Optimal Maintenance Probabilities and Preventive Replacement Maintenance Policy for Photocopy Machines

Optimal Replacement Maintenance Policy for Photocopy Machines

  • Nse Udoh Department of Staistics, University of Uyo, Nigeria
  • Akaninyene Udom Department of Staistics, University of Nigeria, Nsukka, Nigeria
  • Fredrick Ohaegbunem Department of Staistics, University of Uyo, Nigeria
Keywords: Log-logistic distribution, photocopy machine, replacement policy, availability


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, αˆ=1.723339368 and scale parameter, βˆ=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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Author Biographies

Nse Udoh, Department of Staistics, University of Uyo, Nigeria

Nse Udoh is a Senior Lecturer of Statistics in the Department of Statistics, University of Uyo, Nigeria. He obtained his B.Sc. (Hons (1995) in Statistics, M.Sc. (2002) in Statistics and Operations Research and PhD (2016) in Statistics with specialty in Operations Research respectively from University of Uyo, University of Nigeria, Nsukka and University of Calabar, Nigeria. His research area is Operations Research and Optimization with special interest in Maintenance Theory of Reliability. He has taught and successfully supervised many postgraduate students.

Akaninyene Udom, Department of Staistics, University of Nigeria, Nsukka, Nigeria

Akaninyene Udom is an Associate Professor of Statistics in the department of Statistics, University of Nigeria, Nsukka. His specialty is Stochastic Processes with interest in Control Theory and Optimization. He obtained his B.Sc. (Hons) in Statistics in 1998, M.Sc.(2005) in Statistics and PhD (2014) in Statistics with bias in Stochastic Processes from University of Nigeria, Nsukka. He has taught and successfully supervised many postgraduate students.

Fredrick Ohaegbunem, Department of Staistics, University of Uyo, Nigeria

Fredrick Ohaegbunem is a Postgraduate student in the department of Statistics, University of Uyo, Nigeria. He is currently working on Maintenance Theory of Reliability with interest in replacement problems for his M.Sc degree. In 2020, he obtained his B.Sc. with first class honours in Statistics.


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