Abstract
In this paper, we address the problem of determining optimal inspection schedules for a single machine subject to exponentially distributed failures. We formulated the inspection models using the concept of discounted cash flow analysis to account for the effects of time value of money on the inspection policies. In addition, these models are developed under different assumptions on the planning horizon related to its length (infinite and finite) and nature (deterministic and stochastic). In the finite horizon problem, we considered both cases where the inspection times are treated as continuous and discrete variables. For the case of continuous inspection times, we prove that the equal inspection interval policy is optimal only under certain conditions. In the case of a random horizon, we show that the problem can be transformed to the infinite horizon problem and, consequently, can be solved using the same procedure. Numerical examples are used to illustrate the models and their solution procedures.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Abdel-Hameed, M. Inspection, Maintenance and Replacement Models. Computers & Operations Research, 22-4 (1995) 435–441.
Alfares, H. A Simulation Model for Determining Inspection Frequency. Computers & Industrial Engineering, 36 (1999) 685–696.
Baker, M.J.C. How often should a machine be inspected? International Journal of Quality and Reliability Management, 7 (1990) 14–18.
Banerjee, P.K. and Chuiv, N.N. Inspection Policies for Repairable Systems, IIE Transactions, 28 (1996) 1003–1010.
Ben-Daya, M. and Hariga, M. A Maintenance Inspection Model: Optimal and Heuristic Solutions. International Journal of Quality and Reliability Management, 15 (1998) 481–488.
Chung, K.J. A Note on the Inspection Interval of Machine. International Journal of Quality and Reliability Management, 10 (1993) 71–73.
Cox, D.R. and Smith, W.L. On the Super-Position of Renewal Processes. Biometrica, 41 (1954) 91–99.
Davis, D.J. An Analysis of Some Failure Data. Journal of American Statistical Association, 47 (1952) 113–150.
Drenick, R.F. The Failure Law of Complex Equipment. Journal of Society of Industrial Apllied Mathematics, 8 (1960) 680–690.
Epstein B. The Exponential Distribution and its Role in Life Testing. Industrial Quality Control, 15 (1958) 2–7.
Goldman, A.S. and Slattery, T.B. Maintenability: A Major Element of System Effectiveness. Krieger, Huntington, New York, 1977.
Hariga, M. A Maintenance Inspection Model for a Single Machine with General Failure Distribution. Journal of Microelectronics and Reliability, 36 (1995) 353–358.
Jardine, A.K.S. Maintenance, Replacement and Reliability. Pitman, London, 1973.
McCall, J. Maintenance Policies for Stochastically Failing Equipment: A Survey. Management Science, 11 (1965) 493–524.
Moon, I. and Yun, W. An Economic Order Quantity Model with a Random Planning Horizon. The Engineering Economist, 39 (1993) 77–86.
Rachamadugu, R. and Ramasesh, R. Suboptimality of Equal Lot Sizes for Finite Horizon Problems. Naval Research Logistics, 41 (1994) 1019–1028.
Vaurio, J.K. A note on optimal inspection intervals, International Journal of Quality and Reliability Management, 11 (1994) 65–68.
Wang, W. and Christer, A.H. Modeling Procedure to Optimize Component Safety Inspection Over a Finite Time Horizon. Quality and Reliability Engineering International, 13 (1997) 217–224.
Wells, C.E. and Bryant, J.L. Optimal Preventive Maintenance Policies for Systems with Missions of Random Duration. IIE Transactions, 17 (1985) 338–345.
White, J.A., Case, K.E., Pratt, D.B., and Agee, M.H. Principles of Engineering Economic Analysis. 4th ed., John Wiley & Sons, Inc., New York, 1998.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2000 Springer Science+Business Media New York
About this chapter
Cite this chapter
Hariga, M., Al-Fawzan, M.A. (2000). Discounted Models for the Single Machine Inspection Problem. In: Ben-Daya, M., Duffuaa, S.O., Raouf, A. (eds) Maintenance, Modeling and Optimization. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-4329-9_10
Download citation
DOI: https://doi.org/10.1007/978-1-4615-4329-9_10
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4613-6944-8
Online ISBN: 978-1-4615-4329-9
eBook Packages: Springer Book Archive