Use of delay-time concept in modelling process of technical and logistics systems maintenance performance. Case study

cb – expected cost of repair ccon – the expected consequence costs for the supported system and its environment caused by failure occurrence in logistics system ci – cost of inspection action performance cir – expected repair costs during the implementation of inspections C(T) – function of the expected maintenance costs of a system CC(T) – function of the expected consequences costs for the supported system and its environment Cutrz – the total expected maintenance costs of a system in one inspection cycle d – time of inspection action performance db – random time of system downtime caused by its failure Ed(T) – function of system expected downtime E(h) – expected value of delay time F(T) – cumulative distribution function of the time between failures of a system f(T) – probability density function of the time between failures of a system f1(T) – probability density function of the time to the first failure Fh(h) – cumulative distribution function of the random variable delay time h fh(h) – probability density function of the random variable delay time h h – random variable for delay time k – constant intensity of system failures occurrence MTBF – Mean Time Between Failures MTTR – Mean Time To Repair Pb(T) – function for system downstate probability R(T) – system reliability function T – the time between system consecutive inspection actions performance Topt – the optimal time between system consecutive inspection actions performance