Renewal theory with exponential and hyperbolic discounting

  • Authors:

  • J. a. m. Van der weide; Suyono;J. m. Van noortwijk

  • Affiliations:

  • Faculty of electrical engineering, mathematics and computer sciencedelft university of technologynl-2600 ga delft, the netherlands e-mail: j.m.vanderweide@tudelft.nl;Jurusan matematika fmipa universitas negeri jakartajakarta timur 13200, indonesia e-mail: synjkt@yahoo.com;Hkv consultantsnl-8203 ac lelystad, the netherlands and faculty of electrical engineering, mathematics and computer science delft university of technology nl-2600 ga delft, the netherlands e-mail: ...

  • Venue:
  • Probability in the Engineering and Informational Sciences
  • Year:
  • 2008

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Abstract

To determine optimal investment and maintenance decisions, the total costs should be minimized over the whole life of a system or structure. In minimizing life-cycle costs, it is important to account for the time value of money by discounting and to consider the uncertainties involved. This article presents new results in renewal theory with costs that can be discounted according to any discount function that is nonincreasing and monotonic over time (such as exponential, hyperbolic, generalized hyperbolic, and no discounting). The main results include expressions for the first and second moment of the discounted costs over a bounded and unbounded time horizon as well as asymptotic expansions for nondiscounted costs.