IDEAS home Printed from https://ideas.repec.org/a/eee/reensy/v126y2014icp135-142.html
   My bibliography  Save this article

A drawback and an improvement of the classical Weibull probability plot

Author

Listed:
  • Jiang, R.

Abstract

The classical Weibull Probability Paper (WPP) plot has been widely used to identify a model for fitting a given dataset. It is based on a match between the WPP plots of the model and data in shape. This paper carries out an analysis for the Weibull transformations that create the WPP plot and shows that the shape of the WPP plot of the data randomly generated from a distribution model can be significantly different from the shape of the WPP plot of the model due to the high non-linearity of the Weibull transformations. As such, choosing model based on the shape of the WPP plot of data can be unreliable. A cdf-based weighted least squares method is proposed to improve the parameter estimation accuracy; and an improved WPP plot is suggested to avoid the drawback of the classical WPP plot. The appropriateness and usefulness of the proposed estimation method and probability plot are illustrated by simulation and real-world examples.

Suggested Citation

  • Jiang, R., 2014. "A drawback and an improvement of the classical Weibull probability plot," Reliability Engineering and System Safety, Elsevier, vol. 126(C), pages 135-142.
    • Handle: RePEc:eee:reensy:v:126:y:2014:i:c:p:135-142
    DOI: 10.1016/j.ress.2014.02.001
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0951832014000301
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ress.2014.02.001?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. N. Balakrishnan & E. Beutner & E. Cramer, 2010. "Exact two-sample nonparametric confidence, prediction, and tolerance intervals based on ordinary and progressively type-II right censored data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 19(1), pages 68-91, May.
    2. Hong, H.P., 2013. "Selection of regressand for fitting the extreme value distributions using the ordinary, weighted and generalized least-squares methods," Reliability Engineering and System Safety, Elsevier, vol. 118(C), pages 71-80.
    3. Zhang, Tieling & Dwight, Richard, 2013. "Choosing an optimal model for failure data analysis by graphical approach," Reliability Engineering and System Safety, Elsevier, vol. 115(C), pages 111-123.
    4. Jiang, R., 2013. "A new bathtub curve model with a finite support," Reliability Engineering and System Safety, Elsevier, vol. 119(C), pages 44-51.
    5. Zhang, L.F. & Xie, M. & Tang, L.C., 2007. "A study of two estimation approaches for parameters of Weibull distribution based on WPP," Reliability Engineering and System Safety, Elsevier, vol. 92(3), pages 360-368.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Jiang, Renyan & Qi, Faqun & Cao, Yu, 2023. "Relation between aging intensity function and WPP plot and its application in reliability modelling," Reliability Engineering and System Safety, Elsevier, vol. 229(C).
    2. Jia, Xiang & Wang, Dong & Jiang, Ping & Guo, Bo, 2016. "Inference on the reliability of Weibull distribution with multiply Type-I censored data," Reliability Engineering and System Safety, Elsevier, vol. 150(C), pages 171-181.
    3. Renyan Jiang, 2022. "A novel parameter estimation method for the Weibull distribution on heavily censored data," Journal of Risk and Reliability, , vol. 236(2), pages 307-316, April.

    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. Du, Yi-Mu & Sun, C.P., 2022. "A novel interpretable model of bathtub hazard rate based on system hierarchy," Reliability Engineering and System Safety, Elsevier, vol. 228(C).
    2. Salazar García, Juan Fernando & Guzmán Aguilar, Diana Sirley & Hoyos Nieto, Daniel Arturo, 2023. "Modelación de una prima de seguros mediante la aplicación de métodos actuariales, teoría de fallas y Black-Scholes en la salud en Colombia [Modelling of an insurance premium through the application," Revista de Métodos Cuantitativos para la Economía y la Empresa = Journal of Quantitative Methods for Economics and Business Administration, Universidad Pablo de Olavide, Department of Quantitative Methods for Economics and Business Administration, vol. 35(1), pages 330-359, June.
    3. Xiang Jia & Saralees Nadarajah & Bo Guo, 2020. "Inference on q-Weibull parameters," Statistical Papers, Springer, vol. 61(2), pages 575-593, April.
    4. Gupta, Ashutosh & Mukherjee, Bhaswati & Upadhyay, S.K., 2008. "Weibull extension model: A Bayes study using Markov chain Monte Carlo simulation," Reliability Engineering and System Safety, Elsevier, vol. 93(10), pages 1434-1443.
    5. Li, Der-Chiang & Lin, Liang-Sian, 2013. "A new approach to assess product lifetime performance for small data sets," European Journal of Operational Research, Elsevier, vol. 230(2), pages 290-298.
    6. Sonal Budhiraja & Biswabrata Pradhan, 2020. "Point and interval estimation under progressive type-I interval censoring with random removal," Statistical Papers, Springer, vol. 61(1), pages 445-477, February.
    7. Volterman, William & Balakrishnan, N. & Cramer, Erhard, 2012. "Exact nonparametric meta-analysis for multiple independent doubly Type-II censored samples," Computational Statistics & Data Analysis, Elsevier, vol. 56(5), pages 1243-1255.
    8. Almalki, Saad J. & Nadarajah, Saralees, 2014. "Modifications of the Weibull distribution: A review," Reliability Engineering and System Safety, Elsevier, vol. 124(C), pages 32-55.
    9. Ahmad, Abd EL-Baset A. & Ghazal, M.G.M., 2020. "Exponentiated additive Weibull distribution," Reliability Engineering and System Safety, Elsevier, vol. 193(C).
    10. Hong, H.P., 2013. "Selection of regressand for fitting the extreme value distributions using the ordinary, weighted and generalized least-squares methods," Reliability Engineering and System Safety, Elsevier, vol. 118(C), pages 71-80.
    11. N. Balakrishnan & E. Beutner & E. Cramer, 2013. "Computational aspects of statistical intervals based on two Type-II censored samples," Computational Statistics, Springer, vol. 28(3), pages 893-917, June.
    12. Dey Sanku & Waymyers Sophia & Kumar Devendra, 2020. "The Reflected-Shifted-Truncated Lindley Distribution with Applications," Stochastics and Quality Control, De Gruyter, vol. 35(2), pages 67-77, December.
    13. Beutner, E. & Cramer, E., 2014. "Using linear interpolation to reduce the order of the coverage error of nonparametric prediction intervals based on right-censored data," Journal of Multivariate Analysis, Elsevier, vol. 129(C), pages 95-109.
    14. Santosh B. Rane & Yahya A.M. Narvel & Niloy Khatua, 2017. "Development of mechanism for mounting secondary isolating contacts (SICs) in air circuit breakers (ACBs) with high operational reliability," 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. 8(2), pages 1816-1831, November.
    15. Santosh B. Rane & Yahya A. M. Narvel, 2016. "Reliability assessment and improvement of air circuit breaker (ACB) mechanism by identifying and eliminating the root causes," 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. 7(1), pages 305-321, December.
    16. Zhu, Tiefeng, 2020. "Reliability estimation for two-parameter Weibull distribution under block censoring," Reliability Engineering and System Safety, Elsevier, vol. 203(C).
    17. Francesca Condino & Filippo Domma, 2017. "A new distribution function with bounded support: the reflected generalized Topp-Leone power series distribution," METRON, Springer;Sapienza Università di Roma, vol. 75(1), pages 51-68, April.
    18. Zeng, Hongtao & Lan, Tian & Chen, Qiming, 2016. "Five and four-parameter lifetime distributions for bathtub-shaped failure rate using Perks mortality equation," Reliability Engineering and System Safety, Elsevier, vol. 152(C), pages 307-315.
    19. Negreiros, Ana Cláudia Souza Vidal de & Lins, Isis Didier & Moura, Márcio José das Chagas & Droguett, Enrique López, 2020. "Reliability data analysis of systems in the wear-out phase using a (corrected) q-Exponential likelihood," Reliability Engineering and System Safety, Elsevier, vol. 197(C).
    20. William Volterman & N. Balakrishnan, 2013. "Efficient iterative computation of mixture weights for pooled order statistics for meta-analysis of multiple type-II right censored data," Computational Statistics, Springer, vol. 28(5), pages 2231-2239, October.

    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:eee:reensy:v:126:y:2014:i:c:p:135-142. 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: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/reliability-engineering-and-system-safety .

    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.