Skip to main content
Log in

Start-Up Demonstration Tests Under Markov Dependence Model with Corrective Actions

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

Abstract

A general probability model for a start-up demonstration test is studied. The joint probability generating function of some random variables appearing in the Markov dependence model of the start-up demonstration test with corrective actions is derived by the method of probability generating function. By using the probability generating function, several characteristics relating to the distribution are obtained.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

REFERENCES

  • Aki, S. and Hirano, K. (1989). Estimation of parameters in the discrete distributions, of order k, Ann. Inst. Statist. Math., 41, 47–61.

    Google Scholar 

  • Aki, S. and Hirano, K. (1993). Discrete distributions related to succession events in a two-state Markov chain, Statistical Science & Data Analysis; Proceeding of the Third Pacific Area Statistical Conference (eds. K. Matusita, M. L. Puri and T. Hayakawa), 467–474, VSP International Science Publishers, Utrecht.

    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 

  • Balakrishnan, N., Balasubramanian, K. and Viveros, R. (1995). Start-up demonstration tests under correlation and corrective action, Naval Research Logistics, 42, 1271–1276.

    Google Scholar 

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

    Google Scholar 

  • Feller, W. (1968). An Introduction to Probability Theory and Its Applications, Vol. I, 3rd ed., Wiley, New York.

    Google Scholar 

  • Godbole, A. P. and Papastavridis, S. G. (1994). Runs and Patterns in Probability: Selected Papers, Kluwer Academic Publishers, Dordrecht.

    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, Wiley, New York.

    Google Scholar 

  • Mohanty, S. G. (1994). Success runs of length k in Markov dependent trials, Ann. Inst. Statist. Math., 46, 777–796.

    Google Scholar 

  • Philippou, A. N., Georghiou, C. and Philippou, G. N. (1983). A generalized geometric distribution and some of its properties, Statist. Probab. Lett., 1, 171–175.

    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

Authors

About this article

Cite this article

Balakrishnan, N., Mohanty, S.G. & Aki, S. Start-Up Demonstration Tests Under Markov Dependence Model with Corrective Actions. Annals of the Institute of Statistical Mathematics 49, 155–169 (1997). https://doi.org/10.1023/A:1003122908057

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1003122908057

Navigation