This study examines the consistency metrics used to evaluate the durability of a spirulina production plant, which consists of seven subsystems: cultivation pond, paddlewheel, filter unit, washing unit, spray dryer, ribbon blender, and packaging. By studying the spirulina firm, we can repair it by discovering future failures. We can increase spirulina production so that untimely failure can be prevented and production can be increased. There are two types of system failures: partial and total. While a full failure renders the system incapable of operating, a partial failure is thought to degrade the system. In contrast, repair rates follow two different types of distributions: an ordinary and an exponential distribution. The system in a partially failed or degraded condition is thought to be repaired using general time distribution. In contrast, fully failed systems are thought to be fixed using the Gumbel-Hougaard family copula distribution. Using the supplementary variable approach, the system is examined. A Chapmen-Kolmogorov differential equation is created and solved by applying the Gumbel-Haugaard family Copula approach, employing the schematic representation of the system's state. supplementary variable approaches are applied to develop and resolve the differential equations related to transition diagrams, which are significant to this research. Reliability, availability, profitability, and MTTF are the critical performance metrics for the spirulina production plant. Moreover, sensitivity analysis is carried out for MTTF.