Reliability analysis of Polytube industry using supplementary variable technique

Keywords: Supplementary variable technique Chapman–Kolmogorov Variable failure and repair rates Lagrange's method Runge–Kutta fourth order a b s t r a c t The purpose of this paper is to compute reliability of Polytube manufacturing plant having four units using supplementary variable technique. The failure and repair rates of the subsystems are variable. The mathematical equations are derived using Chapman–Kol-mogorov differential equations which are formed using mnemonic rule from the transition diagram of Polytube manufacturing plant. The system of partial differential equations obtained has been solved using Lagrange's method and reliability of the system for the various choices of constant transition rates is solved numerically using Runge–Kutta fourth order. A sensitive analysis of subsystem is finally carried out to improve overall availability. The goal of maximum production and long run availability under the given operative condition can be achieved by making the system failure free as far as possible by proper maintenance, planning and control. Due to increasing complexity of modern engineering systems, which involve high risks, the concept of reliability has become a very important factor in the overall system design. While dealing with reliability-based design of machines and structures, we can study the relative importance of mechanical and structural failures from the point of view of loss of human lives. Reliability analysis of such a system helps us to obtain the necessary information about the control of various parameters. Most of the authors discussed the system possessing markovian properties. The system having non-Markovian property can be converted into a system having markovian nature by introducing a new variable called supplementary variable. Initially, Cox [1] used supplementary variable in analyzing non-markovian system and presented a systematic solutions of reliability and availability of that system using supplementary variable technique. Gaver [2] studied a parallel redundant system with constant state dependent hazard rates and arbitrary repair rates. Kumar et al. [3] discussed the availability of the feeding system in the sugar industry. Since then several authors have studied the reliability of the various systems using supplementary variable technique. Singh and Dayal [4] used supplementary variable technique for problem formulation. Subsequently, Kumar et al. [5] used it to study the maintenance planning of pulping system, screening system in paper industry, and availability of crystallization system in paper industry. Alfa and Srinivada Rao [6] discussed supplementary variable technique in stochastic models. Gupta [7] studied availability analysis assuming constant failure rates but repair rates …