Effect of measurement error on exponentially weighted moving average control charts under ranked set sampling schemes

The AEWMA chart is an Adaptive EWMA (Exponentially Weighted Moving Average)–type chart that combines the Shewhart and the classical EWMA schemes in a smooth way. Its performance has been studied under the assumption that there is no measurement error in the quality characteristic. In this paper, we investigate the performance of the AEWMA chart when measurement errors exist using a linearly covariate error model. The presence of measurement errors with a linearly increasing measurement error standard deviation is also investigated. It turns out that, with the existence of measurement errors, the efficiency of the AEWMA chart can be strongly affected, and the negative effect can be compensated by taking multiple measurements at each sample point. Comparisons with the classical EWMA scheme confirm the superiority of the AEWMA scheme in detecting a wide range of shifts even in the presence of measurement errors. An example is provided to illustrate the use of the AEWMA chart with measurement errors.

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The effect of measurement errors on the adaptive EWMA chart

Tang

Castagliola

Sun

et al. 2018

“…In this paper, they investigated the properties of the Shewhart

\overset{X}{true}

and the S 2 charts with measurement errors, and they suggested taking multiple measurements to compensate for the effect of measurement errors, Maravelakis et al() evaluated the performance of the EWMA

\overset{X}{true}

and the CUSUM

\overset{X}{true}

charts, respectively, in the presence of measurement errors using the same linear covariate model. More recently, Haq et al studied the effect of measurement errors on the performance of the EWMA chart based on the ranked set sampling (RSS), median RSS (MRSS), imperfect RSS (IRSS), and imperfect MRSS (IMRSS) schemes. The statistical design of the synthetic chart with measurement errors has been studied by Hu et al Tang et al evaluated the properties of the AEWMA

\overset{X}{true}

chart in the presence of measurement errors, and they showed that the AEWMA

\overset{X}{true}

chart had a better overall performance compared with the EWMA

\overset{X}{true}

chart.…”

Section: Introductionmentioning

confidence: 99%

The performance of the adaptive EWMA median chart in the presence of measurement error

Tang

Castagliola

et al. 2018

In quality control applications, the control chart is a powerful tool but its performance is adversely affected by the contamination from either the inspector or the measuring device leading to measurement errors. In this paper, we investigate the performance of the AEWMA median chart with measurement errors, and a methodology is proposed to obtain the optimal parameters by considering a linearly covariate error model. Several figures and tables show that, with the existence of measurement errors, the efficiency of the AEWMA median chart can be strongly affected, but this negative effect can be compensated by taking multiple measurements at each sample point. Comparisons with the Shewhart and the classical EWMA schemes confirm the superiority of the AEWMA scheme for detecting a wide range of shifts in the case of precise and imprecise data. An example is provided to illustrate the use of the AEWMA median chart with measurement errors.

“…They showed that the RSS‐based mean charts are more powerful than the Shewhart mean chart based on SRS. For more details about the control charts based on different RSS schemes, refer to Abujiya and Muttlak, Abujiya et al , Abujiya et al , Al‐Omari and Haq, Mehmood, Haq, Haq et al , Haq et al , and the references cited therein.…”

Section: Introductionmentioning

confidence: 99%

A New Exponentially Weighted Moving Average Control Chart for Monitoring Process Dispersion

Haq

Brown

Moltchanova

2014

Self Cite

Exponentially weighted moving average (EWMA) control charts have been widely recognized as an advanced statistical process monitoring tool due to their excellent performance in detecting small to moderate shifts in process parameters. In this paper, we propose a new EWMA control chart for monitoring the process dispersion based on the best linear unbiased absolute estimator (BLUAE) obtained under paired ranked set sampling (PRSS) scheme, which we name EWMA‐PRSS chart. The performance of the EWMA‐PRSS chart is evaluated in terms of the average run length and standard deviation of run length, estimated using Monte Carlo simulations. These control charts are compared with their existing counterparts for detecting both increases and decreases in the process dispersion. It is observed that the proposed EWMA‐PRSS chart performs uniformly better than the EWMA dispersion charts based on simple random sampling and ranked set sampling (RSS) schemes. We also construct an EWMA chart based on imperfect PRSS (IPRSS) scheme, named EWMA‐IPRSS chart, for detecting overall changes in the process variability. It turns out that, with reasonable assumptions, the EWMA‐IPRSS chart outperforms the existing EWMA dispersion charts. A real data set is used to explain the construction and operation of the proposed EWMA‐PRSS chart. Copyright © 2014 John Wiley & Sons, Ltd.