Performance of the Variable Parameters X¯ Control Chart in Presence of Measurement Errors

Self Cite

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

Section: Introductionmentioning

confidence: 99%

A variable parameters multivariate control chart for simultaneous monitoring of the process mean and variability with measurement errors

Sabahno

Castagliola

Amiri

2020

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“…The SPM literature of approximately 60 articles dealing with measurement errors are reviewed in Maleki et al For some more recent research works on measurement errors, see Yeong et al, Zaidi et al, Sabahno et al, Tang et al, Nguyen et al, and Tran et al A number of methods used as remedial approaches are outlined in Maleki et al, and the most used methodology to reduce measurement inaccuracy is by taking multiple measurements of each item, which was first proposed by Linna and Woodall . The multiple measurements approach keeps being investigated in research works to this day; hence, in this paper too, this remedial approach for measurement inaccuracy is implemented.…”

Section: Introductionmentioning

confidence: 99%

On monitoring the process mean of autocorrelated observations with measurement errors using the w‐of‐w runs‐rules scheme

Shongwe

Malela‐Majika

Castagliola

2020

Self Cite

Runs‐rules have been widely used since the 1950s in industrial and nonindustrial process monitoring applications to improve the performance of basic and other traditional monitoring schemes. However, none of the studies on runs‐rules have accounted for a process with a combined effect of measurement errors and autocorrelation. Hence, in this paper, the use of the w‐of‐w runs‐rules to improve the performance of the Shewhart trueX¯ scheme using an additive model with a constant variance and a first‐order autoregressive model is proposed. To reduce the combined negative effect of measurement errors and autocorrelation, we implement a sampling strategy based on rational subgroups in which (a) multiple measurements per item are taken (instead of a standard single measurement) and (b) non‐neighboring observations are gathered. Moreover, the latter sampling strategy is incorporated into the values of probability elements of a Markov chain matrix which is used to derive some closed‐form expressions for the zero‐ and steady‐state run‐length distribution. The main finding of this study is that, with respect to some overall performance measures, the proposed scheme outperforms the existing Shewhart trueX¯ scheme by a significant margin. A real‐life example is used to illustrate the practical implementation of the proposed scheme.

“…Lee presented the statistical designs of the VP R chart while Pourtaheri developed the VP chart for multinomial data with a three‐level classification scheme. The effect of measurement errors on the performance of the VP

\overset{X}{true}

chart was considered by Sabahno et al In view of the importance of monitoring the CV, coupled by the fact that most real‐life data in process monitoring are multivariate in nature and the salient feature of the VP strategy, this research develops a VP chart for monitoring the MCV (VP MCV). In the existing literature, none of the researchers have incorporated the VP strategy into the standard MCV chart for monitoring the MCV.…”

Section: Introductionmentioning

confidence: 99%

A proposed variable parameter control chart for monitoring the multivariate coefficient of variation

Chew

Khoo

Khaw

et al. 2019

An efficient process monitoring system is important for achieving sustainable manufacturing. The control charting technique is one of the most effective techniques to monitor process quality. In certain processes where the process mean and variance are not independent of one another, the coefficient of variation (CV), which measures the ratio of the standard deviation to the mean, should be monitored. In line with industrial settings, where at least two or more variables are monitored simultaneously in most processes, this paper proposes a variable parameter (VP) chart to monitor the multivariate CV (MCV). Formulae and algorithms to optimize the various performance measures are discussed. The proposed VP MCV chart is designed based on a Markov chain approach. The performance comparison shows that the proposed VP MCV chart prevails over the existing MCV charts, in terms of the average time to signal (ATS), standard deviation of the time of signal (SDTS), and expected average time to signal (EATS) criteria. An example is presented to illustrate the implementation of the proposed VP MCV chart.