Renewal Function under Prefailure Lives Distributed as a Mixture of n Exponential Distributions: Obtaining the Parameters of Mixtures Using the Method of Moments

This paper deals with the problems of the theory of reliability of technical systems for the case when the prefailure lives of the restored (replaced) elements are distributed as a mixture of distributions. For a simple renewal process, when the prefailure lives are distributed as a mixture of expon...

Full description

Saved in:
Bibliographic Details
Published in:Journal of machinery manufacture and reliability 2019-05, Vol.48 (3), p.275-282
Main Authors: Fedotova, I. M., Vaynshtein, V. I., Tsibul’skii, G. M., Vaynshtein, Yu. V.
Format: Article
Language:English
Subjects:
Algorithms
Automation and Control in Mechanical Engineering
Engineering
Machines
Manufacturing
Method of moments
Parameter estimation
Processes
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:This paper deals with the problems of the theory of reliability of technical systems for the case when the prefailure lives of the restored (replaced) elements are distributed as a mixture of distributions. For a simple renewal process, when the prefailure lives are distributed as a mixture of exponential distributions, a method for obtaining the renewal function (average number of failures in the range from 0 to t) is presented. For the case n = 3, its explicit formula is written out. The case of n = 2 was considered in [1]. For mixtures of two and three distributions, such as exponential, Erlang, Rayleigh, and Maxwell distributions, an algorithm to obtain point estimates of the unknown parameters of the mixture in an explicit form is presented. In this work, the studies begun in [1, 2] are continued.
ISSN:1052-6188
1934-9394
DOI:10.3103/S105261881903004X