IDEAS home Printed from https://ideas.repec.org/a/spr/aistmt/v66y2014i4p759-787.html
   My bibliography  Save this article

Some binary start-up demonstration tests and associated inferential methods

Author

Listed:
  • N. Balakrishnan
  • M. Koutras
  • F. Milienos

Abstract

During the past few decades, substantial research has been carried out on start-up demonstration tests. In this paper, we study the class of binary start-up demonstration tests under a general framework. Assuming that the outcomes of the start-up tests are described by a sequence of exchangeable random variables, we develop a general form for the exact waiting time distribution associated with the length of the test (i.e., number of start-ups required to decide on the acceptance or rejection of the equipment/unit under inspection). Approximations for the tail probabilities of this distribution are also proposed. Moreover, assuming that the probability of a successful start-up follows a beta distribution, we discuss several estimation methods for the parameters of the beta distribution, when several types of observed data have been collected from a series of start-up tests. Finally, the performance of these estimation methods and the accuracy of the suggested approximations for the tail probabilities are illustrated through numerical experimentation. Copyright The Institute of Statistical Mathematics, Tokyo 2014

Suggested Citation

  • N. Balakrishnan & M. Koutras & F. Milienos, 2014. "Some binary start-up demonstration tests and associated inferential methods," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(4), pages 759-787, August.
    • Handle: RePEc:spr:aistmt:v:66:y:2014:i:4:p:759-787
    DOI: 10.1007/s10463-013-0424-y
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10463-013-0424-y
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10463-013-0424-y?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. DePoy Smith, Michelle L. & Griffith, William S., 2008. "The analysis and comparison of start-up demonstration tests," European Journal of Operational Research, Elsevier, vol. 186(3), pages 1029-1045, May.
    2. Martin, Donald E. K., 2004. "Markovian start-up demonstration tests with rejection of units upon observing d failures," European Journal of Operational Research, Elsevier, vol. 155(2), pages 474-486, June.
    3. N. Balakrishnan & P. Chan, 2000. "Start-Up Demonstration Tests with Rejection of Units upon Observing d Failures," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 52(1), pages 184-196, March.
    4. N. Balakrishnan & S. Mohanty & S. Aki, 1997. "Start-Up Demonstration Tests Under Markov Dependence Model with Corrective Actions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 49(1), pages 155-169, March.
    5. Martin, Donald E.K., 2008. "Application of auxiliary Markov chains to start-up demonstration tests," European Journal of Operational Research, Elsevier, vol. 184(2), pages 574-583, January.
    6. P. S. Chan & H. K. T. Ng & N. Balakrishnan, 2008. "Statistical inference for start-up demonstration tests with rejection of units upon observing d failures," Journal of Applied Statistics, Taylor & Francis Journals, vol. 35(8), pages 867-878.
    7. Ram Tripathi & Ramesh Gupta & John Gurland, 1994. "Estimation of parameters in the beta binomial model," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 46(2), pages 317-331, June.
    8. David Scollnik, 2010. "Bayesian statistical inference for start-up demonstration tests with rejection of units upon observing d failures," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(7), pages 1113-1121.
    9. Lee, Jack C & Sabavala, Darius J, 1987. "Bayesian Estimation and Prediction for the Beta-Binomial Model," Journal of Business & Economic Statistics, American Statistical Association, vol. 5(3), pages 357-367, July.
    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. N. Balakrishnan & M. V. Koutras & F. S. Milienos, 2017. "On the identifiability of start-up demonstration mixture models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(4), pages 717-735, August.
    2. Kiyoshi Inoue, 2021. "On Homogeneous Multivariate Distributions in Random Occupancy Models and Their Applications," Methodology and Computing in Applied Probability, Springer, vol. 23(3), pages 1129-1153, September.

    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. Xian Zhao, 2014. "On generalized start-up demonstration tests," Annals of Operations Research, Springer, vol. 212(1), pages 225-239, January.
    2. Athanasios Rakitzis & Demetrios Antzoulakos, 2015. "Start-up demonstration tests with three-level classification," Statistical Papers, Springer, vol. 56(1), pages 1-21, February.
    3. N. Balakrishnan & M. V. Koutras & F. S. Milienos, 2017. "On the identifiability of start-up demonstration mixture models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(4), pages 717-735, August.
    4. Zhao, Xian & Wang, Xiaoyue & Sun, Ge, 2015. "Start-up demonstration tests with sparse connection," European Journal of Operational Research, Elsevier, vol. 243(3), pages 865-873.
    5. Fang, Chen & Cui, Lirong, 2020. "Reliability analysis for balanced engine systems with m sectors by considering start-up probability," Reliability Engineering and System Safety, Elsevier, vol. 197(C).
    6. DePoy Smith, Michelle L. & Griffith, William S., 2008. "The analysis and comparison of start-up demonstration tests," European Journal of Operational Research, Elsevier, vol. 186(3), pages 1029-1045, May.
    7. Martin, Donald E.K., 2008. "Application of auxiliary Markov chains to start-up demonstration tests," European Journal of Operational Research, Elsevier, vol. 184(2), pages 574-583, January.
    8. Maria Iannario, 2015. "Detecting latent components in ordinal data with overdispersion by means of a mixture distribution," Quality & Quantity: International Journal of Methodology, Springer, vol. 49(3), pages 977-987, May.
    9. Domenico Piccolo & Rosaria Simone, 2019. "The class of cub models: statistical foundations, inferential issues and empirical evidence," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 28(3), pages 389-435, September.
    10. Martin, Donald E. K., 2004. "Markovian start-up demonstration tests with rejection of units upon observing d failures," European Journal of Operational Research, Elsevier, vol. 155(2), pages 474-486, June.
    11. Ali Jafari, 2012. "Inferences on the ratio of two generalized variances: independent and correlated cases," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 21(3), pages 297-314, August.
    12. Stathis Chadjiconstantinidis & Serkan Eryilmaz, 2023. "Computing waiting time probabilities related to $$ (k_{1},k_{2},\ldots ,k_{l})$$ ( k 1 , k 2 , … , k l ) pattern," Statistical Papers, Springer, vol. 64(5), pages 1373-1390, October.
    13. Roland Rathelot, 2012. "Measuring Segregation When Units are Small: A Parametric Approach," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 30(4), pages 546-553, June.
    14. Aubry, Philippe & Francesiaz, Charlotte & Guillemain, Matthieu, 2024. "On the impact of preferential sampling on ecological status and trend assessment," Ecological Modelling, Elsevier, vol. 492(C).
    15. D. Antzoulakos & S. Bersimis & M. Koutras, 2003. "On the distribution of the total number of run lengths," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 55(4), pages 865-884, December.
    16. A. N. Kumar & N. S. Upadhye, 2019. "Generalizations of distributions related to ( $$k_1,k_2$$ k 1 , k 2 )-runs," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 82(2), pages 249-268, March.
    17. Kolev Nikolai, 2005. "Run and Frequency Quotas Under Markovian Fashion and their Application in Risk Analysis," Stochastics and Quality Control, De Gruyter, vol. 20(1), pages 97-109, January.
    18. Gera, Amos E., 2018. "Simultaneous demonstration tests involving sparse failures," Statistics & Probability Letters, Elsevier, vol. 135(C), pages 26-31.
    19. Hekimoğlu, Mustafa & Karlı, Deniz, 2023. "Modeling repair demand in existence of a nonstationary installed base," International Journal of Production Economics, Elsevier, vol. 263(C).
    20. Kirtee Kamalja, 2014. "On the joint distribution of success runs of several lengths in the sequence of MBT and its applications," Statistical Papers, Springer, vol. 55(4), pages 1179-1206, November.

    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:aistmt:v:66:y:2014:i:4:p:759-787. 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.