Measurement errors in statistical process monitoring

Recently, monitoring the process mean and variability simultaneously for multivariate processes by using a single control chart has drawn some attention. However, due to the complexity of multivariate distributions, existing methods in univariate processes cannot be readily extended to multivariate processes. In this paper, we propose a new single control chart which integrates the exponentially weighted moving average (EWMA) procedure with the generalized likelihood ratio (GLR) test for jointly monitoring both the multivariate process mean and variability. Due to the powerful properties of the GLR test and the EWMA procedure, the new chart provides quite robust and satisfactory performance in various cases, including detection of the decrease in variability and individual observation at the sampling point, which are very important cases in many practical applications but may not be well handled by existing approaches in the literature. The application of our proposed method is illustrated by a real data example in ambulatory monitoring.

A multivariate control chart for simultaneously monitoring process mean and variability

An overview on recent profile monitoring papers (2008–2018) based on conceptual classification scheme

The effect of measurement errors on the adaptive EWMA chart

Simultaneous monitoring of linear profile parameters under progressive setup

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. Copyright © 2016 John Wiley & Sons, Ltd.

Effect of Measurement Error on Joint Monitoring of Process Mean and Variability under Ranked Set Sampling

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. Copyright © 2016 John Wiley & Sons, Ltd.

Sum of Squares Control Charts for Monitoring of Multivariate Multiple Linear Regression Profiles in Phase II

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.

On the effect of measurement errors in simultaneous monitoring of mean vector and covariance matrix of multivariate processes

In recent years, some researches have been done on simultaneous monitoring of multivariate process mean vector and covariance matrix. However, the effect of measurement error, which exists in many practical applications, on the performance of these control charts is not well studied. In this paper, the effect of measurement error with linearly increasing variance on the performance of ELR control chart for simultaneous monitoring of multivariate process mean vector and covariance matrix is investigated. The multiple measurement approach is also extended to reduce this effect. Also, the performance of the proposed multiple measurement approach is evaluated in terms of average run length (ARL) and standard deviation run length (SDRL). Finally, the application of the proposed monitoring method is illustrated by a real data in manufacturing industry.

https://www.ije.ir/article_72703_416316cb0c21c4bd68977806b226b345.pdf

Simultaneous Monitoring of Multivariate Process Mean and Variability in the Presence of Measurement Error with Linearly Increasing Variance under Additive Covariate Model (RESEARCH NOTE)

Simultaneous monitoring of the mean vector and covariance matrix in multivariate processes allows practitioners to avoid the inflated false alarm rate that results from using two independent contro...

Reza Ghashghaei

Papers

Effect of Measurement Error on Joint Monitoring of Process Mean and Variability under Ranked Set Sampling

Sum of Squares Control Charts for Monitoring of Multivariate Multiple Linear Regression Profiles in Phase II

On the effect of measurement errors in simultaneous monitoring of mean vector and covariance matrix of multivariate processes

Simultaneous Monitoring of Multivariate Process Mean and Variability in the Presence of Measurement Error with Linearly Increasing Variance under Additive Covariate Model (RESEARCH NOTE)

New control charts for simultaneous monitoring of the mean vector and covariance matrix of multivariate multiple linear profiles