ࡱ> iq`bjbjqPqP l>::B B B B B $ sssPtlu\! v}}}}4J~vxxxxxx$˨h3\ @B B }}*eB }j 8}vvV,@ T }v `Ksfl \{0x0|& ΟLf(!!!D/P"!!!P dB B B B B B B  EL T0P0 FATURALANDIRMA B0LG0SAYARLARI 00N HATALI G0R0^ NLEME YAZILIMI ALGOR0TMASI R. Haluk KUL* (*) Beykent niversitesi, Ynetim Bili_im Sistemleri Blm, 0STANBUL HYPERLINK "mailto:hkul@beykent.edu.tr"hkul@beykent.edu.tr ZET Bilgisayar destekli faturaland1rma ile yerinde saya okuma ve faturaland1rma i_lemlerinin yap1ld11 avuii bilgisayarlarda nadiren de olsa saya okuma ve veri giri_i srecinde personel hata yapabilmektedir. Eer saya deeri okunan abonenin genel kullan1m tarz1 konusundaki nceden edinilen istatistiksel veriler kullan1l1rsa belli bir gvenirlik aral11nda olmas1 gereken harcama miktar1 tahmin edilebilir. Faturaland1rma personelinin yanl1_ okuma veya basamaklar1n yerini dei_tirme gibi yap1labilecek hatala1r alg1lan1p uyar1 sinyali gnderilebilir. Bu al1_mada uyar1 sistemi iin abonenin mevcut ortalama ayl1k tketim deerleri ve bu deerlerin standart sapma deerine gre 1 Sigma (%68 )ve 2 Sigma(%95) aral11nda tketim deerleri sorgulanm1_ ve buna gre gvenirlik aral11 d1_1nda kalan deer girildiinde uyar1 sinyali veren bir algoritma nerilmi_tir. Anahtar Kelimeler: Hata Uyar1 Sistemi,Saya Okuma Hatalar1, Ortalama, Standart Sapma, Normal Da1l1m A SOFTWARE ALGHORITHM for PREVENTING THE READING AND BILLING ERRORS in HAND HELD COMPUTERS ABSTRACT It is seldomly possible to have reading and writing errors for the staff performing in site counter reading and billing by the Personal Digital Assistance Computer systems. If some statistical information about the consumer is used it is possible to forecast the conmsumption amount within a certain confidence level. By this way it is possible to recognize any false reading or decimal change errors made by the counter readers and a warning signal can be sent. In this study, different type of consumers consumptions are analyzed and these consumption values are compared with a range of 1 Sigma (%68) and 2 Sigma (%95). If the input data about consumption amount is out of the range, the alghoritm proposed creates a warning signal to the staff. Keywords: Error Warning Systems, Counter Reading Errors, Average, Standard Deviation, Normal Distribution 1. G0R0^ Gnlk ya_ant1m1zda ister evimizde, isterse retim yapt11m1z birimlerde elektrik , su, doalgaz gibi rnleri kullanmaktay1z. Tketilen rn miktar1n1 belirlemek iin kullan1lan sayalar da belirli zaman aral1klar1nda da1t1m kurulu_una ait grevliler taraf1ndan okunmakta ve iki okuma i_lemi aras1nda harcanan miktara gre faturaland1rma i_lemi saya mekan1nda gerekle_tirilmektedir [1]. Saya okuma ile ilgili grevlendirilen personel gn iinde youn bir al1_ma temposu iinde al1_makta ve insan doas1n1n iinde bulunan miktarlarda hatal1 okuma veya hatal1 giri_ yapma gibi durumlarla kar_1 kar_1ya kalmaktad1r. Bu gibi hatal1 faturaland1rma i_lemlerinde ise ounlukla faturaland1r1lm1_ fazla miktar aboneden tahsil edilmekte, daha sonraki tahsilat dnemlerinde deme emri olu_turulmayarak hata telafi edilmektedir. Tahsilat1 yap1lan rnlere ait abonelerin tketim rejimleri konusunda asl1nda e_itli tahmin ve hatal1 giri_leri nleme uslleri geli_tirilebilir. Bunlardan bir tanesi Zaman Serisi Analizi olabilecei gibi bir tanesi de tketim miktar1n1n normal da1l1m gsterdii varsay1m1 ile Ortalama ve Standart sapma deerlerini kullanarak belirli gvenirlik aral11nda tahminlerde bulunmak ve bu gvenlik aral11 d1_1nda kalan deerler iin uyar1 sinyali vermek ve grevliyi yeniden okuma ve veri giri_i yapmaya ynlendirmek _eklinde olabilir. Bu al1_mada 0stanbul Byk_ehir Belediyesi ne ait ^ebeke Suyu harcamalar1n1n Ev, 0_yeri, Hastane, Fabrika ve imalathane s1n1fland1rmalar1na gre zmlemesi yap1lm1_ ve Normal Da1l1m erevesinde gvenirlik Aral11 yakla_1m1n1n tutarl1l11 sorgulanm1_t1r. Sorgulaman1n doruluu lsnde de hatal1 veri okuma / giri_lerini nleyecek bir algoritma geli_tirilmi_tir. 2. MODEL Doada dei_kenlik ieren ve olas1l1k kuram1 iinde incelenebilen bir ok olguda Normal Da1l1m 1n geerli olduu gzlenmektedir. Normal da1l1m, srekli bir fonksiyon iin tan1mlanm1_ olsa da sonlu say1da tekrar eden lmler iin de kullan1labilir baz1 zelliklere sahiptir. Normal da1l1m1 tan1mlamadan nce k1saca ortalama ve standart sapma ifadelerinin verilmesi gerekmektedir. lm say1s1 n olan bir olguda i ninci llen deer xi olmak zere  EMBED Equation.3  Ortalama y1 ve  EMBED Equation.3  Standart Sapma y1 belirtmektedir. Ortalama ve standart sapma ifadesi a_a1da sunulmaktad1r [2].  EMBED Equation.3 (1) EMBED Equation.3 (2) Normal da1l1m gsteren bir fonksiyonda ortalama, ortanca ve mod deerleri ayn1 olmaktad1r. Standart sapma ne kadar kk ise llen deerlerin ortalama civar1na yak1n olduu anla_1lmaktad1r. 0deal normal da1l1m gsteren fonksiyonlar iin ortalaman1n solunda ve sa1ndaki standart sapma deerleri aras1nda olu_an deerlerin toplam deerlere oran1 kesin olarak bilinebilmektedir [3]. Bu konudaki oranlar Tablo 1 de sunulmaktad1r. Baz1 endstri iinde uygulamalarda 6 Sigma ( EMBED Equation.3 ) dzenlemeleri ile s1f1r hatay1 amalayan uygulamalarda milyonda 2 hataya izin veren retim sreleri gerekle_tirilmi_tir [4]. Tablo 1. Standart Sapmaya Gre Deer Kmesi iinde Olma Olas1l1k Deerleri [3]  EMBED Equation.3 Olas1l1k (%)168.27295.45399.73499.9937599.999943699.9999998 al1_man1n konusu olan saya okuma srecinde ele al1nan tketicilerin tketim miktarlar1n1n ncelikle normal da1l1m varsay1m1na uyumluluu incelenecektir. Eer normal da1l1m varsay1m1na uygunluk tespit edilirse veri giri_inin belirli bir gvenirlik s1n1r1nda tahmin edilen deer aral11 iinde olmamas1 durumunda veri okuma ve faturalama i_lemini yapan personel iin dorulama yap1lmas1n1 neren bir uyar1 sinyalinin etkinle_tirilmesi salanacakt1r. al1_ma iin incelemek zere 0stanbul Byk_ehir belediyesi ne ait da1t1m sorumluluunda olan _ebeke suyu harcama miktarlar1 ev i_yeri fabrika imalathane hastane _eklinde s1n1fland1r1lm1_ yakla_1k 20 _er rnek kullan1c1 iin 15 ila 40 periyotluk bir aral1kta zmlenmi_tir [5]. zmleme s1ras1nda s1ras1 ile her kullan1c1 iin ortalama ( EMBED Equation.3 ) standart sapma ( EMBED Equation.3 ) minimum deer (xmin) maksimum deer (xmaks) 1  EMBED Equation.3  alt s1n1r1 ( EMBED Equation.3  -  EMBED Equation.3  ) 1  EMBED Equation.3  st s1n1r1 ( EMBED Equation.3  + EMBED Equation.3 ) 2  EMBED Equation.3  alt s1n1r1 ( EMBED Equation.3  - 2 EMBED Equation.3 ) 2  EMBED Equation.3  st s1n1r1 ( EMBED Equation.3  +2 EMBED Equation.3 ) Menzil tutarl1l11 (xmaks - xmin)/ EMBED Equation.3  Da1l1m tutarl1l11 ( EMBED Equation.3 / EMBED Equation.3 ) deerleri olu_turulmu_tur. Daha sonras1nda da 1  EMBED Equation.3  aral11  EMBED Equation.3 (3) ve 2  EMBED Equation.3  aral11 da  EMBED Equation.3 (4) _eklinde tan1mlanm1_t1r. Ard1ndan her lm deerinin aral1klar1n iinde olup olmad11 sorgulanm1_t1r Toplam lm iinde aral1kta olan lm say1s1n1n oran1 1 EMBED Equation.3  aral11 iin %68 civar1nda 2 EMBED Equation.3  aral11 iin ise %95 civar1nda olmas1 beklenmektedir. Sorgulama bir hesaplama tablosu iin =EER(xi< EMBED Equation.3  -  EMBED Equation.3 ;"";EER(xi> EMBED Equation.3 + EMBED Equation.3 ;"";1))(5) tarz1nda bir komut ile gerekle_tirilebilir. 3. ZMLEME SONULARI nerilen algoritman1n geerliliini kan1tlamak iin ncelikle tketim miktarlar1n1n normal da1l1ma uygunluu zmlenmelidir. Bu amala tketiciler Ev, 0_yeri, Fabrika, 0malathane, Hastane olarak s1n1fland1r1lm1_ ve herkullan1c1n1n tketim miktarlar1na gre ortalama ve standart sapma deeri hesaplanm1_t1r. Ard1ndan her kullan1c1da periyotlara gre ayl1k tketim miktar1n1n 1 EMBED Equation.3  ve 2 EMBED Equation.3  aral11nda olup olmad11 incelenmi_tir. Aral1k iinde olan periyot say1s1n1n toplam periyot say1s1na oran1n1n 1 EMBED Equation.3  iin % 68, 2 EMBED Equation.3 iin de % 95 civar1nda olup olmad11 ara_t1r1lm1_t1r. Ev Kullan1c1lar1 zmleme iin ncelikli olarak ev kullan1c1lar1n1n durumu 19 ayr1 abone iin incelenmi_tir. 0ncelemede en az 15 en fazla 21 periyot iin abonelerin durumu ele al1nm1_t1r. ^ekil 1 de rnek bir ev kullan1c1s1n1n zamana gre tketim miktar1 grlmektedir. Ayn1 grafikte ayr1ca ortalama ve 1 EMBED Equation.3  ve 2 EMBED Equation.3  iin deer aral1klar1 da gsterilmektedir..  ^ekil 1. Bir ev kullan1c1s1 iin kullan1m grafii ve deer aral1klar1 (1 EMBED Equation.3  iin % 62, 2 EMBED Equation.3  iin % 95 doruluk) 0ncelenen 19 abone iin 1 EMBED Equation.3  ve 2 EMBED Equation.3  deer aral11 (menzil) iinde bulunma yzdeleri ise Tablo 2 de sunulmaktad1r. Tablo 2. 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Bu analiz, 2 EMBED Equation.3  iin yap1ld11nda ise yaln1zca 19. kullan1c1n1n teorinin d1_1nda kald11 grlmektedir. Tablo 2 de sunulan veriler ^ekil 2 de grafik olarak verilmektedir.  ^ekil 2. Ev Kullan1c1lar1 iin 1 EMBED Equation.3  ve 2 EMBED Equation.3  deer aral11 iinde bulunma yzdeleri Ev kullan1c1lar1n1n tketimlerinin da1l1m1nda anormallik olup olmad11 konusunda incelenebilecek dier parametreler ise Menzil tutarl1l11 (xmaks - xmin)/ EMBED Equation.3 , ve Da1l1m Tutarl1l11 ( EMBED Equation.3 / EMBED Equation.3 ) olarak saptanm1_t1r. ^ekil 3, incelenen ev kullan1c1lar1 iin bu deerlerin dei_imlerini gstermektedir.  ^ekil 3. Ev Kullan1c1lar1 iin Menzil Tutarl1l11 (xmaks - xmin)/ EMBED Equation.3  ve Da1l1m Tutarl1l11 ( EMBED Equation.3 / EMBED Equation.3 ) deerleri ^ekil 2 ve ^ekil 3 incelendiinde tketim miktarlar1n1n normal da1l1ma genel olarak uyduu, ancak menzil tutarl11n1n 4.0  5.0 aral11 d1_1na 1k1nca kk sapmalar meydana getirdii, ayn1 sapmalar1n Da1l1m tutarl1l11 iin byk deerlere ula_t1ka yeniden ortaya 1kt11 gzlenmi_tir. 0_yerleri 0_yerleri iin yap1lan al1_mada da benzer sonular elde edilmi_tir. ^ekil 4 te da1l1mlar1n deer aral1klar1ndaki yzdeleri, ^ekil 5 te da Menzil tutarl1l11 (xmaks - xmin)/ EMBED Equation.3 ), ve Da1l1m Tutarl1l11 ( EMBED Equation.3 / EMBED Equation.3 ) deerleri gsterilmektedir.  ^ekil 4. 0_yeri Kullan1c1lar1 iin 1 EMBED Equation.3  ve 2 EMBED Equation.3  deer aral11 iinde bulunma yzdeleri  ^ekil 5. 0_yeri Kullan1c1lar1 iin Menzil Tutarl1l11 (xmaks - xmin)/ EMBED Equation.3  ve Da1l1m Tutarl1l11 ( EMBED Equation.3 / EMBED Equation.3 ) deerleri 0_yerlerinde de ev kullan1c1lar1na benzer zellikte bir tketim olduu gzlenmektedir. Fabrikalar Fabrikalar bu ara_t1rmada vardiyal1 al1_man1n getirdii sreklilik nedeniyle ev ve i_yerlerinden fakl1 sonular1n beklendii bir kullan1c1 s1n1f1 olarak ele al1nm1_t1r. Analiz sonular1na bak1ld11nda gerekten de tketimdeki srekliliin Menzil Tutarl1l11 n1 ve Da1l1m Tutarl1l11n1 art1rd11 sonucunu ortaya 1karm1_t1r. ^ekil 6 da da1l1mlar1n deer aral1klar1ndaki yzdeleri, ^ekil 7 de de Menzil tutarl1l11 (xmaks - xmin)/ EMBED Equation.3 ), ve Da1l1m Tutarl1l11 ( EMBED Equation.3 / EMBED Equation.3 ) deerleri gsterilmektedir.  ^ekil 6. Fabrika Kullan1c1lar1 iin 1 EMBED Equation.3  ve 2 EMBED Equation.3  deer aral11 iinde bulunma yzdeleri  ^ekil 7. Fabrika Kullan1c1lar1 iin Menzil Tutarl1l11 (xmaks - xmin)/ EMBED Equation.3  ve Da1l1m Tutarl1l11 ( EMBED Equation.3 / EMBED Equation.3 ) deerleri 0malathaneler 0malathanelerde retimin ve dolay1s1 ile rt tketiminin ok olmamas1 nedeniyle ev kullan1c1lar kadar olmasa da Menzil Tutarl1l11 nda ve Da1l1m Tutarl1l11 nda bir dzensizlik ortaya 1km1_t1r. Ancak yine de incelenen 19 kullan1c1dan 17 sinde kuram a uygun yzdeler elde edilmi_tir. Sapma grlen 18. ve 19. kullan1c1larda gerekten Menzil Tutarl1l11 ve Da1l1m Tutarl1l11 sorunlar1 olduu gze arpm1_t1r. 0malathaneler iin Deer Aral11nda Bulunma Yzdeleri ^ekil 8 de, Menzil Tutarl1l11 ve Da1l1m Tutarl1l11 Deerleri de ^ekil 9 da sunulmaktad1r.  ^ekil 8. 0malathane Kullan1c1lar1 iin 1 EMBED Equation.3  ve 2 EMBED Equation.3  deer aral11 iinde bulunma yzdeler i  ^ekil 9. 0malathane Kullan1c1lar1 iin Menzil Tutarl1l11 (xmaks - xmin)/ EMBED Equation.3  ve Da1l1m Tutarl1l11 ( EMBED Equation.3 / EMBED Equation.3 ) deerleri Hastaneler Hastane kullan1c1lar1 nda tketim miktarlar1 fabrika kullan1c1lar1 ile ayn1 byklk mertebesine ula_abilmektedir. Bu benzerlik kendini Menzil Tutarl1l11 ve Da1l1m Tutarl1l11 nda da kendini gstermektedir. Hastane kullan1c1lar1 iin de normal da1l1m varsay1m1n1n geerlilii ^ekil 10 da gzlenmektedir. Hastaneler iin Menzil Tutarl1l11 ve Da1l1m Tutarl1l11 Deerleri de ^ekil 11 de sunulmaktad1r.  ^ekil 10. Hastane Kullan1c1lar1 iin 1 EMBED Equation.3  ve 2 EMBED Equation.3  deer aral11 iinde bulunma yzdeleri  ^ekil 11. Hastane Kullan1c1lar1 iin iin Menzil Tutarl1l11 (xmaks - xmin)/ EMBED Equation.3  ve Da1l1m Tutarl1l11 ( EMBED Equation.3 / EMBED Equation.3 ) deerleri 3.6 Kullan1c1 Trlerine Gre Yakla_1mlar nerilen algoritman1n kullan1c1lar1n tketim rejimini tahmin etme konusunda ba_lang1 iin yeterli olabilecei d_nlmektedir. Ancak, yazl1k evlerdeki kullan1m ve _imdiden ngrlmemi_ durumlar1n da gz nne al1nmas1 iin Menzil Tutarl1l11 ve Da1l1m Tutarl1l11 parametrelerini de gz nne alan, hatta zaman serisine gre mevsimsel veya dnemsel (Ramazan ay1 gibi) durumlar1 da inceleyen bir model geli_tirilebilir. Ayr1ca kurulu_lar kendi kullan1c1lar1n1n zelliklerine gre standart sapma dzeylerini 1 ve 2 d1_1nda bir ba_ka say1 ile dzenleyebilirler. Algoritmada bu say1 k ile simgelenmi_tir. Ba_lang1 iin k=2 al1nmas1 nerilmektedir. 4. ALGOR0TMA Algoritma veritaban1n bulunduu bilgisayarda ve faturalaman1n yap1ld11 bilgisayarda olmak zere iki ayr1 modlden olu_maktad1r. Modl 1. Veritaban1 k1sm1nda her kullan1c1ya ili_kin ortalama ( EMBED Equation.3 ) standart sapma ( EMBED Equation.3 ) minimum deer (xmin) maksimum deer (xmaks) alt s1n1r1 ( EMBED Equation.3  - k EMBED Equation.3  ) st s1n1r1 ( EMBED Equation.3  +k EMBED Equation.3 ) Menzil tutarl1l11 (xmaks - xmin)/ EMBED Equation.3  Da1l1m tutarl1l11 ( EMBED Equation.3 / EMBED Equation.3 ) deerleri hesaplan1r. Modl 2. Saya okuma ve faturalama yap1lan ayg1tta olu_turulmu_ bir politika erevesinde saptanan standart sapma deeri  EMBED Equation.3  ya gre her kullanc1lar iin hesaplanan alt s1n1r xmin ve st s1n1r xmax deeri faturalama dneminde gncellenerek yklenir. Tketim miktar1 x olmak zere  EMBED Equation.3  veya  EMBED Equation.3 durumunda ayg1t yeniden okuma ve veri giri_i konusunda personeli uyar1r. 5. SONU ve NER0LER Byk_ehirlerdeki _ebeke suyu tketim miktarlar1n1n e_itli kullan1c1 trleri iin normal da1l1ma uyduu gzlenmi_tir. Normal da1l1ma uyum iin Menzil Tutarl1l11 ve Da1l1m Tutarl1l11 aral1klar1na gre daha ayr1nt1l1 bir ara_t1rma yap1lmas1n1n uygun olduu gzlenmi_tir. Hatal1 faturalaman1n nne gemek iin faturalama ayg1tlar1nda belirtilen algoritmaya uygun bir yaz1l1m tadilat1 ile bu tr hatalar1n nne geilebilecei d_nlmektedir. TE^EKKR Yazar, ara_t1rmada zmlemesi yap1lan verinin elde edilmesi konusundaki i_birlii nedeniyle 0stanbul Byk_ehir Belediyesi ne, 0stanbul Su ve Kanalizasyon 0daresi ne ve say1n Salih AKIROLU na te_ekkr bir bor bilmektedir. KAYNAKLAR [1]0GDA^, Faturaland1rma Nas1l Yap1l1r?  HYPERLINK "http://www.igdas.com.tr/Content_View. aspx?MI=2&CMI=133&MCI=37" http://www.igdas.com.tr/Content_View. aspx?MI=2&CMI=133&MCI=37[2]Taylor III B. W., Introduction to Management Science, Prentice Hall, 2001[3]Schwalbe K.,  Information Technology Project Management , Course Technology, 2001[4]David L. Goetsch, Stanley B. Davis; Quality Management, Pearson Prentice Hall, 2006[5]R. H. 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Eer saya deeri %&!&!&&!%&& &%&&6!!!&.&!& &!&!&!L2 +`gokunan abonenin genel kullanm tarz konusu &!&%&%%&%&!&%& &!!&&&5&!%&&%2 ;`gnda&%&2 `gki!z2 J`g nceden edinilen istatistiksel veriler kullanlrsa belli bir gvenirlik &&!!&!%!&%!&&!!!!!!&&%&&!%%&!!&!2 k`garalnda olmas gereken harcama miktar tahmin edilebilir. Faturalandrma personelinin yanl okuma veya h&&&%&%2&5&2&!!!!&2%&!&6&26!&1%&6&2 &!&2.&&&&%&6&1&!&&!&%2!&&1&!&6%2!!!%_2 j8`gbasamaklarn yerini deitirme gibi yaplabilecek hatala&&&5&!&& !!% &!&6!&& &&&&!!!! &&&& 2 j `g2 j `gr alglanp u &&&&& &S2 jY 0`gyar sinyali gnderilebilir. Bu almada uyar !& &!&&%&&!!& .& !&6%&&&!&2 l`gsistemi iin abonenin mevcut ortalama aylk tketim deerleri ve bu deerlerin standart sapma deerine gre !6!&&&&&!%&6!!!&&&&6&&!!&!!6&!&!!!"&&&!&!!&%&%&&&6&& &!&!&&!2 `g1 Sigma &&&5%2  `g(%<2  `g68&&2  gX`g )ve 2 Sigma(%95) aralnda tketim deerleri sorgulanm ve buna gre gvenirlik aral!"&&&6&;&&&&&&&&&!!6&!&!!&&&%&6!"&&&&%&!&&!!&!&%/2  L`g dnda kalan deer &&&%&!&%&&!&!e2 l <`ggirildiinde uyar sinyali veren bir algoritma nerilmitir.&&&&&!&!&& &!!!&%&%&6&&&!6 2 l `g  2 l `g & 2 `g ' 2  `g '@Times New Roman-%2 o `gAnahtar Kelimeler 2*&*&2!<!!2 o `g: -2 o 3`gHata6%&- 2 o `g -12 o `gUyar Sistemi,Saya Okuma6!&%!6&&!&!6!&5&2 o ' `g Hatalar6&&&J2 o < *`g, Ortalama, Standart Sapma, Normal Dalm6&&5&&%&%&&%&6&1&6&6&&6- 2 o `g - 2 o `g &- 2 `g )-[2 P 5`gA SOFTWARE ALGHORITHM for PREVENTING THE READING AND aN<TBIlNNHNHUTTN*HUf$60CNINHNH*OTHUHNHON*NTNON2  `gBILLING ERROH*HH*OTHNOT22 A`gRS in HAND HELD COMPUTERS N<<TNNNTHHONUfBNHHO< 2 `g ;- 2 7 `g )- 2 `gABSTRACTB>3=BBB= 2 `g 2- 2 `g )-2 d }`gIt is seldomly possible to have reading and writing errors for the staff performing in site counter reading and billing by !%&6!%&&!&&&!!!&&&%%&&2%&!&&&!&&!&6%&&!!&%&!!&&&%%&&%&&& 2 ]`gthe Personal Digital Assistance Computer systems. If some statistical information about the ci&!".!&&%"6&&!.&&! "2&6&%!"!!6""&6!"&!&"&&6%%&"%&%&"&!"!,2 q`gonsumer is used it is &&&6!""&!&!"U2 1`gpossible to forecast the conmsumption amount withA&&& %&!!&&!!%&6&5&%&&6%&&2%72 `gin a certain confidence level&&!!&& %&& &!!!!!I2 V )`g. By this way it is possible to recognizem.!%2&!&&& %!!&&%! 2 `g 2 g`gany&&!2 g2f`g false reading or decimal change errors made by the counter readers and a warning signal can be sent.&!!&&&&&&!!6&!%%&&!!&6%&!&!&!!&%&!!&&!&%&&2&&%&%&%!%&&!!& 2 gf`g & 2 `g '2 `gIn thisT&&2 p`g study, different type of consumers consumptions are analyzed and these consumption values are compared with a %&!&!!&!&!&!&%&6!!&&&6&%&&!%&&!!&&%&&!!!&&&6%%&!&&!&!!&6&&!&2&%2 jn`grange of 1 Sigma (%68) and 2 Sigma (%95). 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