The Effect of Measurement Errors on the Synthetic Chart

Abstract

Measurement errors often exist in quality control applications. In this paper, the performance of the synthetic N X chart is investigated when measurement errors exist using a linearly covariate error model. It is shown that the performance of the synthetic N X chart is significantly affected in the presence of measurement errors. The effect of taking multiple measurements for each item in a subgroup on the performance of synthetic N X chart is also investigated in this paper. An example is provided in order to illustrate the application of the synthetic N X chart with measurement errors.

The performance of the Shewhart-RZ control chart in the presence of measurement error

“…Since Bennet (1954) investigated the effect of measurement errors on the ShewhartX chart, there are many studies about the actual performance of various control charts in the presence of measurement error, for further details see for instance: Kanazuka (1986), , Linna, Woodall, and Busby (2001), Maravelakis (2004), Costa and Castagliola (2011), Maravelakis (2012). Recently, Hu et al (2015) investigated the performance of the syntheticX chart when measurement errors exist using a linear covariate error model and they showed that the performance of the syntheticX chart is significantly affected in the presence of measurement error. Very recently, Noorossana and Zerehsaz (2015) studied the effect of classical additive measurement error model on the most commonly used control charts for monitoring simple linear profiles with random explanatory variable.…”

On the Performance of Shewhart median Chart in the Presence of Measurement Errors

“…As recommended by Linna and Woodall, taking multiple measurements per item, in each sample, is a good strategy to compensate for the effect of measurement errors. However, the quality practitioner will have to balance between the extra cost and time associated with multiple measurements and an acceptable level of measurement error; see Hu et al …”

“…The control charts cited earlier for monitoring the sample median are designed under the assumption that the observations are obtained using measurements that are without error, but, in practice, the measurement process often involves error which may adversely affect the performance of the implemented control charts. Because Bennet investigated the effect of measurement errors on the Shewhart chart, the consequences of the measurement errors on the performance of various control charts have been studied by a number of authors, see, for example, Kanzuka, Linna and Woodall, Linna et al , Maravelakis, Costa and Castagliola, Maravelakis, Hu et al ., Noorossana and Zerehsaz, and Tran et al …”

The effect of measurement errors on the adaptive EWMA chart

“…Noorossana and Zerehsaz studied the effect of measurement errors on 3 control charts, including EWMA‐3, EWMA/R, and T 2 charts, for monitoring simple linear profiles with random explanatory variable. Hu et al investigated the statistical design of the synthetic chart in the presence of measurement errors. In some environments, the measurement error variance changes linearly with the process level.…”