Interval-Valued Parametric Distribution Functions: Application to System Reliability Analysis

Authors

  • Jalal Chachi
  • Gholamreza Hesamian Payamnoor University

DOI:

https://doi.org/10.30495/jme.v10i0.355

Keywords:

Reliability system, Interval-valued parameter, Random variable, Probability of an event

Abstract

A lot of methods and models in classical reliability theory assume that all parameters of lifetime density function are precise.But in the real world applications imprecise information is often mixed up in the lifetimes and/or parameters of systems.However, the parameters sometimes cannot be recorded precisely due to machine errors, experiment, personal judgment, estimation or some other unexpected situations.When parameters in the lifetime distribution are interval-valued, the conventional reliability system may have difficulty for handling reliability function.Therefore, estimation methods for reliability characteristics have to be adapted to the situation of interval-valued parameters of life times in order to obtain realistic results.In this regard, the present paper will discuss  the system reliability for coherent system based on a new notion of random variable withinterval-valued parameters.The concepts of  probability density function and cumulative distribution function of the random variable with interval-valued parameters will be stated in this paper.Using the same techniques in probability theory, the probability measure of the random variable  can be constructed from the   probability density function and cumulative distribution function.In the proceeding discussion,  numerical  examples are provided in reliability systems to clarify our discussions.

Downloads

Published

2015-12-23

Issue

Vol. 10

Section

Vol. 10, No 1, (2016)

License

Upon acceptance of an article, authors will be asked to complete a 'Journal Publishing Agreement'. An e-mail will be sent to the corresponding author confirming receipt of the manuscript together with a "Journal Publishing Agreement" form or a link to the online version of this agreement.

Journal author rights

Authors have copyright but license exclusive rights in their article to the publisher. In this case authors have the right to:

  • Share their article in the same ways permitted to third parties under the relevant user license (together with Personal use rights) so long as it contains a link to the version of record on this website.
  • Retain patent, trademark and other intellectual property rights (including raw research data).
  • Proper attribution and credit for the published work.

Rights granted to this journal

The Journal of Mathematical Extension is granted the following rights:

  • This journal will apply the relevant third party user license where this journal publishes the article on its online platforms.
  • The right to provide the article in all forms and media so the article can be used on the latest technology even after publication.
  • The authority to enforce the rights in the article, on behalf of an author, against third parties, for example in the case of plagiarism or copyright infringement.

Protecting author right

Copyright aims to protect the specific way the article has been written to describe an experiment and the results. This journal is committed to its authors to protect and defend their work and their reputation and takes allegations of infringement, plagiarism, ethic disputes and fraud very seriously.

If an author becomes aware of a possible plagiarism, fraud or infringement we recommend contacting the editorial office immediately.

Personal use

Authors can use their articles, in full or in part, for a wide range of scholarly, non-commercial purposes as outlined below:

  • Use by an author in the author’s classroom teaching (including distribution of copies, paper or electronic)
  • Distribution of copies (including through e-mail) to known research colleagues for their personal use (but not for Commercial Use)
  • Inclusion in a thesis or dissertation (provided that this is not to be published commercially)
  • Use in a subsequent compilation of the author’s works
  • Extending the Article to book-length form
  • Preparation of other derivative works (but not for Commercial Use)
  • Otherwise using or re-using portions or excerpts in other works

These rights apply for all authors who publish their article in this journal. In all cases we require that all authors always include a full acknowledgement and, if appropriate, a link to the final published version hosted on this website.