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On the estimation of serial correlation in Markov-dependent production processes

Author

Listed:
  • Sueli Mingoti
  • Julia De Carvalho
  • Joab De Oliveira Lima

Abstract

In this paper, we present a study about the estimation of the serial correlation for Markov chain models which is used often in the quality control of autocorrelated processes. Two estimators, non-parametric and multinomial, for the correlation coefficient are discussed. They are compared with the maximum likelihood estimator [U.N. Bhat and R. Lal, Attribute control charts for Markov dependent production process, IIE Trans. 22 (2) (1990), pp. 181-188.] by using some theoretical facts and the Monte Carlo simulation under several scenarios that consider large and small correlations as well a range of fractions (p) of non-conforming items. The theoretical results show that for any value of p≠0.5 and processes with autocorrelation higher than 0.5, the multinomial is more precise than maximum likelihood. However, the maximum likelihood is better when the autocorrelation is smaller than 0.5. The estimators are similar for p=0.5. Considering the average of all simulated scenarios, the multinomial estimator presented lower mean error values and higher precision, being, therefore, an alternative to estimate the serial correlation. The performance of the non-parametric estimator was reasonable only for correlation higher than 0.5, with some improvement for p=0.5.

Suggested Citation

  • Sueli Mingoti & Julia De Carvalho & Joab De Oliveira Lima, 2008. "On the estimation of serial correlation in Markov-dependent production processes," Journal of Applied Statistics, Taylor & Francis Journals, vol. 35(7), pages 763-771.
    • Handle: RePEc:taf:japsta:v:35:y:2008:i:7:p:763-771
    DOI: 10.1080/02664760802005688
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    References listed on IDEAS

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    1. Nien Fan Zhang, 1998. "Estimating process capability indexes for autocorrelated data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 25(4), pages 559-574.
    2. C. D. Lai & M. Xie & K. Govindaraju, 2000. "Study of a Markov model for a high-quality dependent process," Journal of Applied Statistics, Taylor & Francis Journals, vol. 27(4), pages 461-473.
    3. Lee Ho, Linda & de Medeiros, Pledson Guedes & Borges, Wagner, 2007. "An alternative model for on-line quality monitoring for variables," International Journal of Production Economics, Elsevier, vol. 107(1), pages 202-222, May.
    4. V. S. Sampath Kumar & M. B. Rajarshi, 1987. "Continuous sampling plans for markov‐dependent production processes," Naval Research Logistics (NRL), John Wiley & Sons, vol. 34(5), pages 629-644, October.
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    Cited by:

    1. K. K. Kamalja, 2017. "Markov binomial distribution of order k and its applications," Statistical Papers, Springer, vol. 58(3), pages 831-853, September.

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