# Laplace-Stieltjes transform of the system mean lifetime via geometric process model

Open Mathematics (2016)

• Volume: 14, Issue: 1, page 384-392
• ISSN: 2391-5455

top

## Abstract

top
Operation principle of the engineering systems occupies an important role in the reliability theory. In most of the studies, the reliability function of the system is obtained analytically according to the structure of the system. Also in such studies the mean operating time of the system is calculated. However, the reliability function of some systems, such as repairable system, cannot be easily obtained analytically. In this case, forming Laplace-Stieltjes transform of the system can provide a solution to the problem. In this paper, we have designed a system which consists of two components that can be repairable with the aging property. Firstly, the Laplace-Stieltjes transform of the system is formed. Later, the mean operating time of the system is calculated by means of Laplace-Stieltjes transform. The system’s repair policy is evaluated depending on the geometric process. This property provides the aging of the system. We also provide special systems with different marginal lifetime distributions to illustrate the theoretical results in this study.

## How to cite

top

Gökhan Gökdere, and Mehmet Gürcan. "Laplace-Stieltjes transform of the system mean lifetime via geometric process model." Open Mathematics 14.1 (2016): 384-392. <http://eudml.org/doc/281134>.

@article{GökhanGökdere2016,
abstract = {Operation principle of the engineering systems occupies an important role in the reliability theory. In most of the studies, the reliability function of the system is obtained analytically according to the structure of the system. Also in such studies the mean operating time of the system is calculated. However, the reliability function of some systems, such as repairable system, cannot be easily obtained analytically. In this case, forming Laplace-Stieltjes transform of the system can provide a solution to the problem. In this paper, we have designed a system which consists of two components that can be repairable with the aging property. Firstly, the Laplace-Stieltjes transform of the system is formed. Later, the mean operating time of the system is calculated by means of Laplace-Stieltjes transform. The system’s repair policy is evaluated depending on the geometric process. This property provides the aging of the system. We also provide special systems with different marginal lifetime distributions to illustrate the theoretical results in this study.},
author = {Gökhan Gökdere, Mehmet Gürcan},
journal = {Open Mathematics},
keywords = {Cold standby system; Laplace-Stieltjes transform; System mean lifetime; Geometric process; cold standby system; system mean lifetime; geometric process},
language = {eng},
number = {1},
pages = {384-392},
title = {Laplace-Stieltjes transform of the system mean lifetime via geometric process model},
url = {http://eudml.org/doc/281134},
volume = {14},
year = {2016},
}

TY - JOUR
AU - Gökhan Gökdere
AU - Mehmet Gürcan
TI - Laplace-Stieltjes transform of the system mean lifetime via geometric process model
JO - Open Mathematics
PY - 2016
VL - 14
IS - 1
SP - 384
EP - 392
AB - Operation principle of the engineering systems occupies an important role in the reliability theory. In most of the studies, the reliability function of the system is obtained analytically according to the structure of the system. Also in such studies the mean operating time of the system is calculated. However, the reliability function of some systems, such as repairable system, cannot be easily obtained analytically. In this case, forming Laplace-Stieltjes transform of the system can provide a solution to the problem. In this paper, we have designed a system which consists of two components that can be repairable with the aging property. Firstly, the Laplace-Stieltjes transform of the system is formed. Later, the mean operating time of the system is calculated by means of Laplace-Stieltjes transform. The system’s repair policy is evaluated depending on the geometric process. This property provides the aging of the system. We also provide special systems with different marginal lifetime distributions to illustrate the theoretical results in this study.
LA - eng
KW - Cold standby system; Laplace-Stieltjes transform; System mean lifetime; Geometric process; cold standby system; system mean lifetime; geometric process
UR - http://eudml.org/doc/281134
ER -

## NotesEmbed?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.