Development of Time Series Disorder Detection Algorithms Based on Nonparametric Hypothesis Testing Criteria
DOI:
https://doi.org/10.24160/1993-6982-2021-3-67-77Keywords:
time series disorder, disorder detection, nonparametric detection methods, igns criterion, series criterion, Ramachandran–Ranganathan criterion, detection algorithm probabilistic characteristics, synthesis of a monitoring procedureAbstract
The solution of the problem of detecting, in the online mode, a spontaneous change in the probabilistic characteristics (“disorder” or “breakdown”) of a time series is given. It is pointed out that there is a growing interest in the development of so-called nonparametric disorder detection methods, i.e., methods the application of which does not require the knowledge of the probability distribution function of the controlled process values. It is stated that the majority of the known versions of such methods are based on using a number of standard nonparametric criteria transformed for solving disorder detection problems. It is proposed to use the signs criterion, the series criterion, and the Ramachandran–Ranganathan criterion as a basis for construction of disorder detection algorithms. The methodical aspects of studying the statistical properties and efficiency of the disorder detection algorithms built on their basis are considered. The simulation method was used as a study tool. The plan of carrying out simulation experiments was developed separately for each of the proposed algorithms, taking into account their individual characteristics, but based on the general requirement of fully reproducing the monitoring algorithm performance dynamics under real conditions, when a disorder can appear at any time and there is a transient in the values of the decisive function. By using a simulation experiment for each of the algorithms under consideration, data on their statistical characteristics were obtained and systematized in a scope sufficient for synthesizing a monitoring procedure with the specified properties.
References
1. Shewhart W.A. Quality Control Charts // Bell Syst. Techn. J. 1926. V. 5(4). Pp. 593—603.
2. Адлер Ю.П., Максимова О.В., Шпер В.Л. Контрольные карты Шухарта в России и за рубежом: краткий обзор современного состояния (статистические аспекты) // Стандарты и качество. 2011. № 7. С. 82—87; № 8. С. 82—87.
3. Shafid A. Bibliometric Analysis of EWMA and CUSUM Control Chart Schemes // ITEE J. 2018. V. 7(2). Pp. 1—11.
4. Chakraborti S., Van der Laan P., Bakir S.T. Nonparametric Statistical Process Control: an Overview and Some Results // J. Quality Technol. 2001. V. 33(3). Pp. 304—315.
5. Bakir S. Classification Distribution-free Quality Control Charts // Proc. Annual Meeting of the American Statistical Association. 2001. V. 5(9). Pp. 1—7.
6. Chakraborti S., Graham M.A. Nonparametric Statistical Process Control. N.-Y.: John Wiley&Sons, 2019.
7. Page E.S. Continuous Inspection Schemes // Biometrika. 1954. V. 41. No. 1. Pp. 100—115.
8. Roberts, S.W. Control Chart Tests Based on Geometric Moving Averages // Technometrics. 1959. V. 1(3). Pp. 239—250.
9. Chakraborti S., Van der Laan P., Van de Wiel M.A. A Сlass of Distribution-free Control Charts // J. Royal Statistical Soc.: Series C: Appl. Stat. 2004. V. 53(3). Pp. 443—462.
10. Bakir S.T., Reynolds Jr.M.R. A Nonparametric Procedure for Process Control Based on Within-group Ranking // Technometrics. 1979. V. 21(2). Pp. 175—183.
11. Amin R.W., Reynolds Jr.M.R., Bakir S.T. Nonparametric Quality Control Charts Based on the Sign Statistic // Communications in Statistics: Theory and Methods. 1995. V. 24(6). Pp. 1597—1623.
12. Janacek G.J., Meikle S.E. Control Charts Based on Medians // J. Royal Statistical Soc.: Series D: Statistician. 1997. V. 46(1). Pp. 19—31.
13. McDonald D. A CUSUM Procedure Based On Sequential Ranks // Naval Research Logistics. 1999. V. 37. Pp. 627—646.
14. Bakir S.T. A Distribution-free Shewhart Quality Control Chart Based on Signed-ranks // Quality Eng. 2004. V. 16(4). Pp. 613—623.
15. Митрохин И.Н., Орлов А.И. Обнаружение разладки с помощью контрольных карт // Заводская лаборатория. Диагностика материалов. 2007. № 5. С. 74—78.
16. Chakraborti S.б Van de Wiel M.A. A Nonparametric Control Chart Based on the Mann–Whitney Statistic // IMS Collections. 2008. V. 1. Pp. 156—172.
17. Кузнецов Л.А., Журавлева М.Г. Построение карт контроля качества с помощью непараметрического критерия Вилкоксона–Манна–Уитни // Заводская лаборатория. Диагностика материалов. 2009. № 1. C. 70—95.
18. Human S.W., Chakraborti S., Smit C.F. Nonparametric Shewhart-type Sign Control Charts Based on Runs // Communications in Statistics: Theory and Methods. 2010. V. 39(11). Pp. 2046—2062.
19. Веретельникова И.В. Исследование и применение критериев проверки гипотез об отсутствии тренда и критериев однородности: автореферат … дис. канд. техн. наук. Новосибирск: Типография НГТУ, 2019.
20. Кендалл М., Стьюарт А. Статистические выводы и связи. М.: Наука, 1973.
21. Филаретов Г.Ф. Диалоговая программная система «STATCONT» // Приборы и системы управления. 1998. № 5. С. 16—18.
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Для цитирования: Филаретов Г.Ф., Бучаала З. Разработка алгоритмов обнаружения разладки временных рядов на основе непараметрических критериев проверки гипотез // Вестник МЭИ. 2021. № 3. С. 67—77. DOI: 10.24160/1993-6982-2021-3-67-77.
#
1. Shewhart W.A. Quality Control Charts. Bell Syst. Techn. J. 1926;5(4):593—603.
2. Adler Yu.P., Maksimova O.V., Shper V.L. Kontrol'nye Karty Shukharta v Rossii i za Rubezhom: Kratkiy Obzor Sovremennogo Sostoyaniya (Statisticheskie Aspekty). Standarty i kachestvo. 2011;7:82—87; 8:82—87. (in Russian).
3. Shafid A. Bibliometric Analysis of EWMA and CUSUM Control Chart Schemes. ITEE J. 2018;7(2):1—11.
4. Chakraborti S., Van der Laan P., Bakir S.T. Nonparametric Statistical Process Control: an Overview and Some Results. J. Quality Technol. 2001;33(3):304—315.
5. Bakir S. Classification Distribution-free Quality Control Charts. Proc. Annual Meeting of the American Statistical Association. 2001;5(9):1—7.
6. Chakraborti S., Graham M.A. Nonparametric Statistical Process Control. N.-Y.: John Wiley&Sons, 2019.
7. Page E.S. Continuous Inspection Schemes. Biometrika. 1954;41;1:100—115.
8. Roberts, S.W. Control Chart Tests Based on Geometric Moving Averages. Technometrics. 1959;1(3):239—250.
9. Chakraborti S., Van der Laan P., Van de Wiel M.A. A Slass of Distribution-free Control Charts. J. Royal Statistical Soc.: Series C: Appl. Stat. 2004;53(3):443—462.
10. Bakir S.T., Reynolds Jr.M.R. A Nonparametric Procedure for Process Control Based on Within-group Ranking. Technometrics. 1979;21(2):175—183.
11. Amin R.W., Reynolds Jr.M.R., Bakir S.T. Nonparametric Quality Control Charts Based on the Sign Statistic. Communications in Statistics: Theory and Methods. 1995;24(6):1597—1623.
12. Janacek G.J., Meikle S.E. Control Charts Based on Medians. J. Royal Statistical Soc.: Series D: Statistician. 1997;46(1):19—31.
13. McDonald D. A CUSUM Procedure Based On Sequential Ranks. Naval Research Logistics. 1999;37:627—646.
14. Bakir S.T. A Distribution-free Shewhart Quality Control Chart Based on Signed-ranks. Quality Eng. 2004;16(4):613—623.
15. Mitrokhin I.N., Orlov A.I. Obnaruzhenie Razladki s Pomoshch'yu Kontrol'nykh Kart. Zavodskaya Laboratoriya. Diagnostika Materialov. 2007;5:74—78. (in Russian).
16. Chakraborti S.b Van de Wiel M.A. A Nonparametric Control Chart Based on the Mann–Whitney Statistic. IMS Collections. 2008;1:156—172.
17. Kuznetsov L.A., Zhuravleva M.G. Postroenie Kart Kontrolya Kachestva s Pomoshch'yu Neparametricheskogo Kriteriya Vilkoksona–Manna–Uitni. Zavodskaya Laboratoriya. Diagnostika Materialov. 2009;1:70—95. (in Russian).
18. Human S.W., Chakraborti S., Smit C.F. Nonparametric Shewhart-type Sign Control Charts Based on Runs. Communications in Statistics: Theory and Methods. 2010;39(11):2046—2062.
19. Veretel'nikova I.V. Issledovanie i Primenenie Kriteriev Proverki Gipotez ob Otsutstvii Trenda i Kriteriev Odnorodnosti: Avtoreferat … Dis. Kand. Tekhn. Nauk. Novosibirsk: Tipografiya NGTU, 2019. (in Russian).
20. Kendall M., St'yuart A. Statisticheskie Vyvody i Svyazi. M.: Nauka, 1973. (in Russian).
21. Filaretov G.F. Dialogovaya Programmnaya Sistema «STATCONT». Pribory i Sistemy Upravleniya. 1998;5:16—18. (in Russian).
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For citation: Filaretov G.F., Bouchaala Z. Development of Time Series Disorder Detection Algorithms Based on Nonparametric Hypothesis Testing Criteria. Bulletin of MPEI. 2021;3:67—77. (in Russian). DOI: 10.24160/1993-6982-2021-3-67-77.
2. Адлер Ю.П., Максимова О.В., Шпер В.Л. Контрольные карты Шухарта в России и за рубежом: краткий обзор современного состояния (статистические аспекты) // Стандарты и качество. 2011. № 7. С. 82—87; № 8. С. 82—87.
3. Shafid A. Bibliometric Analysis of EWMA and CUSUM Control Chart Schemes // ITEE J. 2018. V. 7(2). Pp. 1—11.
4. Chakraborti S., Van der Laan P., Bakir S.T. Nonparametric Statistical Process Control: an Overview and Some Results // J. Quality Technol. 2001. V. 33(3). Pp. 304—315.
5. Bakir S. Classification Distribution-free Quality Control Charts // Proc. Annual Meeting of the American Statistical Association. 2001. V. 5(9). Pp. 1—7.
6. Chakraborti S., Graham M.A. Nonparametric Statistical Process Control. N.-Y.: John Wiley&Sons, 2019.
7. Page E.S. Continuous Inspection Schemes // Biometrika. 1954. V. 41. No. 1. Pp. 100—115.
8. Roberts, S.W. Control Chart Tests Based on Geometric Moving Averages // Technometrics. 1959. V. 1(3). Pp. 239—250.
9. Chakraborti S., Van der Laan P., Van de Wiel M.A. A Сlass of Distribution-free Control Charts // J. Royal Statistical Soc.: Series C: Appl. Stat. 2004. V. 53(3). Pp. 443—462.
10. Bakir S.T., Reynolds Jr.M.R. A Nonparametric Procedure for Process Control Based on Within-group Ranking // Technometrics. 1979. V. 21(2). Pp. 175—183.
11. Amin R.W., Reynolds Jr.M.R., Bakir S.T. Nonparametric Quality Control Charts Based on the Sign Statistic // Communications in Statistics: Theory and Methods. 1995. V. 24(6). Pp. 1597—1623.
12. Janacek G.J., Meikle S.E. Control Charts Based on Medians // J. Royal Statistical Soc.: Series D: Statistician. 1997. V. 46(1). Pp. 19—31.
13. McDonald D. A CUSUM Procedure Based On Sequential Ranks // Naval Research Logistics. 1999. V. 37. Pp. 627—646.
14. Bakir S.T. A Distribution-free Shewhart Quality Control Chart Based on Signed-ranks // Quality Eng. 2004. V. 16(4). Pp. 613—623.
15. Митрохин И.Н., Орлов А.И. Обнаружение разладки с помощью контрольных карт // Заводская лаборатория. Диагностика материалов. 2007. № 5. С. 74—78.
16. Chakraborti S.б Van de Wiel M.A. A Nonparametric Control Chart Based on the Mann–Whitney Statistic // IMS Collections. 2008. V. 1. Pp. 156—172.
17. Кузнецов Л.А., Журавлева М.Г. Построение карт контроля качества с помощью непараметрического критерия Вилкоксона–Манна–Уитни // Заводская лаборатория. Диагностика материалов. 2009. № 1. C. 70—95.
18. Human S.W., Chakraborti S., Smit C.F. Nonparametric Shewhart-type Sign Control Charts Based on Runs // Communications in Statistics: Theory and Methods. 2010. V. 39(11). Pp. 2046—2062.
19. Веретельникова И.В. Исследование и применение критериев проверки гипотез об отсутствии тренда и критериев однородности: автореферат … дис. канд. техн. наук. Новосибирск: Типография НГТУ, 2019.
20. Кендалл М., Стьюарт А. Статистические выводы и связи. М.: Наука, 1973.
21. Филаретов Г.Ф. Диалоговая программная система «STATCONT» // Приборы и системы управления. 1998. № 5. С. 16—18.
---
Для цитирования: Филаретов Г.Ф., Бучаала З. Разработка алгоритмов обнаружения разладки временных рядов на основе непараметрических критериев проверки гипотез // Вестник МЭИ. 2021. № 3. С. 67—77. DOI: 10.24160/1993-6982-2021-3-67-77.
#
1. Shewhart W.A. Quality Control Charts. Bell Syst. Techn. J. 1926;5(4):593—603.
2. Adler Yu.P., Maksimova O.V., Shper V.L. Kontrol'nye Karty Shukharta v Rossii i za Rubezhom: Kratkiy Obzor Sovremennogo Sostoyaniya (Statisticheskie Aspekty). Standarty i kachestvo. 2011;7:82—87; 8:82—87. (in Russian).
3. Shafid A. Bibliometric Analysis of EWMA and CUSUM Control Chart Schemes. ITEE J. 2018;7(2):1—11.
4. Chakraborti S., Van der Laan P., Bakir S.T. Nonparametric Statistical Process Control: an Overview and Some Results. J. Quality Technol. 2001;33(3):304—315.
5. Bakir S. Classification Distribution-free Quality Control Charts. Proc. Annual Meeting of the American Statistical Association. 2001;5(9):1—7.
6. Chakraborti S., Graham M.A. Nonparametric Statistical Process Control. N.-Y.: John Wiley&Sons, 2019.
7. Page E.S. Continuous Inspection Schemes. Biometrika. 1954;41;1:100—115.
8. Roberts, S.W. Control Chart Tests Based on Geometric Moving Averages. Technometrics. 1959;1(3):239—250.
9. Chakraborti S., Van der Laan P., Van de Wiel M.A. A Slass of Distribution-free Control Charts. J. Royal Statistical Soc.: Series C: Appl. Stat. 2004;53(3):443—462.
10. Bakir S.T., Reynolds Jr.M.R. A Nonparametric Procedure for Process Control Based on Within-group Ranking. Technometrics. 1979;21(2):175—183.
11. Amin R.W., Reynolds Jr.M.R., Bakir S.T. Nonparametric Quality Control Charts Based on the Sign Statistic. Communications in Statistics: Theory and Methods. 1995;24(6):1597—1623.
12. Janacek G.J., Meikle S.E. Control Charts Based on Medians. J. Royal Statistical Soc.: Series D: Statistician. 1997;46(1):19—31.
13. McDonald D. A CUSUM Procedure Based On Sequential Ranks. Naval Research Logistics. 1999;37:627—646.
14. Bakir S.T. A Distribution-free Shewhart Quality Control Chart Based on Signed-ranks. Quality Eng. 2004;16(4):613—623.
15. Mitrokhin I.N., Orlov A.I. Obnaruzhenie Razladki s Pomoshch'yu Kontrol'nykh Kart. Zavodskaya Laboratoriya. Diagnostika Materialov. 2007;5:74—78. (in Russian).
16. Chakraborti S.b Van de Wiel M.A. A Nonparametric Control Chart Based on the Mann–Whitney Statistic. IMS Collections. 2008;1:156—172.
17. Kuznetsov L.A., Zhuravleva M.G. Postroenie Kart Kontrolya Kachestva s Pomoshch'yu Neparametricheskogo Kriteriya Vilkoksona–Manna–Uitni. Zavodskaya Laboratoriya. Diagnostika Materialov. 2009;1:70—95. (in Russian).
18. Human S.W., Chakraborti S., Smit C.F. Nonparametric Shewhart-type Sign Control Charts Based on Runs. Communications in Statistics: Theory and Methods. 2010;39(11):2046—2062.
19. Veretel'nikova I.V. Issledovanie i Primenenie Kriteriev Proverki Gipotez ob Otsutstvii Trenda i Kriteriev Odnorodnosti: Avtoreferat … Dis. Kand. Tekhn. Nauk. Novosibirsk: Tipografiya NGTU, 2019. (in Russian).
20. Kendall M., St'yuart A. Statisticheskie Vyvody i Svyazi. M.: Nauka, 1973. (in Russian).
21. Filaretov G.F. Dialogovaya Programmnaya Sistema «STATCONT». Pribory i Sistemy Upravleniya. 1998;5:16—18. (in Russian).
---
For citation: Filaretov G.F., Bouchaala Z. Development of Time Series Disorder Detection Algorithms Based on Nonparametric Hypothesis Testing Criteria. Bulletin of MPEI. 2021;3:67—77. (in Russian). DOI: 10.24160/1993-6982-2021-3-67-77.
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2020-11-27
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System Analysis, Management and Information Processing (05.13.01)
