IDEAS home Printed from https://ideas.repec.org/a/sae/risrel/v238y2024i2p304-323.html
   My bibliography  Save this article

A new failure times model for one and two failure modes system: A Bayesian study with Hamiltonian Monte Carlo simulation

Author

Listed:
  • Badamasi Abba
  • Hong Wang

Abstract

This paper presents an additive Gompertz-Weibull (AGW) distribution, a four-parameter hybrid probability distribution, and its applications in reliability engineering. The failure rate (FR) function of the proposed model demonstrates an increasing trend and a variety of bathtub shapes with or without a low and yet long-stable segment, making it appropriate for modelling a wide variety of real-world problems. Some relationships between the AGW’s FR and its mean residual life functions are examined. For parameter estimation, maximum likelihood and Bayesian inferences are considered. For posterior simulations, we use Hamiltonian Monte Carlo to evaluate the Bayes estimators of the AGW parameters. We evaluate the performance of the proposed AGW model to that of other recent bathtub distributions constructed following the same approach on three failure time datasets. The first two datasets represent device failure times, while the third represents early cable-joint failure times, all with bathtub FR. For comparison, five parametric and nonparametric evaluation criteria and the fitted FR and mean residual life curves were employed. The results indicated that the AGW model would be the best choice for describing failure times, especially when the bathtub-shaped FR of the presented dataset exhibits its three segments.

Suggested Citation

  • Badamasi Abba & Hong Wang, 2024. "A new failure times model for one and two failure modes system: A Bayesian study with Hamiltonian Monte Carlo simulation," Journal of Risk and Reliability, , vol. 238(2), pages 304-323, April.
    • Handle: RePEc:sae:risrel:v:238:y:2024:i:2:p:304-323
    DOI: 10.1177/1748006X221146367
    as

    Download full text from publisher

    File URL: https://journals.sagepub.com/doi/10.1177/1748006X221146367
    Download Restriction: no
    File URL: https://libkey.io/10.1177/1748006X221146367?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
    ---><---

    References listed on IDEAS

    as
    1. Abba, Badamasi & Wang, Hong & Bakouch, Hassan S., 2022. "A reliability and survival model for one and two failure modes system with applications to complete and censored datasets," Reliability Engineering and System Safety, Elsevier, vol. 223(C).
    2. Prataviera, Fábio & Ortega, Edwin M.M. & Cordeiro, Gauss M. & Pescim, Rodrigo R. & Verssani, Bruna A.W., 2018. "A new generalized odd log-logistic flexible Weibull regression model with applications in repairable systems," Reliability Engineering and System Safety, Elsevier, vol. 176(C), pages 13-26.
    3. Arne Henningsen & Ott Toomet, 2011. "maxLik: A package for maximum likelihood estimation in R," Computational Statistics, Springer, vol. 26(3), pages 443-458, September.
    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. Maness, Michael & Cirillo, Cinzia, 2016. "An indirect latent informational conformity social influence choice model: Formulation and case study," Transportation Research Part B: Methodological, Elsevier, vol. 93(PA), pages 75-101.
    2. Mazen Nassar & Refah Alotaibi & Ahmed Elshahhat, 2023. "Reliability Estimation of XLindley Constant-Stress Partially Accelerated Life Tests using Progressively Censored Samples," Mathematics, MDPI, vol. 11(6), pages 1-24, March.
    3. John-Fritz Thony & Jean Vaillant, 2022. "Parameter Estimation for a Fractional Black–Scholes Model with Jumps from Discrete Time Observations," Mathematics, MDPI, vol. 10(22), pages 1-17, November.
    4. Logar, Ivana & Brouwer, Roy & Campbell, Danny, 2020. "Does attribute order influence attribute-information processing in discrete choice experiments?," Resource and Energy Economics, Elsevier, vol. 60(C).
    5. Padayachee Trishanta & Khamiakova Tatsiana & Shkedy Ziv & Burzykowski Tomasz & Salo Perttu & Perola Markus, 2019. "A multivariate linear model for investigating the association between gene-module co-expression and a continuous covariate," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 18(2), pages 1-13, April.
    6. Refah Alotaibi & Mazen Nassar & Hoda Rezk & Ahmed Elshahhat, 2022. "Inferences and Engineering Applications of Alpha Power Weibull Distribution Using Progressive Type-II Censoring," Mathematics, MDPI, vol. 10(16), pages 1-21, August.
    7. Muhammet Burak Kılıç & Yusuf Şahin & Melih Burak Koca, 2021. "Genetic algorithm approach with an adaptive search space based on EM algorithm in two-component mixture Weibull parameter estimation," Computational Statistics, Springer, vol. 36(2), pages 1219-1242, June.
    8. Manisera, Marica & Zuccolotto, Paola, 2014. "Modeling rating data with Nonlinear CUB models," Computational Statistics & Data Analysis, Elsevier, vol. 78(C), pages 100-118.
    9. Teresa Backhaus, 2022. "Training in Late Careers - A Structural Approach," CRC TR 224 Discussion Paper Series crctr224_2022_382, University of Bonn and University of Mannheim, Germany.
    10. José H. Dias Gonçalves & João J. Ferreira Gomes & Lihki Rubio & Filipe R. Ramos, 2023. "A Generalized Log Gamma Approach: Theoretical Contributions and an Application to Companies’ Life Expectancy," Mathematics, MDPI, vol. 11(23), pages 1-23, November.
    11. Hancock, Thomas O. & Broekaert, Jan & Hess, Stephane & Choudhury, Charisma F., 2020. "Quantum choice models: A flexible new approach for understanding moral decision-making," Journal of choice modelling, Elsevier, vol. 37(C).
    12. Granado-Díaz, Rubén & Villanueva, Anastasio J. & Gómez-Limón, José A., 2022. "Willingness to accept for rewilding farmland in environmentally sensitive areas," Land Use Policy, Elsevier, vol. 116(C).
    13. Xu, Meng & Jiang, Mengke & Wang, Hua-Feng, 2021. "Integrating metabolic scaling variation into the maximum entropy theory of ecology explains Taylor's law for individual metabolic rate in tropical forests," Ecological Modelling, Elsevier, vol. 455(C).
    14. Thoralf Meyer & Paul Holloway & Thomas B. Christiansen & Jennifer A. Miller & Paolo D’Odorico & Gregory S. Okin, 2019. "An Assessment of Multiple Drivers Determining Woody Species Composition and Structure: A Case Study from the Kalahari, Botswana," Land, MDPI, vol. 8(8), pages 1-14, August.
    15. K Hervé Dakpo & Laure Latruffe & Yann Desjeux & Philippe Jeanneaux, 2021. "Latent Class Modelling for a Robust Assessment of Productivity: Application to French Grazing Livestock Farms," Journal of Agricultural Economics, Wiley Blackwell, vol. 72(3), pages 760-781, September.
    16. Lee, Kyungsub & Seo, Byoung Ki, 2017. "Modeling microstructure price dynamics with symmetric Hawkes and diffusion model using ultra-high-frequency stock data," Journal of Economic Dynamics and Control, Elsevier, vol. 79(C), pages 154-183.
    17. Ahmed Elshahhat & EL-Sayed A. El-Sherpieny & Amal S. Hassan, 2023. "The Pareto–Poisson Distribution: Characteristics, Estimations and Engineering Applications," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(1), pages 1058-1099, February.
    18. Authelet, Manon & Subervie, Julie & Meyfroidt, Patrick & Asquith, Nigel & Ezzine-de-Blas, Driss, 2021. "Economic, pro-social and pro-environmental factors influencing participation in an incentive-based conservation program in Bolivia," World Development, Elsevier, vol. 145(C).
    19. Jens Rommel & Julian Sagebiel & Marieke Cornelia Baaken & Jesús Barreiro‐Hurlé & Douadia Bougherara & Luigi Cembalo & Marija Cerjak & Tajana Čop & Mikołaj Czajkowski & María Espinosa‐Goded & Julia Höh, 2023. "Farmers' risk preferences in 11 European farming systems: A multi‐country replication of Bocquého et al. ()," Applied Economic Perspectives and Policy, John Wiley & Sons, vol. 45(3), pages 1374-1399, September.
    20. Sarrias, Mauricio, 2021. "A two recursive equation model to correct for endogeneity in latent class binary probit models," Journal of choice modelling, Elsevier, vol. 40(C).

    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:sae:risrel:v:238:y:2024:i:2:p:304-323. 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: SAGE Publications (email available below). General contact details of provider: .

    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.