In this paper first we apply ranked set sampling (RSS) procedure in joint monitoring of both process mean and variance. Then, we study the effect of measurement error on joint monitoring of process mean and variance when simple random sampling (SRS) as well as RSS procedure is used. The results prove that the measurement error can seriously deteriorate the ability of the control chart in detecting all out-of-control scenarios. The results also represent that using RSS procedure can improve the ability of the monitoring scheme in detecting mean shifts, variance shifts as well as joint shifts either measurement error exists or not. In other words, RSS procedure can reduce the adverse effect of measurement error on detecting ability of joint monitoring scheme. After that, we utilize multiple measurements at each sample point when both SRS and RSS procedures are used. We investigate the effect of parameters in the covariate model thorough a sensitivity analysis. Finally, the applicability of the proposed control charts is illustrated using a real case of the piston rings in an automotive engine manufactured by a forging process.

In this paper, we propose four control charts for simultaneous monitoring of mean vector and covariance matrix in multivariate multiple linear regression profiles in Phase II. The proposed control charts include sum of squares exponential weighted moving average (SS-EWMA) and sum of squares cumulative sum (SS-CUSUM) for monitoring regression parameters and corresponding covariance matrix and SS-EWMARe and SS-CUSUMRe control charts for monitoring mean vector and covariance matrix of residual. Proposed methods are able to identify the out-of-control parameter responsible for shift. The performance of the proposed control charts is compared with existing method through Monte-Carlo simulations. Moreover, the diagnostic performance of the proposed control charts is evaluated through simulation studies. The results show better performance of the proposed control charts rather than competing control chart. Finally, the applicability of the proposed control charts is illustrated using a real case of calibration application in the automotive industry.

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In this paper, we investigate the misleading effect of measurement errors on simultaneous monitoring of the multivariate process mean and variability. For this purpose, we incorporate the measurement errors into a hybrid method based on the generalized likelihood ratio (GLR) and exponentially weighted moving average (EWMA) control charts. After that, we propose four remedial methods to decrease the effects of measurement errors on the performance of the monitoring procedure. The performance of the monitoring procedure as well as the proposed remedial methods is investigated through extensive simulation studies and a real data example.

Abstract. In some applications, quality of product or performance of a process is described by some functional relationships among some variables known as multivariate linear pro le in the literature. In this paper, we propose Max-MEWMA and Max-MCUSUM control charts for simultaneous monitoring of mean vector and covariance matrix in multivariate multiple linear regression pro les in Phase II. The proposed control charts also have the ability to diagnose whether the location or variation of the process is responsible for out-of-control signal. The performance of the proposed control charts is compared with that of the existing method through Monte-Carlo simulations. Finally, the applicability of the proposed control charts is illustrated using a real case of calibration application in the automotive industry.