IDEAS home Printed from https://ideas.repec.org/a/spr/ijsaem/v14y2023i4d10.1007_s13198-023-01936-x.html
   My bibliography  Save this article

Instantaneous failure analysis on Lindley distribution under progressive type II censoring

Author

Listed:
  • K. Muralidharan

    (The Maharaja Sayajirao University of Baroda)

  • Pratima Bavagosai

    (The Maharaja Sayajirao University of Baroda)

Abstract

This paper deals with the analysis of the occurrence of instantaneous failures in Lindley distribution using progressive type-II censored samples. The test items that fail at a time are called instantaneous failures. Such failures are naturally experienced in life testing experiments, clinical trials, weather predictions, geographic information systems, athlete performance analysis, and many other real fields. These occurrences may be due to the inferior quality of a product or service, faulty construction, or alignment of events/objects, or due to no response to the treatments. Such failures usually discard the assumption of a single-mode distribution and hence the usual method of modeling and inference procedures may not be accurate in practice. To tackle this problem, one must use a non-standard mixture of degenerate distribution degenerated at zero and a standard distribution of a continuous or discrete variable. In this paper, we have considered a non-standard mixture model with continuous Lindley failure distribution for positive components under a progressive type-II censoring scheme. We obtained the maximum likelihood estimators of the proposed distribution and its asymptotic, bootstrap-p (boot-p), and bootstrap-t (boot-t) confidence intervals are derived. The Bayes estimators for the proposed distribution parameters, reliability function, and hazard rate function with their highest posterior density credible intervals using informative priors and non-informative priors under different loss functions are obtained. The performances of different estimators are studied using the MCMC simulation technique. Two real-life data sets have been analyzed for illustration purposes.

Suggested Citation

  • K. Muralidharan & Pratima Bavagosai, 2023. "Instantaneous failure analysis on Lindley distribution under progressive type II censoring," 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(4), pages 1312-1339, August.
    • Handle: RePEc:spr:ijsaem:v:14:y:2023:i:4:d:10.1007_s13198-023-01936-x
    DOI: 10.1007/s13198-023-01936-x
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s13198-023-01936-x
    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/s13198-023-01936-x?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. M. E. Ghitany & D. K. Al-Mutairi, 2008. "Size-biased Poisson-Lindley distribution and its application," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 299-311.
    2. Krishna, Hare & Kumar, Kapil, 2011. "Reliability estimation in Lindley distribution with progressively type II right censored sample," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(2), pages 281-294.
    3. Ghitany, M.E. & Al-Mutairi, D.K. & Nadarajah, S., 2008. "Zero-truncated Poisson–Lindley distribution and its application," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(3), pages 279-287.
    4. Ghitany, M.E. & Atieh, B. & Nadarajah, S., 2008. "Lindley distribution and its application," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 78(4), pages 493-506.
    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. Singh, Bhupendra & Gupta, Puneet Kumar, 2012. "Load-sharing system model and its application to the real data set," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(9), pages 1615-1629.
    2. E.I., Abdul Sathar & K.V., Viswakala, 2019. "Non-parametric estimation of Kullback–Leibler discrimination information based on censored data," Statistics & Probability Letters, Elsevier, vol. 154(C), pages 1-1.
    3. Iman Makhdoom & Parviz Nasiri & Abbas Pak, 2016. "Bayesian approach for the reliability parameter of power Lindley 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. 7(3), pages 341-355, September.
    4. A. Asgharzadeh & A. Fallah & M. Z. Raqab & R. Valiollahi, 2018. "Statistical inference based on Lindley record data," Statistical Papers, Springer, vol. 59(2), pages 759-779, June.
    5. Neha Goel & Hare Krishna, 2022. "Estimation in Residual lifetime Lindley distribution with Type II censored data," 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. 13(1), pages 363-374, February.
    6. Muhammad Aslam Mohd Safari & Nurulkamal Masseran & Muhammad Hilmi Abdul Majid, 2020. "Robust Reliability Estimation for Lindley Distribution—A Probability Integral Transform Statistical Approach," Mathematics, MDPI, vol. 8(9), pages 1-21, September.
    7. Cha, Ji Hwan, 2019. "Poisson Lindley process and its main properties," Statistics & Probability Letters, Elsevier, vol. 152(C), pages 74-81.
    8. Irshad M. R. & Maya R., 2018. "On A Less Cumbersome Method Of Estimation Of Parameters Of Lindley Distribution By Order Statistics," Statistics in Transition New Series, Polish Statistical Association, vol. 19(4), pages 597-620, December.
    9. Yaoting Yang & Weizhong Tian & Tingting Tong, 2021. "Generalized Mixtures of Exponential Distribution and Associated Inference," Mathematics, MDPI, vol. 9(12), pages 1-22, June.
    10. Deepesh Bhati & Mohd. Malik & H. Vaman, 2015. "Lindley–Exponential distribution: properties and applications," METRON, Springer;Sapienza Università di Roma, vol. 73(3), pages 335-357, December.
    11. Festus C. Opone & Nosakhare Ekhosuehi & Sunday E. Omosigho, 2022. "Topp-Leone Power Lindley Distribution(Tlpld): its Properties and Application," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(2), pages 597-608, August.
    12. Marius Giuclea & Costin-Ciprian Popescu, 2022. "On Geometric Mean and Cumulative Residual Entropy for Two Random Variables with Lindley Type Distribution," Mathematics, MDPI, vol. 10(9), pages 1-10, April.
    13. Manal M. Yousef & Amal S. Hassan & Abdullah H. Al-Nefaie & Ehab M. Almetwally & Hisham M. Almongy, 2022. "Bayesian Estimation Using MCMC Method of System Reliability for Inverted Topp–Leone Distribution Based on Ranked Set Sampling," Mathematics, MDPI, vol. 10(17), pages 1-26, August.
    14. Manoj Kumar & Anurag Pathak & Sukriti Soni, 2019. "Bayesian Inference for Rayleigh Distribution Under Step-Stress Partially Accelerated Test with Progressive Type-II Censoring with Binomial Removal," Annals of Data Science, Springer, vol. 6(1), pages 117-152, March.
    15. Shovan Chowdhury, 2019. "Selection between Exponential and Lindley distributions," Working papers 316, Indian Institute of Management Kozhikode.
    16. Duha Hamed & Ahmad Alzaghal, 2021. "New class of Lindley distributions: properties and applications," Journal of Statistical Distributions and Applications, Springer, vol. 8(1), pages 1-22, December.
    17. Kantar, Yeliz Mert & Usta, Ilhan & Arik, Ibrahim & Yenilmez, Ismail, 2018. "Wind speed analysis using the Extended Generalized Lindley Distribution," Renewable Energy, Elsevier, vol. 118(C), pages 1024-1030.
    18. 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.
    19. Rama Shanker & Kamlesh Kumar Shukla, 2017. "Zero-Truncated Poisson-Garima Distribution and its Applications," Biostatistics and Biometrics Open Access Journal, Juniper Publishers Inc., vol. 3(1), pages 14-19, September.
    20. Cesar Augusto Taconeli & Suely Ruiz Giolo, 2020. "Maximum likelihood estimation based on ranked set sampling designs for two extensions of the Lindley distribution with uncensored and right-censored data," Computational Statistics, Springer, vol. 35(4), pages 1827-1851, December.

    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:4:d:10.1007_s13198-023-01936-x. 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.