Reliability and Cost Assessment of Repairable Reverse Osmosis Series-Parallel System Using Gumbel Hougaard Family Copula Analysis

Abstract

This study examined several dependability measures for assessing the power and efficiency of a serial reverse osmosis machine or system made up of subsystems A, B, C, and D. There are two units, A₁ and A₂, in Subsystem A, the Raw Water Tank. One unit will be operating while the other is in standby mode in this scenario. By the current study's supposition, Subsystem B is an arbitrary filter contains only one component, thus if that component fails, the complete system will also fail. The reverse osmosis membrane in Subsystem C is where the system's primary water purification happens. There are two units in the subsystem, C₁ and C₂. Two components, C₁ and C₂, makeup the subsystem; one will be in operation at any given time, while the other will be in a hot standby. The water production tank is represented by Subsystem D. And that is where the clean, drinkable water is kept. It just has one unit. The Subsystems are linked in a series. The entire system will collapse if one subsystem fails. To derive expressions of system reliability measures; including availability, reliability, mean time to failure (MTTF), and profit function. The Gumbel-Hougaard family of copula approach is utilized. The results are illustrated in tables and the effects of different system characteristics were examined. The numerical results were produced using the Maple software and then converted into graphics. Using the Markov birth-death process, the state transition diagram produced a set of first order differential equations. The Copula technique was used to solve the system.