Optimal Design of Second-Order Linear Filters for Control Charting

Chin, Chang Ho; Apley, Daniel W.

doi:10.1198/004017006000000020

Cited by 13 publications

(5 citation statements)

References 32 publications

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“…The use of a linear filter model makes the derivations of the expressions of the process model for the various cases much simpler than the use of the explicit forms. Examples of using the linear filter model are Apley and Chin (2007), Castillo (2002), and Chin and Apley (2006).…”

Section: Introductionmentioning

confidence: 99%

Linear filter model representations for integrated process control with repeated adjustments and monitoring

Park

2010

Journal of the Korean Statistical Society

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a b s t r a c tAn integrated process control (IPC) procedure is a scheme which combines the engineering process control (EPC) and the statistical process control (SPC) procedures for the process where the noise and a special cause are present. The most efficient way of reducing the effect of the noise is to adjust the process by its forecast, which is done by the EPC procedure. The special cause, which produces significant deviations of the process level from the target, can be detected by the monitoring scheme, which is done by the SPC procedure. The effects of special causes can be eliminated by a rectifying action. The performance of the IPC procedure is evaluated in terms of the average run length (ARL) or the expected cost per unit time (ECU). In designing the IPC procedure for practical use, it is essential to derive its properties constituting the ARL or ECU based on the proposed process model. The process is usually assumed as it starts only with noise, and special causes occur at random times afterwards. The special cause is assumed to change the mean as well as all the parameters of the in-control model. The linear filter models for the process level as well as the controller and the observed deviations for the IPC procedure are developed here.

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Section: Introductionmentioning

confidence: 99%

Linear filter model representations for integrated process control with repeated adjustments and monitoring

Park

2010

Journal of the Korean Statistical Society

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“…Chin and Apley [27] considered the design of a control chart as an optimal linear filter design problem in the time domain. One disadvantage of this method is that computing the output of their linear filter can be somewhat time-consuming to implement.…”

Section: Introductionmentioning

confidence: 99%

“…To overcome this drawback, Chin and Apley [28] proposed a control chart based on a secondorder linear filter. However, they only studied the time domain behavior for filter design.…”

Section: Introductionmentioning

confidence: 99%

Constructing a Sensitive Control Chart to Monitor Process Mean using Optimal Filter: Time-Frequency Analysis Approach

2023

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Control charts are one of the critical tools for process monitoring. Test statistics are computed as a function of sample means in control charts for monitoring the process mean. In this study, these functions are modeled by filters. These filters have essential properties in both time and frequency domains. In previous studies, only their properties in the time domain have been considered. Thus, the resulting filters have sub-optimal performance. This study investigates the optimal design of these filters for monitoring the process mean. The behavior of these filters is analyzed not only in the time domain but also in the frequency domain. Properties such as stability are considered in designing this filter. An optimization model is designed and solved using a Genetic Algorithm to minimize the Average Run Length. The proposed optimal filter is compared with other control charts using simulation studies. Results showed the high speed of the proposed filter in detecting shifts in the process mean. The proposed optimal filter is also used to monitor the oil price of the OPEC basket. The results showed that shifts were detected at the right time using the proposed optimal filter.

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“…The Markovian‐type control chart represents an important family of control charts in SPC, which has wide applicability in practice. In addition to the standard EWMA and cumulative sum control charts (Page ), many of the recently proposed control charts in the literature also share the Markovian property, such as the adaptive EWMA charts (Capizzi and Masarotto ), adaptive CUSUM charts (Sparks ; Shu and Jiang ), and the linear filter control charts (Chin and Apley ; Apley and Chin ). In theory, the ARL of a Markovian‐type control chart can often be formulated as an integral equation based on the recurrence relationship.…”

Section: Introductionmentioning

confidence: 99%

A novel gradient approach for optimal design and sensitivity analysis of EWMA control charts

Shu¹,

Huang²,

Jiang

2014

Naval Research Logistics

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Conventional control charts are often designed to optimize out‐of‐control average run length (ARL), while constraining in‐control ARL to a desired value. The widely employed grid search approach in statistical process control (SPC) is time‐consuming with unsatisfactory accuracy. Although the simulation‐based ARL gradient estimators proposed by Fu and Hu [Manag Sci 45 (1999), 395–413] can alleviate this issue, it still requires a large number of simulation runs to significantly reduce the variance of gradient estimators. This article proposes a novel ARL gradient estimation approach based on integral equation for efficient analysis and design of control charts. Although this article compares with the results of Fu and Hu [Manag Sci 45 (1999), 395–413] based on the exponentially weighted moving average (EWMA) control chart, the proposed approach has wide applicability as it can generally fit into any control chart with Markovian property under any distributions. It is shown that the proposed method is able to provide a fast, accurate, and easy‐to‐implement algorithm for the design and analysis of EWMA charts, as compared to the simulation‐based gradient estimation method. Moreover, the proposed gradient estimation method facilitates the computation of high‐order derivatives that are valuable in sensitivity analysis. The code is written in Matlab, which is available on request. © 2014 Wiley Periodicals, Inc. Naval Research Logistics 61: 223–237, 2014

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Optimal Design of Second-Order Linear Filters for Control Charting

Cited by 13 publications

References 32 publications

Linear filter model representations for integrated process control with repeated adjustments and monitoring

Linear filter model representations for integrated process control with repeated adjustments and monitoring

Constructing a Sensitive Control Chart to Monitor Process Mean using Optimal Filter: Time-Frequency Analysis Approach

A novel gradient approach for optimal design and sensitivity analysis of EWMA control charts

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