Monitoring polynomial profiles in quality control applications

Kazemzadeh, Reza Baradaran; Noorossana, Rassoul; Amiri, Amirhossein

doi:10.1007/s00170-008-1633-z

Cited by 53 publications

(48 citation statements)

References 17 publications

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“…Zou et al 7 proposed a multivariate exponentially weighted moving average (MEWMA) control chart to monitor general linear profiles in Phase II. Kazemzadeh et al 21 proposed a transformation based on orthogonal polynomial model and used a EWMA-based monitoring scheme in Phase II. Jin and Shi 22 , Walker and Wright 23 , Ding et al 24 , Williams et al 25 , Moguerza et al 26 , Vaghefi et al 27 , and Jensen and Birch 28 proposed methods for monitoring nonlinear profiles.…”

Section: Introductionmentioning

confidence: 99%

Phase II monitoring of multivariate multiple linear regression profiles

Eyvazian

Noorossana

Saghaei

et al. 2011

Quality & Reliability Eng

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In certain cases, the quality of a process or a product can be effectively characterized by two or more multiple linear regression profiles in which response variables are correlated. This structure can be modeled as multivariate multiple linear regression profiles. When linear profiles are monitored separately, then correlation between response variables is ignored and misleading results could be expected. To overcome this problem, the use of methods that consider the multivariate structure between response variables is inevitable. In this paper, we propose four methods to monitor this structure in Phase II. The performance of the methods is compared through simulation studies in terms of the average run length criterion. Furthermore, a method based on likelihood ratio approach is developed to determine the location of shifts and a numerical simulation is used to evaluate the performance of the proposed method. Finally, the use of the methods is illustrated by a numerical example.

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Section: Introductionmentioning

confidence: 99%

Phase II monitoring of multivariate multiple linear regression profiles

Eyvazian

Noorossana

Saghaei

et al. 2011

Quality & Reliability Eng

Self Cite

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“…Kazemzadeh et al 18 transformed a polynomial regression model to an orthogonal polynomial regression model and proposed a method based on using EWMA control charts to monitor the parameters of orthogonal polynomial regression model in Phase II. Kazemzadeh et al 19 proposed three Phase I methods for monitoring a kth-order polynomial profiles.…”

Section: Introductionmentioning

confidence: 99%

A case study on monitoring polynomial profiles in the automotive industry

Amiri

Jensen

Kazemzadeh

2010

Quality & Reliability Eng

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In some statistical process control applications, the quality of a process or product can be characterized by a relationship between a response variable and one explanatory variable, which is referred to as profile. We give an example here of a profile that can be described using a polynomial model. This example comes from the automotive industry, where one of the most important quality characteristics of an automobile engine is the relationship between the torque produced by an engine and the engine speed in revolutions per minute. We find for this data set that a second-order polynomial works well. In addition, we show that there is autocorrelation within each profile, thus an ordinary least-square method that ignores the autocorrelation is inappropriate. We propose a linear mixed model method as an alternative approach. After the reduction of the data to a series of parameter estimates, we then conduct a step-by-step Phase I analysis of the polynomial profiles monitoring using a T 2 -based procedure to check the stability of the process and whether or not there are outlying profiles. The remaining profiles are used to form the estimated mean vector and variance-covariance matrix to be used in Phase II studies. Finally, a brief discussion is presented to show how one can use these parameters in Phase II.

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“…Mahmoud (2008) and Zou et al (2007) considered the monitoring of multiple linear profiles. Kazemzadeh et al (2008Kazemzadeh et al ( , 2009a investigated some methods for monitoring of polynomial profiles on phase I and II respectively. Noorossana et al (2010a) studied monitoring of multivariate simple linear profiles on phase II.…”

Section: Introductionmentioning

confidence: 99%

Online monitoring of auto correlated linear profiles via mixed model

Soleimani

Narvand

Raissi

2013

IJMTM

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In statistical quality control a profile can be characterised by a given mathematical function between a quality characteristic and one or more explanatory process variables. Most existing control charts in the literature have been proposed for profile monitoring with the independence assumption of the observation within profiles. However in certain situation, this assumption can be violated. The present study focused on phase II of a linear profile monitoring and extends Jensen et al. (2008)'s work in applying linear mixed models on the presence of autocorrelation within profiles. Three methods namely Hotteling T 2 , multivariate exponential weighted moving average (MEWMA) control chart and multivariate cumulative sum (MCUSUM) control chart are discussed and their performances are compared in term of average run length (ARL). These techniques are illustrated with a real data set taken from an agriculture field.

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Monitoring polynomial profiles in quality control applications

Cited by 53 publications

References 17 publications

Phase II monitoring of multivariate multiple linear regression profiles

Phase II monitoring of multivariate multiple linear regression profiles

A case study on monitoring polynomial profiles in the automotive industry

Online monitoring of auto correlated linear profiles via mixed model

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