چكيده به لاتين
There are chances that statistical observations are contaminated with outliers, in which case the resultant estimations and statistical analyses may suffer from inconsistencies. In the field of profile monitoring, presence of outliers will reduce the accuracy of profile’s parameters estimation in Phase I. This improper estimations will reduce the accuracy of process control in Phase II. A workaround for coping with the problem of outliers is to use the so-called robust statistics. As of present, only few research works have elaborated on the robust estimation of generalized linear models-based, GLM, profiles. In the present study, robust statistics were applied to estimate parameters of generalized linear models-based profiles to investigate the effect of such approach on the performance of monitoring such profiles. For this purpose, the parameters of the binomial and Poisson’s profiles were estimated in presence of outliers by using a robust estimator and then further monitored by means of T2 statistics. In order to compare the robust and non-robust estimations in terms of accuracy, a vector difference index, D2, was utilized. The results indicated the superior estimation accuracy of the robust estimators, as compared to the non-robust counterparts. Further analyzed were the effects of the estimations produced by the robust and non-robust estimators in the Phase-I profile monitoring on the Phase-II performance. According to the average run length, ARL, index, the results showed that the Phase II could end up with higher performance should the robust, rather than the non-robust, estimators were used. Investigating the variations of ARL, it was found that the changes in this index can be better evaluated when they are considered in relation to the distance between vectors. Estimation accuracy of the asymptotic distribution of the T2 statistic was also studied for the Poisson’s profiles in the Phase II; in this respect, it was theoretically found that, under a certain set of conditions in terms of the values of different parameters, this statistic exhibits a non-central chi-squared distribution. Sensitivity analysis was further conducted to investigate the behavior of the robust estimator in response to the number of observations in the profile, number of profiles, and percent contamination. The results showed that an increase in the number of observations within a profile tended to improve the estimation accuracy and elevate the breakthrough point. Focusing on the linear profiles, simulation runs were utilized to examine the statistical distributions of the T2 and t statistics in the independent variable coding method by the robust M estimators. The results proved that, in theory, both statistics would exhibit relatively the same statistical distributions should the M estimator was applied on a relatively large sample.
