Numerical Analysis of Reliability and Availability of a Complex Repairable System

Author(s): 
Munish Mehta†, Jujhar Singh, Manpreet Singh

Affiliation(s): 

†I. K. Gujral Punjab Technical University, Kapurthala, Punjab, 144603, India,
 ‡Deptt. of Mechanical Engineering, I. K. Gujral Punjab Technical University, Kapurthala, Punjab, 144603, India
§Deptt. of Mechanical Engineering, Lovely Professional University, Phagwara, Punjab, 144411, India
Cite this paper
Munish Mehta†, Jujhar Singh, Manpreet Singh, “Numerical Analysis of Reliability and Availability of a Complex Repairable System”, Journal of Mechanical Engineering Research and Developments, vol. 40, no. 4, pp. 619-632, 2017. DOI: 10.7508/jmerd.2017.04.010

ABSTRACT: The purpose of this paper is to compute the reliability/availability of melting system of a steel industry with a view to increase its productivity. Using mnemonic rule, Chapman-Kolmogorov differential equations have been developed from the transition diagram keeping the failure rate constant and varying repair rates by applying supplementary variable technique (SVT). Lagrange’s method has been employed to solve these equations. MATLAB software package has been used to compute the transient state availability of the system by Runge-Kutta fourth order method. Mean time between failure (MTBF) has been calculated using Simpson’s 3/8 rule. The outcomes of current study may lead to increased plant availability resulting in more production. It may also help the plant management in futuristic maintenance planning and scheduling of the system.

Keywords : Reliability; Availability; Supplementary variable technique; Runge-Kutta; MTBF

References
[1] D. K. Kulshrestha, “Reliability of a repairable multicomponent system with redundancy in parallel”, IEEE Trans Reliab, vol. R-19, no. 2, pp. 50-52, May1970.
[2] J. R. Arora, “Reliability of several standby-priority-redundant systems”, IEEE Trans Reliab, vol. R-26, no. 4, pp. 290-293, Oct. 1977.
[3] P. P. Gupta and L. Tyagi, “M.T.T.F. and availability evaluation of a two-unit, two-state, standby redundant complex system with constant human failure”, Microelect Reliab, vol. 26, no. 4, pp. 647-650, 1986.
[4] J. Singh and B. Dayal, “A 1-Out-of-N: G system with common-cause failures and critical human errors”, Microelect Reliab, vol. 31, no. 5, pp. 847-849, 1991.
[5] A. S. Alfa and T. S. S. Srinivasa Rao, “Supplementary variable technique in stochastic models”, J Probab Eng Infor Sci, vol. 14, no. 2, pp. 203-218, 2000.
[6] N. Sah, S. B. Singh and R. S. Rajput, “Stochastic analysis of a web server with different types of failure”, J Reliab Stat Stud, vol. 3, no. 1, pp. 105-116, 2010.
[7] H. Sugiura and T. Torii, “A method for constructing generalized Runge-Kutta methods”, J Comput Appl Math, vol. 38, no. 1-3, pp. 399-410, Dec. 1991.
[8] C. Lindemann, M. Malhotra and K. S. Trivedi, “Numerical methods for reliability evaluation of markov closed fault-tolerant t systems”, IEEE Trans Reliab, vol. 44, no. 4, pp. 694-704, Dec. 1995.
[9] D. J. Higham, “An algorithmic introduction to numerical simulation of stochastic differential equations”, Soc Ind Appl Math, vol. 43, no. 3, pp. 525-546, 2001.
[10] P. Gupta, A. K. Lal, R. K. Sharma and J. Singh, “Analysis of reliability and availability of serial processes of plastic-pipe manufacturing plant: A case study”, Int J Qual Reliab Man, vol. 24, no. 4, pp. 404-419, 2007.
[11] M. N. Uddin, M. M. Uddin and N. K. Mitra, “Solution of ordinary differential equation by Runge-Kutta method”, ASA Univ Rev, vol. 3, no. 2, pp. 227-234, 2009.
[12] S. Garg, J. Singh and D. V. Singh, “Availability and maintenance scheduling of a repairable block-board manufacturing system”, Int J Reliab Safe, vol. 4, no. 1, pp. 104-118, 2010.
[13] H. Musa, S. Ibrahim and M. Y. Waziri, “A simplified derivation and analysis of fourth order Runge-Kutta method”, Int J Comp Appl, vol. 9, no. 8, pp. 51-55, 2010.
[14] A. S. Nugraha, “The selection of time step in Runge-Kutta fourth order for determine deviation in the weapon arm vehicle”, Ener Proc vol. 68, pp. 363-369, April 2015.
[15] C. Amann and K. Kadau, “Numerically efficient modified Runge-Kutta solver for fatigue crack growth analysis”, J Eng Fract Mech, vol. 161, pp. 55-62, August 2016.
[16] K. Hussain, F. Ismail and N, Senu, “Solving directly special fourth-order ordinary differential equations using Runge-Kutta type method”, J Comput Appl Math, vol. 306, pp. 179-199, Nov. 2016.