IDEAS home Printed from https://ideas.repec.org/a/spr/ijsaem/v14y2023i1d10.1007_s13198-022-01832-w.html
   My bibliography  Save this article

Stress–strength reliability models on power-Muth distribution

Author

Listed:
  • Prashant Kumar Sonker

    (Banaras Hindu University)

  • Mukesh Kumar

    (Banaras Hindu University)

  • Agni Saroj

    (Banaras Hindu University)

Abstract

The power Muth distribution (PM), was first introduced by Jodra et al. (Math Model Anal 22(2):186–201, 2017) with great applicability in reliability theory. In this paper, we studied parameter estimation of PM distribution to know the changes in the behaviour of distribution by varying their parameters. Also, the reliability estimation, the stress–strength reliability (SSR) and the multi-component stress–strength reliability (MSSR) estimation are carried out. For the stress–strength model, the component strength and the stress applied to it, both are independent random variables and follow similar PM distribution. SSR describes the probability that the component strength is greater than the stress applied to it. While the MSSR works based on s-out-of-k ( $$1\le s \le k$$ 1 ≤ s ≤ k ) model which is described as the probability that at least s-out-of-k components’ strength are greater than the stress applied on it. Reliability behaviour is the major objective of this paper. For the estimation of parameters, we are inclined towards the maximum likelihood and maximum product spacing method of estimation. Based on their mean square error we compared these two. In the multi-component reliability model, the suitable trend is observed based on the number of components’ strengths exceeding the stresses applied to them. The effect of shape and scale parameters of PM distribution on various reliability models is observed. All the above statistical performances are carried out via the Monte Carlo simulation process. Real data applicability of the distribution is applied to the stress rupture life of Kevlar pressure vessel data on different used reliability models.

Suggested Citation

  • Prashant Kumar Sonker & Mukesh Kumar & Agni Saroj, 2023. "Stress–strength reliability models on power-Muth distribution," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 14(1), pages 173-195, March.
    • Handle: RePEc:spr:ijsaem:v:14:y:2023:i:1:d:10.1007_s13198-022-01832-w
    DOI: 10.1007/s13198-022-01832-w
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s13198-022-01832-w
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s13198-022-01832-w?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Tanmay Kayal & Yogesh Mani Tripathi & Sanku Dey & Shuo-Jye Wu, 2020. "On estimating the reliability in a multicomponent stress-strength model based on Chen distribution," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 49(10), pages 2429-2447, May.
    2. D. K. Al-Mutairi & M. E. Ghitany & Debasis Kundu, 2015. "Inferences on Stress-Strength Reliability from Weighted Lindley Distributions," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 44(19), pages 4096-4113, October.
    3. G. Srinivasa Rao & Muhammad Aslam & Debasis Kundu, 2015. "Burr-XII Distribution Parametric Estimation and Estimation of Reliability of Multicomponent Stress-Strength," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 44(23), pages 4953-4961, December.
    4. Anatolyev, Stanislav & Kosenok, Grigory, 2005. "An Alternative To Maximum Likelihood Based On Spacings," Econometric Theory, Cambridge University Press, vol. 21(2), pages 472-476, April.
    5. Fatih Kızılaslan & Mustafa Nadar, 2018. "Estimation of reliability in a multicomponent stress–strength model based on a bivariate Kumaraswamy distribution," Statistical Papers, Springer, vol. 59(1), pages 307-340, March.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Liang Wang & Huizhong Lin & Kambiz Ahmadi & Yuhlong Lio, 2021. "Estimation of Stress-Strength Reliability for Multicomponent System with Rayleigh Data," Energies, MDPI, vol. 14(23), pages 1-23, November.
    2. Yuhlong Lio & Tzong-Ru Tsai & Liang Wang & Ignacio Pascual Cecilio Tejada, 2022. "Inferences of the Multicomponent Stress–Strength Reliability for Burr XII Distributions," Mathematics, MDPI, vol. 10(14), pages 1-28, July.
    3. Kundan Singh & Amulya Kumar Mahto & Yogesh Mani Tripathi & Liang Wang, 2024. "Estimation in a multicomponent stress-strength model for progressive censored lognormal distribution," Journal of Risk and Reliability, , vol. 238(3), pages 622-642, June.
    4. Hossein Pasha-Zanoosi, 2024. "Estimation of multicomponent stress-strength reliability based on a bivariate Topp-Leone distribution," OPSEARCH, Springer;Operational Research Society of India, vol. 61(2), pages 570-602, June.
    5. Shubham Saini & Renu Garg, 2022. "Reliability inference for multicomponent stress–strength model from Kumaraswamy-G family of distributions based on progressively first failure censored samples," Computational Statistics, Springer, vol. 37(4), pages 1795-1837, September.
    6. M. S. Kotb & M. Z. Raqab, 2021. "Estimation of reliability for multi-component stress–strength model based on modified Weibull distribution," Statistical Papers, Springer, vol. 62(6), pages 2763-2797, December.
    7. Amal S. Hassan & Ibrahim M. Almanjahie & Amer Ibrahim Al-Omari & Loai Alzoubi & Heba Fathy Nagy, 2023. "Stress–Strength Modeling Using Median-Ranked Set Sampling: Estimation, Simulation, and Application," Mathematics, MDPI, vol. 11(2), pages 1-19, January.
    8. Suparna Basu & Sanjay Kumar Singh & Umesh Singh, 2017. "Parameter estimation of inverse Lindley distribution for Type-I censored data," Computational Statistics, Springer, vol. 32(1), pages 367-385, March.
    9. Ehab M. Almetwally & Hanan A. Haj Ahmad, 2020. "A new generalization of the Pareto distribution and its applications," Statistics in Transition New Series, Polish Statistical Association, vol. 21(5), pages 61-84, December.
    10. Liang Wang & Sanku Dey & Yogesh Mani Tripathi, 2022. "Classical and Bayesian Inference of the Inverse Nakagami Distribution Based on Progressive Type-II Censored Samples," Mathematics, MDPI, vol. 10(12), pages 1-18, June.
    11. Cesar Augusto Taconeli & Idemauro Antonio Rodrigues Lara, 2022. "Improved confidence intervals based on ranked set sampling designs within a parametric bootstrap approach," Computational Statistics, Springer, vol. 37(5), pages 2267-2293, November.
    12. Grigoriy Volovskiy & Udo Kamps, 2020. "Maximum product of spacings prediction of future record values," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 83(7), pages 853-868, October.
    13. Suparna Basu & Sanjay K. Singh & Umesh Singh, 2019. "Estimation of Inverse Lindley Distribution Using Product of Spacings Function for Hybrid Censored Data," Methodology and Computing in Applied Probability, Springer, vol. 21(4), pages 1377-1394, December.
    14. Hanem Mohamed & Salwa A. Mousa & Amina E. Abo-Hussien & Magda M. Ismail, 2022. "Estimation of the Daily Recovery Cases in Egypt for COVID-19 Using Power Odd Generalized Exponential Lomax Distribution," Annals of Data Science, Springer, vol. 9(1), pages 71-99, February.
    15. Farha Sultana & Yogesh Mani Tripathi & Shuo-Jye Wu & Tanmay Sen, 2022. "Inference for Kumaraswamy Distribution Based on Type I Progressive Hybrid Censoring," Annals of Data Science, Springer, vol. 9(6), pages 1283-1307, December.
    16. Akram Kohansal, 2019. "On estimation of reliability in a multicomponent stress-strength model for a Kumaraswamy distribution based on progressively censored sample," Statistical Papers, Springer, vol. 60(6), pages 2185-2224, December.
    17. Mohamed Sief & Xinsheng Liu & Abd El-Raheem Mohamed Abd El-Raheem, 2024. "Inference for a constant-stress model under progressive type-II censored data from the truncated normal distribution," Computational Statistics, Springer, vol. 39(5), pages 2791-2820, July.
    18. Liu, Yiming & Shi, Yimin & Bai, Xuchao & Zhan, Pei, 2018. "Reliability estimation of a N-M-cold-standby redundancy system in a multicomponent stress–strength model with generalized half-logistic distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 231-249.
    19. Mazen Nassar & Ahmed Elshahhat, 2023. "Statistical Analysis of Inverse Weibull Constant-Stress Partially Accelerated Life Tests with Adaptive Progressively Type I Censored Data," Mathematics, MDPI, vol. 11(2), pages 1-29, January.
    20. Mazen Nassar & Farouq Mohammad A. Alam, 2022. "Analysis of Modified Kies Exponential Distribution with Constant Stress Partially Accelerated Life Tests under Type-II Censoring," Mathematics, MDPI, vol. 10(5), pages 1-26, March.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:ijsaem:v:14:y:2023:i:1:d:10.1007_s13198-022-01832-w. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.