No abstract

In this article, we investigate the effect of measurement errors on the performance of the VP (Variable Parameters) X¯ control chart. After introducing the VP scheme for the X¯ chart with measurement errors, we evaluate the chart performance by using the average time to signal criterion, and we investigate the effect of measurement errors on the chart’s performance through extensive numerical studies. In addition, we investigate the effect of multiple measurements and the value of the linearly covariate error model’s parameters on the performance of VP X¯ control chart. We also consider the overall performance of the VP X¯ control chart and the optimal design parameters. Finally, the application of the proposed scheme is shown through an illustrative example.

Evaluating the effect of measurement errors on either adaptive or simultaneous control charts has been a topic of interest for the researchers in the recent years. Nevertheless, the effect of measurement errors on both adaptive and simultaneous monitoring control charts has not been considered yet. In this paper, through extensive numerical studies, we evaluate the effect of measurement errors on an adaptive (variable parameters) simultaneous multivariate control chart for the mean vector and the variancecovariance matrix of p quality characteristics assumed to follow a multivariate normal distribution. In order to do so, (a) we use eight performance measures computed using a Markov chain model, (b) we consider the effects of multiple measurements as well as the error model's parameters, and (c) we also consider the overall performance of this adaptive simultaneous chart including the chart parameters values optimization, which have never been considered so far for this scheme. At last, a real case is presented in order to illustrate the proposed scheme. K E Y W O R D S

This paper considers adaptive schemes for the simultaneous monitoring of the mean and variability of a multivariate normal quality characteristic. At first, we extend an already existing bivariate nonadaptive simultaneous control chart to a multivariate one. Then, we develop several adaptive schemes, which will cover both previously bivariate and newly multivariate charts. After having designed adaptive schemes for the multivariate chart, eight performance measures are computed based on the run length, time to signal, number of observations to signal and number of switches to signal and evaluated using a new Markov chain model. With the developed performance measures, non-adaptive and adaptive schemes under different mean, variability, simultaneous shift sizes, and different number of quality characteristics are compared. Our scheme is also compared to one of the best methods available in the literature. A numerical example is also provided in order to demonstrate how the adaptive scheme can be implemented in practice.

No abstract