A Self-Starting Control Chart for Linear Profiles

Zou, Changliang; Zhou, Chunguang; Wang, Zhaojun; Tsung, Fugee

doi:10.1080/00224065.2007.11917702

Cited by 93 publications

(52 citation statements)

References 31 publications

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“…Thus, determination of the required Phase I sample sizes to remove the effects of estimated parameters and a general recommendation are needed. An ongoing effort of the authors is to develop a self-starting version of LEWMA that can handle sequential monitoring by simultaneously updating parameter estimates and checking for OC conditions and to compare it with the self-starting scheme designed under the normality assumption proposed by Zou et al (2007b). Moreover, in the high-dimensional profile monitoring, monitoring all the components of the covariance matrix of the profile may be of practical interest.…”

Section: Discussionmentioning

confidence: 97%

LASSO-based multivariate linear profile monitoring

2010

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In many applications of manufacturing and service industries, the quality of a process is characterized by the functional relationship between a response variable and one or more explanatory variables. Profile monitoring is for checking the stability of this relationship over time. In some situations, multiple profiles are required in order to model the quality of a product or process effectively. General multivariate linear profile monitoring is particularly useful in practice due to its simplicity and flexibility. However, in such situations, the existing parametric profile monitoring methods suffer from a drawback in that when the profile parameter dimensionality is large, the detection ability of the procedures commonly used T 2 -type charting statistics is likely to decline substantially. Moreover, it is also challenging to isolate the type of profile parameter change in such high-dimensional circumstances. These issues actually inherit from those of the conventional multivariate control charts. To resolve these issues, this paper develops a new methodology for monitoring general multivariate linear profiles, including the regression coefficients and profile variation. After examining the connection between the parametric profile monitoring and multivariate statistical process control, we propose to apply a variable-selection-based multivariate control scheme to the transformations of estimated profile parameters. Our proposed control chart is capable of determining the shift direction automatically based on observed profile data. Thus, it offers a balanced protection against various profile shifts. Moreover, the proposed control chart provides an easy but quite effective diagnostic aid. A real-data example from the logistics service shows that it performs quite well in the application.

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Section: Discussionmentioning

confidence: 97%

LASSO-based multivariate linear profile monitoring

2010

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“…In most applications, however, it may not be practical to wait for the accumulation of such large Phase I data set because of the cost or time consideration (Maravelakis & Castagliola, 2009;Teoh, Khoo, Castagliola, & Chakraborti, 2014;Zou, Zhou, Wang, & Tsung, 2007). In practice, one expects that the in-control performance of the synthetic chart is the desired value when the parameters are estimated.…”

Section: The Design Of the Synthetic S 2 Chart When The In-control Vamentioning

confidence: 98%

Optimal design of a synthetic chart for monitoring process dispersion with unknown in-control variance

Guo

Wang

Cheng

2015

Computers & Industrial Engineering

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“…Later on, Quesenberry (1997), Schaffer (1998), Sullivan andJones (2002), Hawkins andMaboudou-Tchao (2007) and Capizzi and Masarotto (2010) proposed self-starting charts for multivariate applications. Zou et al (2007) further extended the self-starting technique to the application of profile monitoring. For monitoring of Poisson rates, control schemes were proposed by Quesenberry (1991b) and Hawkins and Olwell (1998).…”

Section: Accepted Manuscriptmentioning

confidence: 98%

Self-Starting Monitoring Scheme for Poisson Count Data With Varying Population Sizes

et al. 2016

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In this paper we consider the problem of monitoring Poisson rates when the population sizes are time-varying and the nominal value of the process parameter is unavailable. Almost all previous control schemes for the detection of increases in the Poisson rate in Phase II are constructed based on assumed knowledge of the process parameters, e.g., the expectation of the count of a rare event when the process of interest is in control. In practice, however, this parameter is usually unknown and not able to be estimated with a sufficiently large number of reference samples. A self-starting EWMA control scheme based on a parametric bootstrap method is proposed. The success of the proposed method lies in the use of probability control limits, which are determined based on the observations during rather than before monitoring.Simulation studies show that our proposed scheme has good in-control and out-of-control performance under various situations. In particular, our proposed scheme is useful in rare event studies during the start-up stage of a monitoring process.

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A Self-Starting Control Chart for Linear Profiles

Cited by 93 publications

References 31 publications

LASSO-based multivariate linear profile monitoring

LASSO-based multivariate linear profile monitoring

Optimal design of a synthetic chart for monitoring process dispersion with unknown in-control variance

Self-Starting Monitoring Scheme for Poisson Count Data With Varying Population Sizes

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