Comparative performance analysis of the Cumulative Sum chart and the Shiryaev‐Roberts procedure for detecting changes in autocorrelated data
We consider the problem of quickest changepoint detection where the observations form a first‐order autoregressive (AR(1)) process driven by temporally independent standard white Gaussian noise. Subject to possible change are both the drift of the AR(1) process (μ) and its correlation coefficient (λ...
Gespeichert in:
| Veröffentlicht in: | Applied stochastic models in business and industry 2018-11, Vol.34 (6), p.922-948 |
|---|---|
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 948 |
|---|---|
| container_issue | 6 |
| container_start_page | 922 |
| container_title | Applied stochastic models in business and industry |
| container_volume | 34 |
| creator | Polunchenko, Aleksey S. Raghavan, Vasanthan |
| description | We consider the problem of quickest changepoint detection where the observations form a first‐order autoregressive (AR(1)) process driven by temporally independent standard white Gaussian noise. Subject to possible change are both the drift of the AR(1) process (μ) and its correlation coefficient (λ), which are both known. The change is abrupt and persistent, and of known magnitude, with |λ| |
| doi_str_mv | 10.1002/asmb.2372 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_2154045816</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2154045816</sourcerecordid><originalsourceid>FETCH-LOGICAL-c2972-219715b7675c7ca849b1f164528372ba6ba0265b6f46690ac640775858fbb8ae3</originalsourceid><addsrcrecordid>eNp1kMtOwzAQRSMEEuWx4A8ssWKR1nb9SJal4iWBkCiso7EzoUFNXGynqDu-APGNfAlpy5bVjDTnXs29SXLG6JBRykcQGjPkY833kgGTXKWCcrm_3UXKcioOk6MQ3ihlTGg2SL6mrlmCh1ivkCzRV8430Fok0MJiHepAXEXiHMm0a7rFDpt1DbFz8LGHyu1xNq_9GnD18_n95Az6GMjSO4tl55H0lqTEiDbW7etG2L5iIHVLoIvOOu-x98WSlBDhJDmoYBHw9G8eJy_XV8_T2_T-8eZuOrlPLc81TznLNZNGKy2ttpCJ3LCKKSF51kc3oAxQrqRRlVAqp2CVoFrLTGaVMRng-Dg53_n2b753GGLx5jrfRw4FZ1JQITOmeupiR1nvQvBYFUtfN-DXBaPFpu5iU3exqbtnRzv2o17g-n-wmMweLreKX_yzhMU</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2154045816</pqid></control><display><type>article</type><title>Comparative performance analysis of the Cumulative Sum chart and the Shiryaev‐Roberts procedure for detecting changes in autocorrelated data</title><source>EBSCOhost Business Source Complete</source><source>Access via Wiley Online Library</source><creator>Polunchenko, Aleksey S. ; Raghavan, Vasanthan</creator><creatorcontrib>Polunchenko, Aleksey S. ; Raghavan, Vasanthan</creatorcontrib><description>We consider the problem of quickest changepoint detection where the observations form a first‐order autoregressive (AR(1)) process driven by temporally independent standard white Gaussian noise. Subject to possible change are both the drift of the AR(1) process (μ) and its correlation coefficient (λ), which are both known. The change is abrupt and persistent, and of known magnitude, with |λ|<1 throughout. For this scenario, we carry out a comparative performance analysis of the popular cumulative sum (CUSUM) chart and its less well‐known but worthy competitor, ie, the Shiryaev‐Roberts (SR) procedure. Specifically, the performance is measured through Pollak's supremum (conditional) average delay to detection (SADD) constrained to a pre‐specified level of the average run length (ARL) to false alarm. Particular attention is drawn to the sensitivity of each procedure's SADD and ARL with respect to the value of λ before and after the change. The performance is studied through the solution of the respective integral renewal equations obtained via Monte Carlo simulations. The simulations are designed to estimate the sought performance metrics in an unbiased and consistent manner, and within a prescribed proportional closeness (also asymptotically). Our extensive numerical studies suggest that both the CUSUM chart and the SR procedure are asymptotically second‐order optimal, even though the CUSUM chart is found to be slightly better than the SR procedure, irrespective of the model parameters. Moreover, the existence of a worst‐case post‐change correlation parameter corresponding to the poorest detectability of the change for a given ARL to false alarm is established as well. To the best of our knowledge, this is the first time that the performance of the SR procedure is studied for autocorrelated data.</description><identifier>ISSN: 1524-1904</identifier><identifier>EISSN: 1526-4025</identifier><identifier>DOI: 10.1002/asmb.2372</identifier><language>eng</language><publisher>Bognor Regis: Wiley Subscription Services, Inc</publisher><subject>Asymptotic properties ; Autocorrelation ; Autoregressive processes ; Change detection ; Computer simulation ; Control charts ; Correlation coefficients ; CUSUM chart ; CUSUM charts ; False alarms ; Gaussian process ; Mathematical models ; Parameters ; Performance measurement ; Random noise ; sequential analysis ; sequential changepoint detection ; Shiryaev‐Roberts procedure</subject><ispartof>Applied stochastic models in business and industry, 2018-11, Vol.34 (6), p.922-948</ispartof><rights>2018 John Wiley & Sons, Ltd.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c2972-219715b7675c7ca849b1f164528372ba6ba0265b6f46690ac640775858fbb8ae3</citedby><cites>FETCH-LOGICAL-c2972-219715b7675c7ca849b1f164528372ba6ba0265b6f46690ac640775858fbb8ae3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://onlinelibrary.wiley.com/doi/pdf/10.1002%2Fasmb.2372$$EPDF$$P50$$Gwiley$$H</linktopdf><linktohtml>$$Uhttps://onlinelibrary.wiley.com/doi/full/10.1002%2Fasmb.2372$$EHTML$$P50$$Gwiley$$H</linktohtml><link.rule.ids>314,780,784,1417,27924,27925,45574,45575</link.rule.ids></links><search><creatorcontrib>Polunchenko, Aleksey S.</creatorcontrib><creatorcontrib>Raghavan, Vasanthan</creatorcontrib><title>Comparative performance analysis of the Cumulative Sum chart and the Shiryaev‐Roberts procedure for detecting changes in autocorrelated data</title><title>Applied stochastic models in business and industry</title><description>We consider the problem of quickest changepoint detection where the observations form a first‐order autoregressive (AR(1)) process driven by temporally independent standard white Gaussian noise. Subject to possible change are both the drift of the AR(1) process (μ) and its correlation coefficient (λ), which are both known. The change is abrupt and persistent, and of known magnitude, with |λ|<1 throughout. For this scenario, we carry out a comparative performance analysis of the popular cumulative sum (CUSUM) chart and its less well‐known but worthy competitor, ie, the Shiryaev‐Roberts (SR) procedure. Specifically, the performance is measured through Pollak's supremum (conditional) average delay to detection (SADD) constrained to a pre‐specified level of the average run length (ARL) to false alarm. Particular attention is drawn to the sensitivity of each procedure's SADD and ARL with respect to the value of λ before and after the change. The performance is studied through the solution of the respective integral renewal equations obtained via Monte Carlo simulations. The simulations are designed to estimate the sought performance metrics in an unbiased and consistent manner, and within a prescribed proportional closeness (also asymptotically). Our extensive numerical studies suggest that both the CUSUM chart and the SR procedure are asymptotically second‐order optimal, even though the CUSUM chart is found to be slightly better than the SR procedure, irrespective of the model parameters. Moreover, the existence of a worst‐case post‐change correlation parameter corresponding to the poorest detectability of the change for a given ARL to false alarm is established as well. To the best of our knowledge, this is the first time that the performance of the SR procedure is studied for autocorrelated data.</description><subject>Asymptotic properties</subject><subject>Autocorrelation</subject><subject>Autoregressive processes</subject><subject>Change detection</subject><subject>Computer simulation</subject><subject>Control charts</subject><subject>Correlation coefficients</subject><subject>CUSUM chart</subject><subject>CUSUM charts</subject><subject>False alarms</subject><subject>Gaussian process</subject><subject>Mathematical models</subject><subject>Parameters</subject><subject>Performance measurement</subject><subject>Random noise</subject><subject>sequential analysis</subject><subject>sequential changepoint detection</subject><subject>Shiryaev‐Roberts procedure</subject><issn>1524-1904</issn><issn>1526-4025</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2018</creationdate><recordtype>article</recordtype><recordid>eNp1kMtOwzAQRSMEEuWx4A8ssWKR1nb9SJal4iWBkCiso7EzoUFNXGynqDu-APGNfAlpy5bVjDTnXs29SXLG6JBRykcQGjPkY833kgGTXKWCcrm_3UXKcioOk6MQ3ihlTGg2SL6mrlmCh1ivkCzRV8430Fok0MJiHepAXEXiHMm0a7rFDpt1DbFz8LGHyu1xNq_9GnD18_n95Az6GMjSO4tl55H0lqTEiDbW7etG2L5iIHVLoIvOOu-x98WSlBDhJDmoYBHw9G8eJy_XV8_T2_T-8eZuOrlPLc81TznLNZNGKy2ttpCJ3LCKKSF51kc3oAxQrqRRlVAqp2CVoFrLTGaVMRng-Dg53_n2b753GGLx5jrfRw4FZ1JQITOmeupiR1nvQvBYFUtfN-DXBaPFpu5iU3exqbtnRzv2o17g-n-wmMweLreKX_yzhMU</recordid><startdate>201811</startdate><enddate>201811</enddate><creator>Polunchenko, Aleksey S.</creator><creator>Raghavan, Vasanthan</creator><general>Wiley Subscription Services, Inc</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7TA</scope><scope>8FD</scope><scope>JG9</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>201811</creationdate><title>Comparative performance analysis of the Cumulative Sum chart and the Shiryaev‐Roberts procedure for detecting changes in autocorrelated data</title><author>Polunchenko, Aleksey S. ; Raghavan, Vasanthan</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c2972-219715b7675c7ca849b1f164528372ba6ba0265b6f46690ac640775858fbb8ae3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2018</creationdate><topic>Asymptotic properties</topic><topic>Autocorrelation</topic><topic>Autoregressive processes</topic><topic>Change detection</topic><topic>Computer simulation</topic><topic>Control charts</topic><topic>Correlation coefficients</topic><topic>CUSUM chart</topic><topic>CUSUM charts</topic><topic>False alarms</topic><topic>Gaussian process</topic><topic>Mathematical models</topic><topic>Parameters</topic><topic>Performance measurement</topic><topic>Random noise</topic><topic>sequential analysis</topic><topic>sequential changepoint detection</topic><topic>Shiryaev‐Roberts procedure</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Polunchenko, Aleksey S.</creatorcontrib><creatorcontrib>Raghavan, Vasanthan</creatorcontrib><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Materials Business File</collection><collection>Technology Research Database</collection><collection>Materials Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Applied stochastic models in business and industry</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Polunchenko, Aleksey S.</au><au>Raghavan, Vasanthan</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Comparative performance analysis of the Cumulative Sum chart and the Shiryaev‐Roberts procedure for detecting changes in autocorrelated data</atitle><jtitle>Applied stochastic models in business and industry</jtitle><date>2018-11</date><risdate>2018</risdate><volume>34</volume><issue>6</issue><spage>922</spage><epage>948</epage><pages>922-948</pages><issn>1524-1904</issn><eissn>1526-4025</eissn><abstract>We consider the problem of quickest changepoint detection where the observations form a first‐order autoregressive (AR(1)) process driven by temporally independent standard white Gaussian noise. Subject to possible change are both the drift of the AR(1) process (μ) and its correlation coefficient (λ), which are both known. The change is abrupt and persistent, and of known magnitude, with |λ|<1 throughout. For this scenario, we carry out a comparative performance analysis of the popular cumulative sum (CUSUM) chart and its less well‐known but worthy competitor, ie, the Shiryaev‐Roberts (SR) procedure. Specifically, the performance is measured through Pollak's supremum (conditional) average delay to detection (SADD) constrained to a pre‐specified level of the average run length (ARL) to false alarm. Particular attention is drawn to the sensitivity of each procedure's SADD and ARL with respect to the value of λ before and after the change. The performance is studied through the solution of the respective integral renewal equations obtained via Monte Carlo simulations. The simulations are designed to estimate the sought performance metrics in an unbiased and consistent manner, and within a prescribed proportional closeness (also asymptotically). Our extensive numerical studies suggest that both the CUSUM chart and the SR procedure are asymptotically second‐order optimal, even though the CUSUM chart is found to be slightly better than the SR procedure, irrespective of the model parameters. Moreover, the existence of a worst‐case post‐change correlation parameter corresponding to the poorest detectability of the change for a given ARL to false alarm is established as well. To the best of our knowledge, this is the first time that the performance of the SR procedure is studied for autocorrelated data.</abstract><cop>Bognor Regis</cop><pub>Wiley Subscription Services, Inc</pub><doi>10.1002/asmb.2372</doi><tpages>27</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 1524-1904 |
| ispartof | Applied stochastic models in business and industry, 2018-11, Vol.34 (6), p.922-948 |
| issn | 1524-1904 1526-4025 |
| language | eng |
| recordid | cdi_proquest_journals_2154045816 |
| source | EBSCOhost Business Source Complete; Access via Wiley Online Library |
| subjects | Asymptotic properties Autocorrelation Autoregressive processes Change detection Computer simulation Control charts Correlation coefficients CUSUM chart CUSUM charts False alarms Gaussian process Mathematical models Parameters Performance measurement Random noise sequential analysis sequential changepoint detection Shiryaev‐Roberts procedure |
| title | Comparative performance analysis of the Cumulative Sum chart and the Shiryaev‐Roberts procedure for detecting changes in autocorrelated data |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-28T17%3A19%3A35IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Comparative%20performance%20analysis%20of%20the%20Cumulative%20Sum%20chart%20and%20the%20Shiryaev%E2%80%90Roberts%20procedure%20for%20detecting%20changes%20in%20autocorrelated%20data&rft.jtitle=Applied%20stochastic%20models%20in%20business%20and%20industry&rft.au=Polunchenko,%20Aleksey%20S.&rft.date=2018-11&rft.volume=34&rft.issue=6&rft.spage=922&rft.epage=948&rft.pages=922-948&rft.issn=1524-1904&rft.eissn=1526-4025&rft_id=info:doi/10.1002/asmb.2372&rft_dat=%3Cproquest_cross%3E2154045816%3C/proquest_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=2154045816&rft_id=info:pmid/&rfr_iscdi=true |