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

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.