The ARIMA(p,d,q) on Upper Sided of CUSUM Procedure

Abstract In this paper we derive explicit formula for the average run length (ARL) of Cumulative Sum (CUSUM) control chart of autoregressive integrated moving average ARIMA(p,d,q) process observations with exponential white noise. The explicit formula are derived and the numerical integrations algor...
Ausführliche Beschreibung

Gespeichert in:

Autor*in:	Zhang, Lili [verfasserIn] Busababodhin, Piyapatr

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2018

Schlagwörter:	Average run length Cumulative Sum Autoregressive integrated moving average

Anmerkung:	© Pleiades Publishing, Ltd. 2018

Übergeordnetes Werk:	Enthalten in: Lobachevskii journal of mathematics - [Moskva] : Russian Acad. of Sciences [u.a.], 1998, 39(2018), 3 vom: Apr., Seite 424-432
Übergeordnetes Werk:	volume:39 ; year:2018 ; number:3 ; month:04 ; pages:424-432

Links:	Volltext

DOI / URN:	10.1134/S1995080218030216

Katalog-ID:	SPR025232584

Internformat


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520			\|a Abstract In this paper we derive explicit formula for the average run length (ARL) of Cumulative Sum (CUSUM) control chart of autoregressive integrated moving average ARIMA(p,d,q) process observations with exponential white noise. The explicit formula are derived and the numerical integrations algorithm is developed for comparing the accuracy. We derived the explicit formula for ARL by using the Integral equations (IE) which is based on Fredholm integral equation. Then we proof the existence and uniqueness of the solution by using the Banach’s fixed point theorem. For comparing the accuracy of the explicit formulas, the numerical integration (NI) is given by using the Gauss-Legendre quadrature rule. Finally, we compare numerical results obtained from the explicit formula for the ARL of ARIMA(1,1,1) processes with results obtained from NI. The results show that the ARL from explicit formula is close to the numerical integration with an absolute percentage difference less than 0.3% with m = 800 nodes. In addition, the computational time of the explicit formula are efficiently smaller compared with NI.
650		4	\|a Average run length \|7 (dpeaa)DE-He213
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700	1		\|a Busababodhin, Piyapatr \|4 aut
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912			\|a GBV_ILN_22
912			\|a GBV_ILN_23
912			\|a GBV_ILN_24
912			\|a GBV_ILN_31
912			\|a GBV_ILN_32
912			\|a GBV_ILN_39
912			\|a GBV_ILN_40
912			\|a GBV_ILN_60
912			\|a GBV_ILN_62
912			\|a GBV_ILN_63
912			\|a GBV_ILN_65
912			\|a GBV_ILN_69
912			\|a GBV_ILN_70
912			\|a GBV_ILN_73
912			\|a GBV_ILN_74
912			\|a GBV_ILN_90
912			\|a GBV_ILN_95
912			\|a GBV_ILN_100
912			\|a GBV_ILN_105
912			\|a GBV_ILN_110
912			\|a GBV_ILN_120
912			\|a GBV_ILN_138
912			\|a GBV_ILN_150
912			\|a GBV_ILN_151
912			\|a GBV_ILN_161
912			\|a GBV_ILN_170
912			\|a GBV_ILN_171
912			\|a GBV_ILN_187
912			\|a GBV_ILN_213
912			\|a GBV_ILN_224
912			\|a GBV_ILN_230
912			\|a GBV_ILN_250
912			\|a GBV_ILN_281
912			\|a GBV_ILN_285
912			\|a GBV_ILN_293
912			\|a GBV_ILN_370
912			\|a GBV_ILN_602
912			\|a GBV_ILN_636
912			\|a GBV_ILN_702
912			\|a GBV_ILN_2001
912			\|a GBV_ILN_2003
912			\|a GBV_ILN_2004
912			\|a GBV_ILN_2005
912			\|a GBV_ILN_2006
912			\|a GBV_ILN_2007
912			\|a GBV_ILN_2008
912			\|a GBV_ILN_2009
912			\|a GBV_ILN_2010
912			\|a GBV_ILN_2011
912			\|a GBV_ILN_2014
912			\|a GBV_ILN_2015
912			\|a GBV_ILN_2020
912			\|a GBV_ILN_2021
912			\|a GBV_ILN_2025
912			\|a GBV_ILN_2026
912			\|a GBV_ILN_2027
912			\|a GBV_ILN_2031
912			\|a GBV_ILN_2034
912			\|a GBV_ILN_2037
912			\|a GBV_ILN_2038
912			\|a GBV_ILN_2039
912			\|a GBV_ILN_2044
912			\|a GBV_ILN_2048
912			\|a GBV_ILN_2049
912			\|a GBV_ILN_2050
912			\|a GBV_ILN_2055
912			\|a GBV_ILN_2057
912			\|a GBV_ILN_2059
912			\|a GBV_ILN_2061
912			\|a GBV_ILN_2064
912			\|a GBV_ILN_2065
912			\|a GBV_ILN_2068
912			\|a GBV_ILN_2070
912			\|a GBV_ILN_2086
912			\|a GBV_ILN_2088
912			\|a GBV_ILN_2093
912			\|a GBV_ILN_2106
912			\|a GBV_ILN_2107
912			\|a GBV_ILN_2108
912			\|a GBV_ILN_2110
912			\|a GBV_ILN_2111
912			\|a GBV_ILN_2112
912			\|a GBV_ILN_2113
912			\|a GBV_ILN_2116
912			\|a GBV_ILN_2118
912			\|a GBV_ILN_2119
912			\|a GBV_ILN_2122
912			\|a GBV_ILN_2129
912			\|a GBV_ILN_2143
912			\|a GBV_ILN_2144
912			\|a GBV_ILN_2147
912			\|a GBV_ILN_2148
912			\|a GBV_ILN_2152
912			\|a GBV_ILN_2153
912			\|a GBV_ILN_2188
912			\|a GBV_ILN_2190
912			\|a GBV_ILN_2232
912			\|a GBV_ILN_2336
912			\|a GBV_ILN_2446
912			\|a GBV_ILN_2470
912			\|a GBV_ILN_2472
912			\|a GBV_ILN_2507
912			\|a GBV_ILN_2522
912			\|a GBV_ILN_2548
912			\|a GBV_ILN_4035
912			\|a GBV_ILN_4037
912			\|a GBV_ILN_4046
912			\|a GBV_ILN_4112
912			\|a GBV_ILN_4125
912			\|a GBV_ILN_4242
912			\|a GBV_ILN_4246
912			\|a GBV_ILN_4249
912			\|a GBV_ILN_4251
912			\|a GBV_ILN_4305
912			\|a GBV_ILN_4306
912			\|a GBV_ILN_4307
912			\|a GBV_ILN_4313
912			\|a GBV_ILN_4322
912			\|a GBV_ILN_4323
912			\|a GBV_ILN_4324
912			\|a GBV_ILN_4325
912			\|a GBV_ILN_4326
912			\|a GBV_ILN_4333
912			\|a GBV_ILN_4334
912			\|a GBV_ILN_4335
912			\|a GBV_ILN_4336
912			\|a GBV_ILN_4338
912			\|a GBV_ILN_4393
912			\|a GBV_ILN_4700
951			\|a AR
952			\|d 39 \|j 2018 \|e 3 \|c 04 \|h 424-432

Indexfelder

author_variant	l z lz p b pb
matchkey_str	article:18189962:2018----::haiadouprieoc
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publishDate	2018
allfields	10.1134/S1995080218030216 doi (DE-627)SPR025232584 (SPR)S1995080218030216-e DE-627 ger DE-627 rakwb eng Zhang, Lili verfasserin aut The ARIMA(p,d,q) on Upper Sided of CUSUM Procedure 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Pleiades Publishing, Ltd. 2018 Abstract In this paper we derive explicit formula for the average run length (ARL) of Cumulative Sum (CUSUM) control chart of autoregressive integrated moving average ARIMA(p,d,q) process observations with exponential white noise. The explicit formula are derived and the numerical integrations algorithm is developed for comparing the accuracy. We derived the explicit formula for ARL by using the Integral equations (IE) which is based on Fredholm integral equation. Then we proof the existence and uniqueness of the solution by using the Banach’s fixed point theorem. For comparing the accuracy of the explicit formulas, the numerical integration (NI) is given by using the Gauss-Legendre quadrature rule. Finally, we compare numerical results obtained from the explicit formula for the ARL of ARIMA(1,1,1) processes with results obtained from NI. The results show that the ARL from explicit formula is close to the numerical integration with an absolute percentage difference less than 0.3% with m = 800 nodes. In addition, the computational time of the explicit formula are efficiently smaller compared with NI. Average run length (dpeaa)DE-He213 Cumulative Sum (dpeaa)DE-He213 Autoregressive integrated moving average (dpeaa)DE-He213 Busababodhin, Piyapatr aut Enthalten in Lobachevskii journal of mathematics [Moskva] : Russian Acad. of Sciences [u.a.], 1998 39(2018), 3 vom: Apr., Seite 424-432 (DE-627)320467414 (DE-600)2008068-2 1818-9962 nnns volume:39 year:2018 number:3 month:04 pages:424-432 https://dx.doi.org/10.1134/S1995080218030216 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 39 2018 3 04 424-432
spelling	10.1134/S1995080218030216 doi (DE-627)SPR025232584 (SPR)S1995080218030216-e DE-627 ger DE-627 rakwb eng Zhang, Lili verfasserin aut The ARIMA(p,d,q) on Upper Sided of CUSUM Procedure 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Pleiades Publishing, Ltd. 2018 Abstract In this paper we derive explicit formula for the average run length (ARL) of Cumulative Sum (CUSUM) control chart of autoregressive integrated moving average ARIMA(p,d,q) process observations with exponential white noise. The explicit formula are derived and the numerical integrations algorithm is developed for comparing the accuracy. We derived the explicit formula for ARL by using the Integral equations (IE) which is based on Fredholm integral equation. Then we proof the existence and uniqueness of the solution by using the Banach’s fixed point theorem. For comparing the accuracy of the explicit formulas, the numerical integration (NI) is given by using the Gauss-Legendre quadrature rule. Finally, we compare numerical results obtained from the explicit formula for the ARL of ARIMA(1,1,1) processes with results obtained from NI. The results show that the ARL from explicit formula is close to the numerical integration with an absolute percentage difference less than 0.3% with m = 800 nodes. In addition, the computational time of the explicit formula are efficiently smaller compared with NI. Average run length (dpeaa)DE-He213 Cumulative Sum (dpeaa)DE-He213 Autoregressive integrated moving average (dpeaa)DE-He213 Busababodhin, Piyapatr aut Enthalten in Lobachevskii journal of mathematics [Moskva] : Russian Acad. of Sciences [u.a.], 1998 39(2018), 3 vom: Apr., Seite 424-432 (DE-627)320467414 (DE-600)2008068-2 1818-9962 nnns volume:39 year:2018 number:3 month:04 pages:424-432 https://dx.doi.org/10.1134/S1995080218030216 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 39 2018 3 04 424-432
allfields_unstemmed	10.1134/S1995080218030216 doi (DE-627)SPR025232584 (SPR)S1995080218030216-e DE-627 ger DE-627 rakwb eng Zhang, Lili verfasserin aut The ARIMA(p,d,q) on Upper Sided of CUSUM Procedure 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Pleiades Publishing, Ltd. 2018 Abstract In this paper we derive explicit formula for the average run length (ARL) of Cumulative Sum (CUSUM) control chart of autoregressive integrated moving average ARIMA(p,d,q) process observations with exponential white noise. The explicit formula are derived and the numerical integrations algorithm is developed for comparing the accuracy. We derived the explicit formula for ARL by using the Integral equations (IE) which is based on Fredholm integral equation. Then we proof the existence and uniqueness of the solution by using the Banach’s fixed point theorem. For comparing the accuracy of the explicit formulas, the numerical integration (NI) is given by using the Gauss-Legendre quadrature rule. Finally, we compare numerical results obtained from the explicit formula for the ARL of ARIMA(1,1,1) processes with results obtained from NI. The results show that the ARL from explicit formula is close to the numerical integration with an absolute percentage difference less than 0.3% with m = 800 nodes. In addition, the computational time of the explicit formula are efficiently smaller compared with NI. Average run length (dpeaa)DE-He213 Cumulative Sum (dpeaa)DE-He213 Autoregressive integrated moving average (dpeaa)DE-He213 Busababodhin, Piyapatr aut Enthalten in Lobachevskii journal of mathematics [Moskva] : Russian Acad. of Sciences [u.a.], 1998 39(2018), 3 vom: Apr., Seite 424-432 (DE-627)320467414 (DE-600)2008068-2 1818-9962 nnns volume:39 year:2018 number:3 month:04 pages:424-432 https://dx.doi.org/10.1134/S1995080218030216 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 39 2018 3 04 424-432
allfieldsGer	10.1134/S1995080218030216 doi (DE-627)SPR025232584 (SPR)S1995080218030216-e DE-627 ger DE-627 rakwb eng Zhang, Lili verfasserin aut The ARIMA(p,d,q) on Upper Sided of CUSUM Procedure 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Pleiades Publishing, Ltd. 2018 Abstract In this paper we derive explicit formula for the average run length (ARL) of Cumulative Sum (CUSUM) control chart of autoregressive integrated moving average ARIMA(p,d,q) process observations with exponential white noise. The explicit formula are derived and the numerical integrations algorithm is developed for comparing the accuracy. We derived the explicit formula for ARL by using the Integral equations (IE) which is based on Fredholm integral equation. Then we proof the existence and uniqueness of the solution by using the Banach’s fixed point theorem. For comparing the accuracy of the explicit formulas, the numerical integration (NI) is given by using the Gauss-Legendre quadrature rule. Finally, we compare numerical results obtained from the explicit formula for the ARL of ARIMA(1,1,1) processes with results obtained from NI. The results show that the ARL from explicit formula is close to the numerical integration with an absolute percentage difference less than 0.3% with m = 800 nodes. In addition, the computational time of the explicit formula are efficiently smaller compared with NI. Average run length (dpeaa)DE-He213 Cumulative Sum (dpeaa)DE-He213 Autoregressive integrated moving average (dpeaa)DE-He213 Busababodhin, Piyapatr aut Enthalten in Lobachevskii journal of mathematics [Moskva] : Russian Acad. of Sciences [u.a.], 1998 39(2018), 3 vom: Apr., Seite 424-432 (DE-627)320467414 (DE-600)2008068-2 1818-9962 nnns volume:39 year:2018 number:3 month:04 pages:424-432 https://dx.doi.org/10.1134/S1995080218030216 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 39 2018 3 04 424-432
allfieldsSound	10.1134/S1995080218030216 doi (DE-627)SPR025232584 (SPR)S1995080218030216-e DE-627 ger DE-627 rakwb eng Zhang, Lili verfasserin aut The ARIMA(p,d,q) on Upper Sided of CUSUM Procedure 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Pleiades Publishing, Ltd. 2018 Abstract In this paper we derive explicit formula for the average run length (ARL) of Cumulative Sum (CUSUM) control chart of autoregressive integrated moving average ARIMA(p,d,q) process observations with exponential white noise. The explicit formula are derived and the numerical integrations algorithm is developed for comparing the accuracy. We derived the explicit formula for ARL by using the Integral equations (IE) which is based on Fredholm integral equation. Then we proof the existence and uniqueness of the solution by using the Banach’s fixed point theorem. For comparing the accuracy of the explicit formulas, the numerical integration (NI) is given by using the Gauss-Legendre quadrature rule. Finally, we compare numerical results obtained from the explicit formula for the ARL of ARIMA(1,1,1) processes with results obtained from NI. The results show that the ARL from explicit formula is close to the numerical integration with an absolute percentage difference less than 0.3% with m = 800 nodes. In addition, the computational time of the explicit formula are efficiently smaller compared with NI. Average run length (dpeaa)DE-He213 Cumulative Sum (dpeaa)DE-He213 Autoregressive integrated moving average (dpeaa)DE-He213 Busababodhin, Piyapatr aut Enthalten in Lobachevskii journal of mathematics [Moskva] : Russian Acad. of Sciences [u.a.], 1998 39(2018), 3 vom: Apr., Seite 424-432 (DE-627)320467414 (DE-600)2008068-2 1818-9962 nnns volume:39 year:2018 number:3 month:04 pages:424-432 https://dx.doi.org/10.1134/S1995080218030216 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 39 2018 3 04 424-432
language	English
source	Enthalten in Lobachevskii journal of mathematics 39(2018), 3 vom: Apr., Seite 424-432 volume:39 year:2018 number:3 month:04 pages:424-432
sourceStr	Enthalten in Lobachevskii journal of mathematics 39(2018), 3 vom: Apr., Seite 424-432 volume:39 year:2018 number:3 month:04 pages:424-432
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	Average run length Cumulative Sum Autoregressive integrated moving average
isfreeaccess_bool	false
container_title	Lobachevskii journal of mathematics
authorswithroles_txt_mv	Zhang, Lili @@aut@@ Busababodhin, Piyapatr @@aut@@
publishDateDaySort_date	2018-04-01T00:00:00Z
hierarchy_top_id	320467414
id	SPR025232584
language_de	englisch
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author	Zhang, Lili
spellingShingle	Zhang, Lili misc Average run length misc Cumulative Sum misc Autoregressive integrated moving average The ARIMA(p,d,q) on Upper Sided of CUSUM Procedure
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topic_title	The ARIMA(p,d,q) on Upper Sided of CUSUM Procedure Average run length (dpeaa)DE-He213 Cumulative Sum (dpeaa)DE-He213 Autoregressive integrated moving average (dpeaa)DE-He213
topic	misc Average run length misc Cumulative Sum misc Autoregressive integrated moving average
topic_unstemmed	misc Average run length misc Cumulative Sum misc Autoregressive integrated moving average
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title	The ARIMA(p,d,q) on Upper Sided of CUSUM Procedure
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title_full	The ARIMA(p,d,q) on Upper Sided of CUSUM Procedure
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author_browse	Zhang, Lili Busababodhin, Piyapatr
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author-letter	Zhang, Lili
doi_str_mv	10.1134/S1995080218030216
title_sort	arima(p,d,q) on upper sided of cusum procedure
title_auth	The ARIMA(p,d,q) on Upper Sided of CUSUM Procedure
abstract	Abstract In this paper we derive explicit formula for the average run length (ARL) of Cumulative Sum (CUSUM) control chart of autoregressive integrated moving average ARIMA(p,d,q) process observations with exponential white noise. The explicit formula are derived and the numerical integrations algorithm is developed for comparing the accuracy. We derived the explicit formula for ARL by using the Integral equations (IE) which is based on Fredholm integral equation. Then we proof the existence and uniqueness of the solution by using the Banach’s fixed point theorem. For comparing the accuracy of the explicit formulas, the numerical integration (NI) is given by using the Gauss-Legendre quadrature rule. Finally, we compare numerical results obtained from the explicit formula for the ARL of ARIMA(1,1,1) processes with results obtained from NI. The results show that the ARL from explicit formula is close to the numerical integration with an absolute percentage difference less than 0.3% with m = 800 nodes. In addition, the computational time of the explicit formula are efficiently smaller compared with NI. © Pleiades Publishing, Ltd. 2018
abstractGer	Abstract In this paper we derive explicit formula for the average run length (ARL) of Cumulative Sum (CUSUM) control chart of autoregressive integrated moving average ARIMA(p,d,q) process observations with exponential white noise. The explicit formula are derived and the numerical integrations algorithm is developed for comparing the accuracy. We derived the explicit formula for ARL by using the Integral equations (IE) which is based on Fredholm integral equation. Then we proof the existence and uniqueness of the solution by using the Banach’s fixed point theorem. For comparing the accuracy of the explicit formulas, the numerical integration (NI) is given by using the Gauss-Legendre quadrature rule. Finally, we compare numerical results obtained from the explicit formula for the ARL of ARIMA(1,1,1) processes with results obtained from NI. The results show that the ARL from explicit formula is close to the numerical integration with an absolute percentage difference less than 0.3% with m = 800 nodes. In addition, the computational time of the explicit formula are efficiently smaller compared with NI. © Pleiades Publishing, Ltd. 2018
abstract_unstemmed	Abstract In this paper we derive explicit formula for the average run length (ARL) of Cumulative Sum (CUSUM) control chart of autoregressive integrated moving average ARIMA(p,d,q) process observations with exponential white noise. The explicit formula are derived and the numerical integrations algorithm is developed for comparing the accuracy. We derived the explicit formula for ARL by using the Integral equations (IE) which is based on Fredholm integral equation. Then we proof the existence and uniqueness of the solution by using the Banach’s fixed point theorem. For comparing the accuracy of the explicit formulas, the numerical integration (NI) is given by using the Gauss-Legendre quadrature rule. Finally, we compare numerical results obtained from the explicit formula for the ARL of ARIMA(1,1,1) processes with results obtained from NI. The results show that the ARL from explicit formula is close to the numerical integration with an absolute percentage difference less than 0.3% with m = 800 nodes. In addition, the computational time of the explicit formula are efficiently smaller compared with NI. © Pleiades Publishing, Ltd. 2018
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title_short	The ARIMA(p,d,q) on Upper Sided of CUSUM Procedure
url	https://dx.doi.org/10.1134/S1995080218030216
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up_date	2024-07-03T14:42:41.030Z
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fullrecord_marcxml	<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">SPR025232584</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230403064549.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">201007s2018 xx \|\|\|\|\|o 00\| \|\|eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1134/S1995080218030216</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)SPR025232584</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(SPR)S1995080218030216-e</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Zhang, Lili</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="4"><subfield code="a">The ARIMA(p,d,q) on Upper Sided of CUSUM Procedure</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2018</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">Computermedien</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Online-Ressource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© Pleiades Publishing, Ltd. 2018</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract In this paper we derive explicit formula for the average run length (ARL) of Cumulative Sum (CUSUM) control chart of autoregressive integrated moving average ARIMA(p,d,q) process observations with exponential white noise. The explicit formula are derived and the numerical integrations algorithm is developed for comparing the accuracy. We derived the explicit formula for ARL by using the Integral equations (IE) which is based on Fredholm integral equation. Then we proof the existence and uniqueness of the solution by using the Banach’s fixed point theorem. For comparing the accuracy of the explicit formulas, the numerical integration (NI) is given by using the Gauss-Legendre quadrature rule. Finally, we compare numerical results obtained from the explicit formula for the ARL of ARIMA(1,1,1) processes with results obtained from NI. The results show that the ARL from explicit formula is close to the numerical integration with an absolute percentage difference less than 0.3% with m = 800 nodes. In addition, the computational time of the explicit formula are efficiently smaller compared with NI.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Average run length</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Cumulative Sum</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Autoregressive integrated moving average</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Busababodhin, Piyapatr</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Lobachevskii journal of mathematics</subfield><subfield code="d">[Moskva] : Russian Acad. of Sciences [u.a.], 1998</subfield><subfield code="g">39(2018), 3 vom: Apr., Seite 424-432</subfield><subfield code="w">(DE-627)320467414</subfield><subfield code="w">(DE-600)2008068-2</subfield><subfield code="x">1818-9962</subfield><subfield code="7">nnns</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:39</subfield><subfield code="g">year:2018</subfield><subfield code="g">number:3</subfield><subfield code="g">month:04</subfield><subfield code="g">pages:424-432</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://dx.doi.org/10.1134/S1995080218030216</subfield><subfield code="z">lizenzpflichtig</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_USEFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SYSFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_SPRINGER</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield 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