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

Heuchenne

2018

In the literature, coefficient of variation control charts have been introduced under the assumption of no measurement errors. However, measurement errors always exist in practice, and they do affect the performance of control charts in the detection of an out‐of‐control situation. In this paper, we therefore study the performance of a coefficient of variation Shewhart‐type control chart (Shewhart‐CV chart) and also one‐sided coefficient of variation exponentially weighted moving average–type control charts (EWMA‐γ2 charts) using a model with linear covariates. Moreover, we propose and study the performance of a two‐sided EWMA‐γ2 chart using a model with linear covariates. Several figures and tables are provided and analyzed to evaluate the statistical performance of these control charts for different sources of measurement errors. The obtained results show that the precision and accuracy errors significantly affect the performance of both the Shewhart‐CV and EWMA‐γ2 control charts. An example illustrating the use of this study is finally presented.

“…The specific value of η = 0.28 is motivated by assuming an acceptable value for the signal‐to‐noise ratio

S N R = \sqrt{\frac{\frac{2}{1 + η^{2}}}{1 - \frac{1}{1 + η^{2}}}} = \frac{\sqrt{2}}{η},

Section: The Effect Of Measurement Errors On the Shewhart‐cv Control mentioning

confidence: 99%

On the performance of coefficient of variation charts in the presence of measurement errors

Heuchenne

2018

“…As a consequence, the c.d.f., the p.d.f., and the i.d.f. of

{\overset{Z}{true}}_{i}

can be deduced from the their counterparts in , and , see Tran et al for more details. In the resulting functions, we replace the index Z by

{\overset{Z}{true}}_{i}

.…”

Section: A Brief Review Of the Distribution Of The Sample Of The Ratiomentioning

confidence: 99%

Steady‐state ARL analysis of ARL‐unbiased EWMA‐RZ control chart monitoring the ratio of two normal variables

Knoth

2018

Very recently, control charts for monitoring the ratio of 2 normal variables have been investigated in statistical process control. In the two‐sided case, however, these control charts tend to be average run length (ARL) biased, in the sense that some out‐of‐control ARL values are larger than the in‐control ARL. This paper proposes an ARL‐unbiased EWMA control chart for monitoring of this kind of ratio with each subgroup consisting of n⩾1 sample units. Also, to study the long‐term properties of ARL‐unbiased EWMA‐RZ control chart, we investigate the steady‐state ARL. Several tables and figures are given to show the statistical properties of the proposed control charts. The comparison results show that the proposed ARL‐unbiased chart outperforms other two‐sided control charts in terms of the zero‐state and steady‐state ARL. An example illustrates the use of this chart on a real quality control problem from the food industry.

“…Furthermore, in many industrial scenarios, there often exist significant measurement errors that affect the performance of control charts. Since Bennet investigated the effect of measurement errors on the Shewhart

\overset{X}{true}

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, Kanazuka, Linna and Woodall, Linna et al, Maravelakis, Costa and Castagliola, Maravelakis, Hu et al, Noorossana and Zerehsaz, Hu et al, Tran et al, Tran et al, Cheng and Wang, Maleki et al, Tran, and Tran et al According to Maleki et al, an exact measurement is a rare phenomenon in any manufacturing and service environment that involves human intervention. Consequently, the existence of errors due to either the measurement instruments and/or operators is inevitable.…”

Section: Introductionmentioning

confidence: 99%

A Synthetic median control chart for monitoring the process mean with measurement errors

Rakitzis

2019

Recent studies show that the Shewhart median chart is widely used for detecting shifts in a process, but it is often rather inefficient in detecting small or moderate process shifts. In order to overcome this problem, a Synthetic chart can be used. This chart outperforms the Shewhart‐type chart because it uses the information about the time interval between two consecutive nonconforming samples. In this paper, we propose and study the Phase II Synthetic median control chart. A Markov chain methodology is used to evaluate the statistical performance of the proposed chart. Moreover, its performance is investigated in the presence of measurement errors, which are modelled by a linear covariate error model. We provide the results of an extensive numerical analysis with several tables and figures in order to show the statistical performance of the investigated chart, for both cases of measurement errors and no measurement errors. Finally, an example illustrates the use of the Synthetic median chart.