<p>This paper presents a novel reliability analysis of a complex industrial system comprising six interconnected subsystems: Spinning/Twisting, Weaving/Knitting, Pre-treatment &amp; Bleaching, Dyeing, Printing, and Steaming/Finishing. All failure rates within the system are constant and follow a negative exponential distribution. The repair process distinguishes two types of distributions: Gumbel-Hougaard family copula distribution and general distribution. For independent operation of the system, at least "k" out of "n" units must be operational for the Spinning/Twisting subsystem and at least "" out of "m" units must be operational for the Weaving/Knitting subsystem. To analyze system performance and get measures of system availability and operational behavior, researchers employ Laplace transforms and the supplementary variable approach. We obtained various reliability measures under different values of failure and repair rates. The substantial impact of failure rates on system performance metrics like system availability, system reliability, MTTF&amp; profit function have computed. We found that employing joint copula repair led to better system performance. The Maple program generates numerical results and graphical images to show the theoretical conclusions.</p>