Optimal Maintenance Probabilities and Preventive Replacement Maintenance Policy for Photocopy Machines
DOI:
https://doi.org/10.13052/jrss0974-8024.14113Keywords:
Log-logistic distribution, photocopy machine, replacement policy, availabilityAbstract
The need for suitable replacement policies are essential to minimize down time, maintenance cost and maximize the availability and reliability of equipment. On this premise, this work models the failure rate of Photocopy machines and obtain its optimal preventive maintenance policy that would prevent damage and its attendant losses to both users and end-product consumers. The failure distribution of the machine was shown to follow the Log-Logistic distribution with shape parameter, ˆα=1.723339368 and scale parameter, ˆβ=763.9219635. Optimal probabilities of the distribution were obtained and utilized in both the cumulative failure function and cumulative hazard function-based replacement models to formulate a replacement maintenance policy for the machine. The failure cumulative function-based replacement model was found to be a better model which yields optimal replacement maintenance time of 166 hours at a minimum cost of 113 Naira for maintaining the machine per cycle time with 96% availability, 94% reliability and 0.07% chance of failure occurrence in the machine.
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References
Ahmad M. I., Sinclair C. D. and Werritty A. (1988). Log-logistic food frequency analysis. Journal of Hydrology, 98: 205–224.
Akhtar, M. T., and Khan, A. A. (2014). Log-logistic distribution as a reliability model: A Bayesian analysis. American Journal of Mathematics and Statistics, 4(3): 162–170.
Anderson, W. A., McClure P. J., Baird-Parker A. C. and Cole M. B. (1996). The application of a log-logistic model to describe the thermal inactivation of Clostridium botulinum 213 b at temperatures below 121.1 c. Journal of Applied Microbiology 80(3): 283–290.
Ashkar F. and Mahdi S. (2006). Fitting the log-logistic distribution by generalized moments. Journal of Hydrology, 328: 694–703.
Bahrami G.K., Price, J.W.H. and Mathew (2000). The constant interval replacement Model for preventive replacement maintenance: A new perspective. International Journal of Quality and Reliability Management, 17(8): 822–838.
Byon, E., Ntaimo L. and Ding Y. (2010); Optimal maintenance strategies of wind turbine systems under stochastic weather conditions. IEEE Transactions on Reliability; 59: 393–404.
Cassady, C.R., E.A. Pohl and W.P. Murdock (2003); Selective Maintenance Modeling for Industrial Systems. Journal of Quality in Maintenance Engineering, 7(2): 104–117.
Chouhan, R., Gaury, M. and and Tripathi, R. (2013). A Survey of Preventive Maintenance Planning Models, Techniques and Policies for an Ageing and Deteriorating Production Systems. HCTL Open Int. J. of Technology Innovations and Research, 3(May): 1–19.
Clark, D. E. and El-Taha, M. (2015). Some useful properties of Log-Logistic Random Variables for Health Care Simulations. International Journal of Statistics in Medical Research; 4, 79–86.
Fisk, P.R. (1961). The graduation of income distribution. Econometrica, 29: 171–185.
Gupta, R. D., Ahman O. and Lvin, S. (1999). A study of log-logistic model in survival analysis. Biometrical Journal, 41: 431–443.
Huynh, K. T., Castro, I. T. and Berenguer, C. (2012). Modeling age-based maintenance strategies with minimal repairs for systems subject to competing failure models due to degradation and shocks. European Journal of Operations Research, 218: 140–151.
Jibril, Y. and Ekundayo, K. R. (2015). Reliability Assessment of 33 kV Kaduna Electricity Distribution Feeders, Northern Region, Nigeria. World Congress on Engineering and Computer Science, San Francisco, USA: 1–5.
Kurt, M. and Maillart, L. M. (2009). Structured replacement policies for a Markov-modulated shock model. Operations Research Letters; 37: 280–284.
Lamberson, L. R. (2013). Reliability in Engineering Design, New York, USA: John Wiley and Sons, Inc.
Mahdavi, M. and Mahdavi, M. (2009). Optimisation of age replacement policy using reliability based heuristic model. Journal of scientific & Industrial Research, 68: 668–673.
Mahmoud, M. R. and Mohammed, S. M. (2013). Estimation of Parameters of the Marshall-Olkin Extended Log-Logistic Distribution from Progressively Censored Samples. European Journal of Statistics and Probability, 2(3):1–13.
Nakagawa, T. (1984). Periodic inspection policy with preventive maintenance. Naval Research Logistic Quarterly, 31:33–40.
Segawa, Y., Ohnishi, M. and Ibaraki, T. (1992); Optimal minimal-repair and replacement problem with age dependent cost structure. Computers & Mathematics with Applications, 24: 91–101.
Shoukri M. M., Mian I. U. H. and Tracy D. S. (1988); Sampling properties of estimators of the log-logistic distribution with application to Canadian precipitation data. Canadian Journal of Statistics 16: 223–236.
Staye, R. (2014). Reliability Analysis of Electrical Gas cooker. Master of Science Thesis, Faculty of Electrical and Electronic Engineering, University Tun Hussein Onn Malaysia.
Tahara, A. and Nishida, T. (1975). Optimal replacement policy for minimal repair model. Operations Research Society of Japan; 18: 113–124.
Tahir, M. H., Mansoor, M., Zubair, M. and Hamedani, G. G. (2014). McDonald Log-Logistic distribution. Journal of Statistical Theory and Applications, 13: 65–82.
Verhulst, P. F. (1838). Notice sur la loi que la population suit dans son accroissement. Correspondence in Mathematical Physics, 10: 113–121.
Wang, H. and Pham, H. (1996). Optimal age-dependent preventive maintenance policies with imperfect maintenance. International Journal of Reliability, Quality and Safety Engineering, 3: 119–135.
