A Phase I nonparametric Shewhart-type control chart based on the median

In most statistical process control (SPC) applications, quality of a process or product is monitored by univariate or multivariate control charts. However, sometimes a functional relationship between a response variable and one or more explanatory variables is established and monitored over time. This relationship is called “profile” in SPC literature. In this paper, we specifically consider processes with compositional data responses, including multivariate positive observations summing to one. The relationship between compositional data responses and explanatory variables is modeled by a Dirichlet regression profile. We develop a monitoring procedure based on likelihood ratio test (lrt) for Phase I monitoring of Dirichlet regression profiles. Then, we compare the performance of the proposed method with the best method in the literature in terms of probability of signal. The results of simulation studies show that the proposed control chart has better performance in Phase I monitoring than the competing control chart. Moreover, the proposed method is able to estimate the real time of a change as well. The performance of this feature is also investigated through simulation runs which show the satisfactory performance. Finally, the application of the proposed method is illustrated based on a real case in comparison with the existing method.

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An algorithmic approach to outlier detection and parameter estimation in Phase I for designing Phase II EWMA control chart

Computers & Industrial Engineering ◽

10.1016/j.cie.2020.106440 ◽

2020 ◽

Vol 144 ◽

pp. 106440

Author(s):

Murat Caner Testik ◽

Ozge Kara ◽

Sven Knoth

Keyword(s):

Parameter Estimation ◽

Phase I ◽

Outlier Detection ◽

Control Chart ◽

Phase Ii ◽

Algorithmic Approach ◽

Ewma Control Chart

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Risk-adjusted frailty-based CUSUM control chart for phase I monitoring of patients’ lifetime

Journal of Statistical Computation and Simulation ◽

10.1080/00949655.2020.1814775 ◽

2020 ◽

pp. 1-19

Author(s):

Maryam Keshavarz ◽

Shervin Asadzadeh ◽

Seyed Taghi Akhavan Niaki

Keyword(s):

Phase I ◽

Control Chart ◽

Cusum Control Chart

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The X-bar control chart with restriction of the capability indices

International Journal of Quality & Reliability Management ◽

10.1108/ijqrm-08-2014-0103 ◽

2017 ◽

Vol 34 (1) ◽

pp. 38-52 ◽

Cited By ~ 3

Author(s):

Pedro Carlos Oprime ◽

Glauco Henrique de Sousa Mendes

Keyword(s):

Phase I ◽

Control Chart ◽

Design Methodology ◽

Simulation Method ◽

Operating Conditions ◽

Suggested Approach ◽

Content Type ◽

Capability Index ◽

Simulation Techniques ◽

Capability Indices

Purpose The purpose of this paper is to find the configuration of the number (m) and size (n) of the sample in Phase I that would make it possible to detect the out-of-control (OOC) state of the process with the smallest number of samples and ensure a capability index (Cpk) that would meet the customer’s requirements. Design/methodology/approach The suggested approach addresses this problem using simulation techniques and design of experiments (DOE). The simulation techniques made it possible to reproduce the normal operating conditions of the process. The DOE was used to construct a predictive model for control chart performance and thus to determine combinations of m and n in Phase I that would meet the capability objectives of the process. A numerical example and a simulation study were conducted to illustrate the proposed method. Findings Using simulation techniques and DOE, the authors can find the number (m) and size (n) of the sample in Phase I that would make it possible to detect the OOC state of the process with the smallest number of samples and ensure a Cpk that would meet the customer’s requirements. Originality/value In the real situations of many companies, choosing the numbers and sizes of samples (m and n) in Phases I and II is a crucial decision in relation to implementing a control chart. The paper shows that the simulation method and use of linear regression are effective alternatives because they are better known and more easily applied in industrial settings. Therefore, the need for alternatives to the X control chart comes into play.

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Phase I control chart based on a kernel estimator of the quantile function

Quality and Reliability Engineering International ◽

10.1002/qre.1201 ◽

2011 ◽

Vol 27 (8) ◽

pp. 1131-1144 ◽

Cited By ~ 4

Author(s):

Gary R. Mercado ◽

Michael D. Conerly ◽

Marcus B. Perry

Keyword(s):

Phase I ◽

Control Chart ◽

Kernel Estimator ◽

Quantile Function

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Robust approaches for monitoring logistic regression profiles under outliers

International Journal of Quality & Reliability Management ◽

10.1108/ijqrm-04-2015-0053 ◽

2017 ◽

Vol 34 (4) ◽

pp. 494-507 ◽

Cited By ~ 8

Author(s):

Ahmad Hakimi ◽

Amirhossein Amiri ◽

Reza Kamranrad

Keyword(s):

Logistic Regression ◽

Robust Control ◽

Phase I ◽

Control Chart ◽

Phase Ii ◽

Control Charts ◽

Likelihood Estimation ◽

Estimation Of Parameters ◽

Content Type ◽

Practical Applications

Purpose The purpose of this paper is to develop some robust approaches to estimate the logistic regression profile parameters in order to decrease the effects of outliers on the performance of T2 control chart. In addition, the performance of the non-robust and the proposed robust control charts is evaluated in Phase II. Design/methodology/approach In this paper some, robust approaches including weighted maximum likelihood estimation, redescending M-estimator and a combination of these two approaches (WRM) are used to decrease the effects of outliers on estimating the logistic regression parameters as well as the performance of the T2 control chart. Findings The results of the simulation studies in both Phases I and II show the better performance of the proposed robust control charts rather than the non-robust control chart for estimating the logistic regression profile parameters and monitoring the logistic regression profiles. Practical implications In many practical applications, there are outliers in processes which may affect the estimation of parameters in Phase I and as a result of deteriorate the statistical performance of control charts in Phase II. The methods developed in this paper are effective for decreasing the effect of outliers in both Phases I and II. Originality/value This paper considers monitoring the logistic regression profile in Phase I under the presence of outliers. Also, three robust approaches are developed to decrease the effects of outliers on the parameter estimation and monitoring the logistic regression profiles in both Phases I and II.

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Effect of Phase I Estimation on Phase II Control Chart Performance with Profile Data

Quality and Reliability Engineering International ◽

10.1002/qre.1727 ◽

2014 ◽

Vol 32 (1) ◽

pp. 79-87 ◽

Cited By ~ 8

Author(s):

Yajuan Chen ◽

Jeffrey B. Birch ◽

William H. Woodall

Keyword(s):

Phase I ◽

Control Chart ◽

Phase Ii ◽

Profile Data

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The Expected Average Run Length of the EWMA Median Chart with Estimated Process Parameters

Austrian Journal of Statistics ◽

10.17713/ajs.v49i3.1020 ◽

2020 ◽

Vol 49 (3) ◽

pp. 19-24

Author(s):

Huay Woon You ◽

Michael Khoo Boon Chong ◽

Chong Zhi Lin ◽

Teoh Wei Lin

Keyword(s):

Phase I ◽

Control Chart ◽

Process Parameters ◽

Average Run Length ◽

Moving Average ◽

Background Knowledge ◽

Exponentially Weighted Moving Average ◽

Control Phase ◽

Run Length ◽

Weighted Moving Average

The performance of a control chart is commonly investigated based on the assumption of known process parameters. Nevertheless, in most manufacturing and service applications, the process parameters are usually unknown to practitioners. Hence, they are estimated from an in-control Phase-I samples. As such, the performance of the control chart with estimated process parameters will behave differently from the corresponding chart with known process parameters. To study this issue, the exponentially weighted moving average (EWMA) median chart is examined in this article. The EWMA median chart is traditionally investigated based on the average run length (ARL). The limitation of the ARL is that it requires practitioners to specify the shift size in advance. This phenomenon is not ideal for practitioners who do not have background knowledge of the process. In view of this, the EWMA median chart with known and estimated process parameters is studied based on the ARL and expected average run length (EARL). The results indicate that as long as the particular shift size is within the range of shifts, the performance of the chart is almost the same, for the EWMA median chart with known and estimated process parameters.

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