SEQUENTIAL DETECTION OF TAIL-RISK GROWTH (EXPECTED SHORTFALL) IN NONSTATIONARY MEASUREMENT STREAMS UNDER TIME-UNIFORM FALSE-ALARM CONTROL FOR MONITORING COAL INDUSTRY EQUIPMENT

Authors:

A.A. Tarasenko, E.V. Prokopenko, A.S. Ashcheulova
T.F. Gorbachev Kuzbass State Technical University (KuzSTU), Branch in Novokuznetsk, Novokuznetsk, 654000, Russian Federation, e-mail: pet.vtit@kuzstu.ru
Authors Information
Tarasenko A.A. – Student, T.F. Gorbachev Kuzbass State Technical University (KuzSTU), Branch in Novokuznetsk, Novokuznetsk, 654000, Russian Federation, e-mail: gamenk987@gmail.com
Prokopenko E.V. – PhD (Physics and Mathematics), Associate Professor, T.F. Gorbachev Kuzbass State Technical University (KuzSTU), Branch in Novokuznetsk, Novokuznetsk, 654000, Russian Federation, e-mail: pev.vtit@kuzstu.ru
Ashcheulova A.S. – PhD (Physics and Mathematics), Associate Professor, T.F. Gorbachev Kuzbass State Technical University (KuzSTU), Kemerovo, 650000, Russian Federation, e-mail: asheulovaas@kuzstu.ru

UDC: 004.942:519.2:519.87 c A.A. Tarasenko, E.V. Prokopenko, A.S. Ashcheulova, 2026
DOI: http://dx.doi.org/10.18796/0041-5790-2026-8-113-118

Abstract

We study online detection of tail-risk growth in nonstationary measurement streams, where rare large deviations are critical. This setting arises in continuous equipment monitoring, where failures are preceded by rare extreme events. In vibration diagnostics and impact-load monitoring, mean-level indicators may change only slightly, while short acceleration impulses appear; these impulses excite the system’s natural frequencies and lead to an increase of extremes in a high-frequency band and in the envelope spectrum. In hydraulic systems, a similar pattern is observed as bursts of pressure surges, while the baseline level may drift with the operating regime. The proposed procedure is designed for early detection of tail thickening in such extreme indicators and provides a time-uniform control of the false-alarm probability via the parameter ?. The risk is quantified by Expected Shortfall ES1??. To separate tail behavior from slow level drift, we build an adaptive threshold qt and analyze exceedances (Xt ? qt)+, truncated by a constant B for robustness. Based on normalized truncated exceedances we construct an evidence process Lt (an e-process). Under a nominal conditional bound E[Zt | ?t?1] ? m0 we prove time uniform false alarm control: ?H0(supt ? 0 Lt ? 1/?) ? ? for any ? ? (0, 1). We present a limited-memory mixture procedure over change points; simulations with a tail change illustratecontrolled dete ction delay and no premature alarms under the nominal regime.

Keywords: Expected Shortfall; tail risk; change-point detection; e-values; test martingales; time-uniform control; nonstationary data; limited memory

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For citation

Tarasenko A.A., Prokopenko E.V., Ashcheulova A.S. Sequential detection of tail-risk growth (Expected Shortfall) in nonstationary measurement streams under time-uniform false-alarm control for monitoring coal industry equipment. Ugol’. 2026;(8):113-118. (In Russ.). DOI: 10.18796/0041-5790-2026-8-113-118.

Paper Info
Received: June 30, 2026
Reviewed: July 17, 2026
Accepted: July 30, 2026