# Optimal strategies for a replacement model

P.B. Bruns

Research output: Book/ReportReportOther research output

### Abstract

We examine a replacement system with discrete-time Markovian deterioration and finite state space $\{0,\ldots,N\}$. State 0 stands for a new system, and the higher the state the worse the system; a system in state $N$ is considered to be in a {\it bad state}. We impose the condition that the fraction of replacements in state $N$ should not be larger than some fixed number. We prove that a generalized control limit policy maximizes the expected time between two successive replacements and we explain explicitly how to derive this optimal policy. Some numerical examples are given.
Original language Undefined Enschede University of Twente, Department of Applied Mathematics Published - 2000

### Publication series

Name Department of Applied Mathematics, University of Twente 1518 0169-2690

• EWI-3338
• MSC-90B25
• IR-65706
• MSC-93E20

### Cite this

Bruns, P. B. (2000). Optimal strategies for a replacement model. Enschede: University of Twente, Department of Applied Mathematics.
Bruns, P.B. / Optimal strategies for a replacement model. Enschede : University of Twente, Department of Applied Mathematics, 2000.
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title = "Optimal strategies for a replacement model",
abstract = "We examine a replacement system with discrete-time Markovian deterioration and finite state space $\{0,\ldots,N\}$. State 0 stands for a new system, and the higher the state the worse the system; a system in state $N$ is considered to be in a {\it bad state}. We impose the condition that the fraction of replacements in state $N$ should not be larger than some fixed number. We prove that a generalized control limit policy maximizes the expected time between two successive replacements and we explain explicitly how to derive this optimal policy. Some numerical examples are given.",
keywords = "EWI-3338, MSC-90B25, IR-65706, MSC-93E20",
author = "P.B. Bruns",
note = "Imported from MEMORANDA",
year = "2000",
language = "Undefined",
publisher = "University of Twente, Department of Applied Mathematics",
number = "1518",

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Bruns, PB 2000, Optimal strategies for a replacement model. University of Twente, Department of Applied Mathematics, Enschede.

Optimal strategies for a replacement model. / Bruns, P.B.

Enschede : University of Twente, Department of Applied Mathematics, 2000.

Research output: Book/ReportReportOther research output

TY - BOOK

T1 - Optimal strategies for a replacement model

AU - Bruns, P.B.

N1 - Imported from MEMORANDA

PY - 2000

Y1 - 2000

N2 - We examine a replacement system with discrete-time Markovian deterioration and finite state space $\{0,\ldots,N\}$. State 0 stands for a new system, and the higher the state the worse the system; a system in state $N$ is considered to be in a {\it bad state}. We impose the condition that the fraction of replacements in state $N$ should not be larger than some fixed number. We prove that a generalized control limit policy maximizes the expected time between two successive replacements and we explain explicitly how to derive this optimal policy. Some numerical examples are given.

AB - We examine a replacement system with discrete-time Markovian deterioration and finite state space $\{0,\ldots,N\}$. State 0 stands for a new system, and the higher the state the worse the system; a system in state $N$ is considered to be in a {\it bad state}. We impose the condition that the fraction of replacements in state $N$ should not be larger than some fixed number. We prove that a generalized control limit policy maximizes the expected time between two successive replacements and we explain explicitly how to derive this optimal policy. Some numerical examples are given.

KW - EWI-3338

KW - MSC-90B25

KW - IR-65706

KW - MSC-93E20

M3 - Report

BT - Optimal strategies for a replacement model

PB - University of Twente, Department of Applied Mathematics

CY - Enschede

ER -

Bruns PB. Optimal strategies for a replacement model. Enschede: University of Twente, Department of Applied Mathematics, 2000.