The Palm transformation method for reliability analysis of on‑board spacecraft equipment within an orbital satellite constellation


Аuthors

Volovik A. V.1*, Klavdiev A. A.2**, Efimenko S. V.3***, Garanin D. A.3****

1. UEC-Klimov, 11, Kantemirovskaya Str., Saint-Petersburg, 194100, Russia
2. IP Klavdiev A.A., St. Petersburg, Russia
3. Peter the Great St. Petersburg Polytechnic University, 29, Polytechnicheskaya str., St. Petersburg, 195251, Russia

*e-mail: volovik_aleksandr@mail.ru
**e-mail: kss1959@mail.ru
***e-mail: falcon.sergey@yandex.ru
****e-mail: garanin@spbstu.ru

Abstract

The article focuses on transforming Palm flows into simple (Poisson) flows to apply the mathematical apparatus of Markov random processes for reliability system analysis. A Palm flow is an ordinary flow of events where time intervals between consecutive events are independent, identically distributed random variables with an arbitrary distribution law. The main problem is that many real event flows in technical systems are recurrent (Palm flows), which complicates their analytical description. The article proposes a method for Markovizing the process by introducing additional variables and transforming the flow parameters using the moment method. This makes it possible to reduce a non-Markov process to a Markov one and use Kolmogorov differential equations to describe the process. The work considers a system with two states – operational and faulty. To transform flows with normal and uniform distributions of time between events into equivalent Poisson flows, formulas derived from the equality of the second initial moments are used. The proposed approach allows calculating both stationary and non-stationary probabilities of system states. In the aerospace field, this method can be applied to model the reliability of complex systems such as spacecraft onboard equipment or aviation control systems. This makes it possible to reasonably schedule maintenance periods, estimate gamma-percent resources and equipment service life, and optimize system recovery and redundancy strategies.

Keywords:

Palm flow, Markov processes, system reliability, stationary and non-stationary system state probabilities, and Poisson event streams

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