A combined mixed-s-skip sampling strategy to reduce the effect of autocorrelation on the X̄ scheme with and without measurement errors

In order to reduce the effect of autocorrelation on theX ¯ monitoring scheme, a new sampling strategy is proposed to form rational subgroup samples of size n. It requires sampling to be done such that: (i) observations from two consecutive samples are merged, and (ii) some consecutive observations are skipped before sampling. This technique which is a generalized version of the mixed samples strategy is shown to yield a better reduction of the negative effect of autocorrelation when monitoring the mean of processes with and without measurement errors. For processes subjected to a combined effect of autocorrelation and measurement errors, the proposed sampling technique, together with multiple measurement strategy, yields an uniformly better zero-state run-length performance than its two main existing competitors for any autocorrelation level. However, in steady-state mode, it yields the best performance only when the monitoring process is subject to a high level of autocorrelation, for any given level of measurement errors. A real life example is used to illustrate the implementation of the proposed sampling strategy.

Evaluating environmental performance using new process capability indices for autocorrelated data

Traditionally, the process capability index is developed by assuming that the process output data are independent and follow normal distribution. However, in most environmental cases, the process data are autocorrelated. The autocorrelated process, if unrecognized as an independent process, can lead to erroneous decision making and unnecessary quality loss. In this paper, three new capability indices with unbiased estimators are proposed to relieve the independence assumption for the-nominal-the-best and the-smaller-the-better cases. Furthermore, we use mean squared error (MSE) and mean absolute percent error (MAPE) to compare the accuracy of our proposed indices to previous autocorrelated indices. The results show that our proposed capability indices outperform the predecessors.