Comparing the Times Between Successive Failures by Using the Weibull Distribution with Time-Varying Scale Parameter

Nuri Çelik; Aziz Kemal Konyalıoğlu

doi:10.1007/978-3-030-90421-0_46

Comparing the Times Between Successive Failures by Using the Weibull Distribution with Time-Varying Scale Parameter

Nuri Çelik
, Aziz Kemal Konyalıoğlu^*

^*Corresponding author for this work

Department of Management Engineering

Gebze Technical University

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

In this study, we propose a method for comparing three or more means of time between two failures (TBF) for different systems or processes. Traditionally, one-way ANOVA is used to compare the means of three or more group, however, this method is based on the normal distribution assumption. For this reason, we propose one-way ANOVA model whose error distribution is the Weibull distribution with time-varying scale parameter. Since, in reliability analysis, the TBFs are generally not identically and independently distributed and the Weibull distribution with time-varying scale parameter has been proposed to analyse the TBFs. We obtain the estimations of the unknown parameters with the maximum likelihood methodology. We also propose a new test statistic for testing the difference mean time failures. A Monte Carlo simulation study is performed for comparing the power of this proposed test statistics with the traditional ones. Simulation results show that the proposed methodologies are more preferable.

Original language	English
Title of host publication	Digitizing Production Systems - Selected Papers from ISPR 2021
Editors	Numan M. Durakbasa, M. Güneş Gençyılmaz
Publisher	Springer Science and Business Media Deutschland GmbH
Pages	541-549
Number of pages	9
ISBN (Print)	9783030904203
DOIs	https://doi.org/10.1007/978-3-030-90421-0_46
Publication status	Published - 2022
Event	International Symposium for Production Research, ISPR2021 - Virtual, Online Duration: 7 Oct 2021 → 9 Oct 2021

Publication series

Name	Lecture Notes in Mechanical Engineering
ISSN (Print)	2195-4356
ISSN (Electronic)	2195-4364

Conference

Conference	International Symposium for Production Research, ISPR2021
City	Virtual, Online
Period	7/10/21 → 9/10/21

Bibliographical note

Publisher Copyright:
© 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.

Keywords

Failure process
One-way ANOVA
Time-varying parameter
Weibull distribution

Access to Document

10.1007/978-3-030-90421-0_46

Cite this

Çelik, N., & Konyalıoğlu, A. K. (2022). Comparing the Times Between Successive Failures by Using the Weibull Distribution with Time-Varying Scale Parameter. In N. M. Durakbasa, & M. G. Gençyılmaz (Eds.), Digitizing Production Systems - Selected Papers from ISPR 2021 (pp. 541-549). (Lecture Notes in Mechanical Engineering). Springer Science and Business Media Deutschland GmbH. https://doi.org/10.1007/978-3-030-90421-0_46

Çelik, Nuri ; Konyalıoğlu, Aziz Kemal. / Comparing the Times Between Successive Failures by Using the Weibull Distribution with Time-Varying Scale Parameter. Digitizing Production Systems - Selected Papers from ISPR 2021. editor / Numan M. Durakbasa ; M. Güneş Gençyılmaz. Springer Science and Business Media Deutschland GmbH, 2022. pp. 541-549 (Lecture Notes in Mechanical Engineering).

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abstract = "In this study, we propose a method for comparing three or more means of time between two failures (TBF) for different systems or processes. Traditionally, one-way ANOVA is used to compare the means of three or more group, however, this method is based on the normal distribution assumption. For this reason, we propose one-way ANOVA model whose error distribution is the Weibull distribution with time-varying scale parameter. Since, in reliability analysis, the TBFs are generally not identically and independently distributed and the Weibull distribution with time-varying scale parameter has been proposed to analyse the TBFs. We obtain the estimations of the unknown parameters with the maximum likelihood methodology. We also propose a new test statistic for testing the difference mean time failures. A Monte Carlo simulation study is performed for comparing the power of this proposed test statistics with the traditional ones. Simulation results show that the proposed methodologies are more preferable.",

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Çelik, N & Konyalıoğlu, AK 2022, Comparing the Times Between Successive Failures by Using the Weibull Distribution with Time-Varying Scale Parameter. in NM Durakbasa & MG Gençyılmaz (eds), Digitizing Production Systems - Selected Papers from ISPR 2021. Lecture Notes in Mechanical Engineering, Springer Science and Business Media Deutschland GmbH, pp. 541-549, International Symposium for Production Research, ISPR2021, Virtual, Online, 7/10/21. https://doi.org/10.1007/978-3-030-90421-0_46

Comparing the Times Between Successive Failures by Using the Weibull Distribution with Time-Varying Scale Parameter. / Çelik, Nuri; Konyalıoğlu, Aziz Kemal.
Digitizing Production Systems - Selected Papers from ISPR 2021. ed. / Numan M. Durakbasa; M. Güneş Gençyılmaz. Springer Science and Business Media Deutschland GmbH, 2022. p. 541-549 (Lecture Notes in Mechanical Engineering).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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N2 - In this study, we propose a method for comparing three or more means of time between two failures (TBF) for different systems or processes. Traditionally, one-way ANOVA is used to compare the means of three or more group, however, this method is based on the normal distribution assumption. For this reason, we propose one-way ANOVA model whose error distribution is the Weibull distribution with time-varying scale parameter. Since, in reliability analysis, the TBFs are generally not identically and independently distributed and the Weibull distribution with time-varying scale parameter has been proposed to analyse the TBFs. We obtain the estimations of the unknown parameters with the maximum likelihood methodology. We also propose a new test statistic for testing the difference mean time failures. A Monte Carlo simulation study is performed for comparing the power of this proposed test statistics with the traditional ones. Simulation results show that the proposed methodologies are more preferable.

AB - In this study, we propose a method for comparing three or more means of time between two failures (TBF) for different systems or processes. Traditionally, one-way ANOVA is used to compare the means of three or more group, however, this method is based on the normal distribution assumption. For this reason, we propose one-way ANOVA model whose error distribution is the Weibull distribution with time-varying scale parameter. Since, in reliability analysis, the TBFs are generally not identically and independently distributed and the Weibull distribution with time-varying scale parameter has been proposed to analyse the TBFs. We obtain the estimations of the unknown parameters with the maximum likelihood methodology. We also propose a new test statistic for testing the difference mean time failures. A Monte Carlo simulation study is performed for comparing the power of this proposed test statistics with the traditional ones. Simulation results show that the proposed methodologies are more preferable.

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Çelik N, Konyalıoğlu AK. Comparing the Times Between Successive Failures by Using the Weibull Distribution with Time-Varying Scale Parameter. In Durakbasa NM, Gençyılmaz MG, editors, Digitizing Production Systems - Selected Papers from ISPR 2021. Springer Science and Business Media Deutschland GmbH. 2022. p. 541-549. (Lecture Notes in Mechanical Engineering). doi: 10.1007/978-3-030-90421-0_46

Comparing the Times Between Successive Failures by Using the Weibull Distribution with Time-Varying Scale Parameter

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Keywords

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