Asymptotic optimized CUSUM and EWMA multi-charts for jointly detecting and diagnosing unknown change

ABSTRACT This article not only shows that the CUSUM multi-chart which consists of several CUSUM charts, has the asymptotic optimal performance in jointly detecting and diagnosing the unknown change in a sequence of observations but also provides a design method of optimizing the CUSUM and EWMA multi-charts. The numerical comparisons illustrate that the optimized CUSUM multi-chart has better performance in jointly detecting and diagnosing the mean and variance shifts in normal observations than that of the optimized EWMA multi-chart. A real example for engineering surveillance using the electric power generation data was used to demonstrate the practicality of the schemes.

[1]  G. Lorden PROCEDURES FOR REACTING TO A CHANGE IN DISTRIBUTION , 1971 .

[2]  Ronald D. Fricker Introduction to Statistical Methods for Biosurveillance: With an Emphasis on Syndromic Surveillance , 2013 .

[3]  H. Vincent Poor,et al.  Bayesian Sequential Change Diagnosis , 2007, Math. Oper. Res..

[4]  Murat Kulahci,et al.  Real-time fault detection and diagnosis using sparse principal component analysis , 2017, Journal of Process Control.

[5]  Venugopal V. Veeravalli,et al.  Multihypothesis sequential probability ratio tests - Part II: Accurate asymptotic expansions for the expected sample size , 2000, IEEE Trans. Inf. Theory.

[6]  D. Xiang,et al.  CUSUM chart for detecting range shifts when monotonicity of likelihood ratio is invalid , 2015 .

[7]  Stelios Psarakis,et al.  Multivariate statistical process control charts: an overview , 2007, Qual. Reliab. Eng. Int..

[8]  S. Chakraborti,et al.  Nonparametric Control Charts: An Overview and Some Results , 2001 .

[9]  J. Andel Sequential Analysis , 2022, The SAGE Encyclopedia of Research Design.

[10]  Fugee Tsung,et al.  Detection and Diagnosis of Distribution Changes of Degree Ratio in Complex Networks , 2015 .

[11]  G. Peskir,et al.  Detecting changes in real-time data: a user’s guide to optimal detection , 2017, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[12]  James M. Lucas,et al.  Combined Shewhart-CUSUM Quality Control Schemes , 1982 .

[13]  Shengwei Wang,et al.  A statistical fault detection and diagnosis method for centrifugal chillers based on exponentially-weighted moving average control charts and support vector regression , 2013 .

[14]  W. H. Deitenbeck Introduction to statistical process control. , 1995, Healthcare facilities management series.

[15]  Fugee Tsung,et al.  Detection and Diagnosis of Unknown Abrupt Changes Using CUSUM Multi-Chart Schemes , 2007 .

[16]  Douglas C. Montgomery,et al.  Some Current Directions in the Theory and Application of Statistical Process Monitoring , 2014 .

[17]  D. Siegmund Sequential Analysis: Tests and Confidence Intervals , 1985 .

[18]  I. Eisenberger,et al.  Detection of Failure Rate Increases , 1971 .

[19]  Tze Leung Lai Sequential multiple hypothesis testing and efficient fault detection-isolation in stochastic systems , 2000, IEEE Trans. Inf. Theory.

[20]  Michèle Basseville,et al.  Detection of Abrupt Changes: Theory and Applications. , 1995 .

[21]  Dong Han,et al.  Multichart Schemes for Detecting Changes in Disease Incidence , 2020, Comput. Math. Methods Medicine.

[22]  G. Moustakides Optimal stopping times for detecting changes in distributions , 1986 .

[23]  Igor V. Nikiforov,et al.  A generalized change detection problem , 1995, IEEE Trans. Inf. Theory.

[24]  M. Basseville,et al.  Sequential Analysis: Hypothesis Testing and Changepoint Detection , 2014 .

[25]  Savas Dayanik,et al.  Sequential Detection and Identification of a Change in the Distribution of a Markov-Modulated Random Sequence , 2009, IEEE Transactions on Information Theory.

[26]  Marianne Frisén,et al.  Optimal Sequential Surveillance for Finance, Public Health, and Other Areas , 2009 .

[27]  Theodor D. Popescu,et al.  Detection and diagnosis of model parameter and noise variance changes with application in seismic signal processing , 2011 .

[28]  D. Siegmund Author's Response , 2013 .

[29]  Abdelmalek Kouadri,et al.  Fault detection and diagnosis in a cement rotary kiln using PCA with EWMA-based adaptive threshold monitoring scheme , 2017 .

[30]  Steven X. Ding,et al.  A Survey of Fault Diagnosis and Fault-Tolerant Techniques—Part I: Fault Diagnosis With Model-Based and Signal-Based Approaches , 2015, IEEE Transactions on Industrial Electronics.

[31]  Aggeliki Sgora,et al.  The application of multivariate statistical process monitoring in non-industrial processes , 2018 .

[32]  Peihua Qiu,et al.  A Change-Point Approach for Phase-I Analysis in Multivariate Profile Monitoring and Diagnosis , 2016, Technometrics.

[33]  Venugopal V. Veeravalli,et al.  Multihypothesis sequential probability ratio tests - Part I: Asymptotic optimality , 1999, IEEE Trans. Inf. Theory.

[34]  Ying Sun,et al.  Reliable fault detection and diagnosis of photovoltaic systems based on statistical monitoring approaches , 2018 .

[35]  Vladimir Dragalin The design and analysis of 2-CUSUM procedure , 1997 .

[36]  William H. Woodall,et al.  An overview and perspective on social network monitoring , 2016, ArXiv.

[37]  Fred Spiring,et al.  Introduction to Statistical Quality Control , 2007, Technometrics.

[38]  Rassoul Noorossana,et al.  Performance evaluation of EWMA and CUSUM control charts to detect anomalies in social networks using average and standard deviation of degree measures , 2018, Qual. Reliab. Eng. Int..

[39]  A. R. Crathorne,et al.  Economic Control of Quality of Manufactured Product. , 1933 .

[40]  Ross Sparks,et al.  CUSUM Charts for Signalling Varying Location Shifts , 2000 .