Behavioural Analysis of a Complex Manufacturing System Having Queue in the Maintenance Section

Abstract

In this paper reliability characteristic of a complex manufacturing system incorporating queue in service is studied. The considered system consists of three units namely A, B and C connected in series. Unit A consists of a main unit a₁ and an active redundant unit a₂, unit B consists of a main unit b₁ and a cold redundant unit b₂ and unit C consists of two units c₁ and c₂ connected in parallel configuration. Considered system can completely fail due to failure of any of the subsystems. It is also assumed that the system can fail due to catastrophic failure. General repair facility is available for units c₁ and c₂ whereas there exits a maintenance section with one repairmen for repairing the units a₁, a₂, b₁ and b₂. Various reliability characteristics such as steady state behavior, availability, reliability, and MTTF and cost analysis have been obtained using supplementary variable technique and Gumble-Hougaard copula methodology.

Keywords: Supplementary variable technique, reliability, MTTF, asymptotic behavior, markov process, Gumble-Hougaard copula, profit function, queue.