IDEAS home Printed from https://ideas.repec.org/a/spr/stpapr/v56y2015i1p1-21.html
   My bibliography  Save this article

Start-up demonstration tests with three-level classification

Author

Listed:
  • Athanasios Rakitzis
  • Demetrios Antzoulakos

Abstract

In this paper, we introduce and study three new start-up demonstration tests with two types of unsuccessful start-ups. The proposed tests use run and frequency quotas acceptance/rejection criteria, providing extensions of binary start-up demonstration tests that have previously appeared in the literature. Using a Markov chain approach we establish general formulas for the distribution of the number of start-ups until the termination of the test, its mean and its variance, as well as for the acceptance probability of the equipment. Numerical results are presented in order to illustrate our method while a practical guidance for the determination of a good start-up demonstration test is also given. Finally, we discuss two inferential procedures for the estimation of the reliability of a single start-up of the test. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • Athanasios Rakitzis & Demetrios Antzoulakos, 2015. "Start-up demonstration tests with three-level classification," Statistical Papers, Springer, vol. 56(1), pages 1-21, February.
  • Handle: RePEc:spr:stpapr:v:56:y:2015:i:1:p:1-21
    DOI: 10.1007/s00362-013-0564-4
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00362-013-0564-4
    Download Restriction: Access to full text is restricted to subscribers.

    File URL: https://libkey.io/10.1007/s00362-013-0564-4?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. Philippou, Andreas N. & Georghiou, Costas & Philippou, George N., 1983. "A generalized geometric distribution and some of its properties," Statistics & Probability Letters, Elsevier, vol. 1(4), pages 171-175, June.
    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 & 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.
    4. Spiros Dafnis & Andreas Philippou & Demetrios Antzoulakos, 2012. "Distributions of patterns of two successes separated by a string of k-2 failures," Statistical Papers, Springer, vol. 53(2), pages 323-344, May.
    5. M. V. Koutras & S. Bersimis & P. E. Maravelakis, 2007. "Statistical Process Control using Shewhart Control Charts with Supplementary Runs Rules," Methodology and Computing in Applied Probability, Springer, vol. 9(2), pages 207-224, June.
    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. Rothenberg, Thomas J, 1971. "Identification in Parametric Models," Econometrica, Econometric Society, vol. 39(3), pages 577-591, May.
    8. 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.
    9. Athanasios C. Rakitzis & Demetrios L. Antzoulakos, 2011. "Chi-square Control Charts with Runs Rules," Methodology and Computing in Applied Probability, Springer, vol. 13(4), pages 657-669, December.
    10. Kiyoshi Inoue & Sigeo Aki, 2009. "On waiting time distributions associated with compound patterns in a sequence of multi-state trials," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 61(2), pages 499-516, June.
    11. 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.
    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. Kiyoshi Inoue & Sigeo Aki, 2018. "Joint distributions of numbers of runs of specified lengths on directed trees," Statistical Papers, Springer, vol. 59(1), pages 249-269, March.

    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. 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.
    2. Xian Zhao, 2014. "On generalized start-up demonstration tests," Annals of Operations Research, Springer, vol. 212(1), pages 225-239, January.
    3. 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.
    4. 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).
    5. 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.
    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. 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.
    8. Gera, Amos E., 2018. "Simultaneous demonstration tests involving sparse failures," Statistics & Probability Letters, Elsevier, vol. 135(C), pages 26-31.
    9. Spiros D. Dafnis & Frosso S. Makri, 2022. "Weak runs in sequences of binary trials," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 85(5), pages 573-603, July.
    10. 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.
    11. Kiyoshi Inoue & Sigeo Aki, 2018. "Joint distributions of numbers of runs of specified lengths on directed trees," Statistical Papers, Springer, vol. 59(1), pages 249-269, March.
    12. Qing Han & Sigeo Aki, 2000. "Waiting Time Problems in a Two-State Markov Chain," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 52(4), pages 778-789, December.
    13. Sotirios Bersimis & Athanasios Sachlas & Philippe Castagliola, 2017. "Controlling Bivariate Categorical Processes using Scan Rules," Methodology and Computing in Applied Probability, Springer, vol. 19(4), pages 1135-1149, December.
    14. 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.
    15. 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.
    16. Sotiris Bersimis & Markos V. Koutras & George K. Papadopoulos, 2014. "Waiting Time for an Almost Perfect Run and Applications in Statistical Process Control," Methodology and Computing in Applied Probability, Springer, vol. 16(1), pages 207-222, March.
    17. Kocięcki, Andrzej & Kolasa, Marcin, 2023. "A solution to the global identification problem in DSGE models," Journal of Econometrics, Elsevier, vol. 236(2).
    18. Carvalho Lopes, Celia Mendes & Bolfarine, Heleno, 2012. "Random effects in promotion time cure rate models," Computational Statistics & Data Analysis, Elsevier, vol. 56(1), pages 75-87, January.
    19. Orazio Attanasio & Sarah Cattan & Emla Fitzsimons & Costas Meghir & Marta Rubio-Codina, 2020. "Estimating the Production Function for Human Capital: Results from a Randomized Controlled Trial in Colombia," American Economic Review, American Economic Association, vol. 110(1), pages 48-85, January.
    20. Markos V. Koutras & Demetrios P. Lyberopoulos, 2018. "Asymptotic results for jump probabilities associated to the multiple scan statistic," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 70(5), pages 951-968, 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:spr:stpapr:v:56:y:2015:i:1:p:1-21. 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.