Simple linear profiles monitoring in the presence of within profile autocorrelation

Soleimani, Paria; Noorossana, Rassoul; Amiri, Amirhossein

doi:10.1016/j.cie.2009.04.005

Cited by 100 publications

(106 citation statements)

References 27 publications

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“…Mahmoud (2008) monitored multiple linear regression model's parameters, intercept, slope, and variance, from the multiple linear profiles. Soleimani et al (2009) dealt with simple linear profiles with a first-order autoregressive relationship among observations within a profile. Zhu and Lin (2010) proposed a Shewhart control chart for monitoring slopes of linear profiles from the truncated vertical density profiles problem (Walker and Wright, 2002).…”

Section: Methods In Linear Profile Monitoringmentioning

confidence: 99%

Real-time detection of wave profile changes

Chang

Tavakkol

Chou

et al. 2014

Computers & Industrial Engineering

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SA statistical process control (SPC) framework is proposed to detect potential changes of a wave profile on a real-time basis. In regular profile monitoring, change detection takes place when a complete profile is generated. In this study, the detection of a potential profile change takes place before the entire information on the profile of interest is fully available. The main research goal is to make a correct process decision as soon as possible. A real-world example of condensation-water-temperature profile monitoring was used to demonstrate the proposed framework. A simulation study was also conducted. The simulation results confirm that the proposed framework is capable of detecting profile changes without having to wait for the entire profile to be generated.

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Section: Methods In Linear Profile Monitoringmentioning

confidence: 99%

Real-time detection of wave profile changes

Chang

Tavakkol

Chou

et al. 2014

Computers & Industrial Engineering

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“…(2), there exist auto-correlations between observations within each profile. Soleimani et al (2009) showed that the existing auto-correlation between the error terms within each profile affects the performance of the control charts for simple linear profiles. Therefore, they applied a transformation to eliminate the effect of auto-correlation.…”

Section: Auto-correlated Simple Linear Regression Modelmentioning

confidence: 99%

“…Now, the EWMA-3 method, first introduced by Kim et al (2003), is applied to monitor the transformed simple linear profile with uncorrelated observations in Phase II. Several researchers showed that the EWMA-3 procedure outperforms other methods such as T 2 and EWMA/R for most of the shift magnitudes in each of the parameters (see Kim et al (2003); Soleimani et al (2009) for more details). In this method, the x 0 -values are coded such that the average coded value is zero.…”

Section: Auto-correlated Simple Linear Regression Modelmentioning

confidence: 99%

“…Such a relationship is commonly referred to as a profile and may be represented by a simple linear, a multiple linear, a polynomial, or a nonlinear regression model. Simple linear profiles are mostly used in calibration applications and are widely studied in the literature for both Phases I and II monitoring; see, for example, Kang and Albin (2000), Kim et al (2003), Zhang et al (2009), Saghaei et al (2009), Mahmoud and Woodall (2004), Mahmoud et al (2010), Soleimani et al (2009), andHossienifard et al (2011). Besides, some authors including Mahmoud (2008), Jensen et al (2008), Amiri et al (2012), and Kazemzadeh et al (2010) considered more complicated models such as multiple linear and polynomial regression profiles.…”

Section: Introduction and Literature Reviewmentioning

confidence: 99%

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Identifying the time of a step change in AR(1) auto-correlated simple linear profiles

Khedmati

Niaki

2015

J Ind Eng Int

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Assuming a first-order auto-regressive model for the auto-correlation structure between observations, in this paper, a transformation method is first employed to eliminate the effect of auto-correlation. Then, a maximum likelihood estimator (MLE) of a step change in the parameters of the transformed model is derived and three separate EWMA control charts are used to monitor the parameters of the profile. The performance of the proposed change-point estimator is next compared to the one of the built-in change-point estimator of EWMA control chart through some simulation experiments. The results show that the proposed MLE of the change point accurately estimates the true change point and outperforms the built-in estimator of EWMA chart for almost all shift values and auto-correlation coefficients, while the built-in estimator of EWMA chart, in general, underestimates the true change point.

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“…Phase-II monitoring of linear profiles in multistage processes has been investigated by authors including Esmaeeli and Sadeghieh (2013) and Eghbali Ghahyazi et al (2014). Soleimani et al (2009) studied the presence of within-profile autocorrelation in simple profile monitoring. Moreover, Atashgar et al (2014) investigated the Phase-I monitoring problem of multistage processes using the T 2 scheme of Stover and Brill (1998), the T 2 control chart of Kang and Albin (2000), and the T 2 chart of Williams et al (2007).…”

Section: Introduction and Literature Reviewmentioning

confidence: 99%

Phase-I monitoring of standard deviations in multistage linear profiles

et al. 2017

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In most modern manufacturing systems, products are often the output of some multistage processes. In these processes, the stages are dependent on each other, where the output quality of each stage depends also on the output quality of the previous stages. This property is called the cascade property. Although there are many studies in multistage process monitoring, there are fewer works on profile monitoring in multistage processes, especially on the variability monitoring of a multistage profile in Phase-I for which no research is found in the literature. In this paper, a new methodology is proposed to monitor the standard deviation involved in a simple linear profile designed in Phase I to monitor multistage processes with the cascade property. To this aim, an autoregressive correlation model between the stages is considered first. Then, the effect of the cascade property on the performances of three types of T 2 control charts in Phase I with shifts in standard deviation is investigated. As we show that this effect is significant, a U statistic is next used to remove the cascade effect, based on which the investigated control charts are modified. Simulation studies reveal good performances of the modified control charts.

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Simple linear profiles monitoring in the presence of within profile autocorrelation

Cited by 100 publications

References 27 publications

Real-time detection of wave profile changes

Real-time detection of wave profile changes

Identifying the time of a step change in AR(1) auto-correlated simple linear profiles

Phase-I monitoring of standard deviations in multistage linear profiles

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