Skip to main content
SpringerLink
Log in

Start-Up Demonstration Tests with Rejection of Units upon Observing d Failures

  • Published:
Annals of the Institute of Statistical Mathematics Aims and scope Submit manuscript

Abstract

The probability generating function of number of trials for the start-up demonstration test with rejection upon d failures is derived. The exact distribution of the number of trials is obtained. Some recurrence relations for the probabilities are also established. The average length of the test is derived. Some illustrative examples are finally presented.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Aki, S. (1997). On sooner and later problems between success and failure runs, Advances in Combinatorial Methods and Applications to Probability and Statistics (ed. N. Balakrishnan), 385–400, Birkhäuser, Boston.

    Google Scholar 

  • Aki, S. and Hirano, K. (1994). Distributions of numbers of failures and successes until the first consecutive k successes, Ann. Inst. Statist. Math., 46, 193–202.

    Google Scholar 

  • Aki, S. and Hirano, K. (1995). Joint distributions of numbers of success-runs and failures until the first consecutive k successes, Ann. Inst. Statist. Math., 47, 225–235.

    Google Scholar 

  • Balakrishnan, N. and Koutras, M. V. (2000). Runs and Scans with Applications, Wiley, New York (to appear).

    Google Scholar 

  • Balasubramanian, K., Viveros, R. and Balakrishnan, N. (1993). Sooner and later waiting time problems for Markovian Bernoulli trials, Statist. Probab. Lett., 18, 153–161.

    Google Scholar 

  • Ebneshahrashoob, M. and Sobel, M. (1990). Sooner and later waiting time problems for Bernoulli trials: Frequency and run quotas, Statist. Probab. Lett., 9, 5–11.

    Google Scholar 

  • Hahn, G. J. and Gage, J. B. (1983). Evaluation of a start-up demonstration test, Journal of Quality Technology, 15, 103–106.

    Google Scholar 

  • Johnson, N. L., Kotz, S. and Kemp, A. W. (1992). Univariate Discrete Distributions, 2nd ed., Wiley, New York.

    Google Scholar 

  • Koutras, M. V. (1996). On a waiting time distribution in a sequence of Bernoulli trials, Ann. Inst. Statist. Math., 48, 789–806.

    Google Scholar 

  • Koutras, M. V. and Balakrishnan, N. (1999). A start-up demonstration test using a simple scan-based statistic, Scan Statistics and Applications (eds. J. Glaz and N. Balakrishnan), 251–267, Birkhäuser, Boston.

    Google Scholar 

  • Viveros, R. and Balakrishnan, N. (1993). Statistical inference from start-up demonstration test data, Journal of Quality Technology, 25, 119–130.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, Canada, L8S 4K1

    N. Balakrishnan

  2. Department of Statistics, The Chinese University of Hong Kong, Shatin, Hong Kong, China

    P. S. Chan

Authors
  1. N. Balakrishnan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. P. S. Chan
    View author publications

    You can also search for this author in PubMed Google Scholar

About this article

Cite this article

Balakrishnan, N., Chan, P.S. Start-Up Demonstration Tests with Rejection of Units upon Observing d Failures. Annals of the Institute of Statistical Mathematics 52, 184–196 (2000). https://doi.org/10.1023/A:1004101402897

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1004101402897

Search

Navigation