journal-title":"Process Saf. Environ. Prot."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Rahimi, Y., Mohan Rao, H.R., and Chen, T. (2024, January 8\u201310). Optimizing Alarm Design: A Comparison of Delay-Timers, Counters, and Time-Deadbands. Proceedings of the 2024 IEEE 3rd Industrial Electronics Society Annual On-Line Conference (ONCON), Beijing, China.","DOI":"10.1109\/ONCON62778.2024.10931662"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"282","DOI":"10.1016\/j.isatra.2019.08.015","article-title":"Performance Evaluation and Design for Variable Threshold Alarm Systems through Semi-Markov Process","volume":"97","author":"Aslansefat","year":"2020","journal-title":"ISA Trans."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1173","DOI":"10.1016\/j.psep.2022.12.069","article-title":"Design of Alarm Thresholds and Delay Timers for Non-IID Process Variables Based on Alarm Durations","volume":"170","author":"Gyasi","year":"2023","journal-title":"Process Saf. Environ. Prot."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"120","DOI":"10.1016\/j.jprocont.2022.04.002","article-title":"Assessment of Alarm Systems for Mixture Processes and Intermittent Faults","volume":"114","author":"Asaadi","year":"2022","journal-title":"J. Process Control"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"100","DOI":"10.1093\/biomet\/41.1-2.100","article-title":"Continuous inspection schemes","volume":"41","author":"Page","year":"1954","journal-title":"Biometrika"},{"key":"ref_20","unstructured":"Wald, A. (1947). Sequential Analysis, John Wiley & Sons."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1897","DOI":"10.1214\/aoms\/1177693055","article-title":"Procedures for reacting to a change in distribution","volume":"42","author":"Lorden","year":"1971","journal-title":"Ann. Math. Stat."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1379","DOI":"10.1214\/aos\/1176350164","article-title":"Optimal stopping times for detecting changes in distributions","volume":"14","author":"Moustakides","year":"1986","journal-title":"Ann. Stat."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"457","DOI":"10.1016\/j.spl.2003.10.004","article-title":"A unified Markov chain approach for computing the run length distribution in control charts with simple or compound rules","volume":"65","author":"Fu","year":"2003","journal-title":"Stat. Probab. Lett."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"8289","DOI":"10.3182\/20110828-6-IT-1002.01758","article-title":"Wind turbine fault detection using counter-based residual thresholding","volume":"44","author":"Ozdemir","year":"2011","journal-title":"IFAC Proc. Vol."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"768","DOI":"10.1109\/19.930452","article-title":"A novel DSP-based LVDT signal conditioner","volume":"50","author":"Ford","year":"2001","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"2294","DOI":"10.1109\/TIM.2007.908248","article-title":"Least Mean Square Method for LVDT Signal Processing","volume":"56","author":"Flammini","year":"2007","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"524","DOI":"10.1016\/j.conengprac.2010.12.009","article-title":"AIRBUS state of the art and practices on FDI and FTC in flight control system","volume":"19","author":"Goupil","year":"2011","journal-title":"Control Eng. Pract."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1329","DOI":"10.1177\/0954410011421717","article-title":"Model-based fault diagnosis for aerospace systems: A survey","volume":"226","author":"Marzat","year":"2012","journal-title":"Proc. Inst. Mech. Eng. G J. Aerospace Eng."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Fu, S., and Avdelidis, N.P. (2023). Prognostic and Health Management of Critical Aircraft Systems and Components: An Overview. Sensors, 23.","DOI":"10.3390\/s23198124"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1436","DOI":"10.1109\/TMECH.2021.3096375","article-title":"Fault-Tolerant Control of Switched LPV Systems: A Bumpless Transfer Approach","volume":"27","author":"Zong","year":"2022","journal-title":"IEEE\/ASME Trans. Mechatron."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"7479","DOI":"10.1109\/TCYB.2024.3463689","article-title":"Adaptive Fuzzy Tracking Control for Switched Nonlinear Systems Under FDI Attacks and Input Saturation: A Flexible Transient Performance Approach","volume":"54","author":"Zong","year":"2024","journal-title":"IEEE Trans. Cybern."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"762","DOI":"10.1109\/TFUZZ.2025.3648401","article-title":"Guaranteed State and Fault Interval Estimation for Local Nonlinear Takagi\u2013Sugeno Fuzzy Systems Based on Zonotopic Analysis","volume":"34","author":"Zhang","year":"2026","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"1065","DOI":"10.1214\/aoms\/1177704472","article-title":"On estimation of a probability density function and mode","volume":"33","author":"Parzen","year":"1962","journal-title":"Ann. Math. Stat."},{"key":"ref_34","unstructured":"Silverman, B.W. (1986). Density Estimation for Statistics and Data Analysis, Chapman & Hall."},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"McLachlan, G.J., and Peel, D. (2000). Finite Mixture Models, John Wiley & Sons.","DOI":"10.1002\/0471721182"},{"key":"ref_36","unstructured":"(2023). Guidelines for Conducting the Safety Assessment Process on Civil Aircraft, Systems, and Equipment (Standard No. SAE ARP4761A)."},{"key":"ref_37","unstructured":"(2024). System Design and Analysis (Standard No. AC 25.1309-1B)."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/26\/16\/5115\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,14]],"date-time":"2026-08-14T04:10:54Z","timestamp":1786680654000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/26\/16\/5115"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,8,12]]},"references-count":37,"journal-issue":{"issue":"16","published-online":{"date-parts":[[2026,8]]}},"alternative-id":["s26165115"],"URL":"https:\/\/doi.org\/10.3390\/s26165115","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,8,12]]}}}