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Haluk KUL* (*) Beykent Üniversitesi, Yönetim Bili_im Sistemleri Bölümü, 0STANBUL HYPERLINK "mailto:hkul@beykent.edu.tr"hkul@beykent.edu.tr ÖZET Bilgisayar destekli faturaland1rma ile yerinde sayaç okuma ve faturaland1rma i_lemlerinin yap1ld11 avuçiçi bilgisayarlarda nadiren de olsa sayaç okuma ve veri giri_i sürecinde personel hata yapabilmektedir. Eer sayaç deeri okunan abonenin genel kullan1m tarz1 konusundaki önceden edinilen istatistiksel veriler kullan1l1rsa belli bir güvenirlik aral11nda olmas1 gereken harcama miktar1 tahmin edilebilir. Faturaland1rma personelinin yanl1_ okuma veya basamaklar1n yerini dei_tirme gibi yap1labilecek hatala1r alg1lan1p uyar1 sinyali gönderilebilir. Bu çal1_mada uyar1 sistemi için abonenin mevcut ortalama ayl1k tüketim deerleri ve bu deerlerin standart sapma deerine göre 1 Sigma (%68 )ve 2 Sigma(%95) aral11nda tüketim deerleri sorgulanm1_ ve buna göre güvenirlik aral11 d1_1nda kalan deer girildiinde uyar1 sinyali veren bir algoritma önerilmi_tir. Anahtar Kelimeler: Hata Uyar1 Sistemi,Sayaç 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^ Günlük ya_ant1m1zda ister evimizde, isterse üretim yapt11m1z birimlerde elektrik , su, doalgaz gibi ürünleri kullanmaktay1z. Tüketilen ürün miktar1n1 belirlemek için kullan1lan sayaçlar da belirli zaman aral1klar1nda da1t1m kurulu_una ait görevliler taraf1ndan okunmakta ve iki okuma i_lemi aras1nda harcanan miktara göre faturaland1rma i_lemi sayaç mekan1nda gerçekle_tirilmektedir [1]. Sayaç okuma ile ilgili görevlendirilen personel gün içinde youn bir çal1_ma temposu içinde çal1_makta ve insan doas1n1n içinde bulunan miktarlarda hatal1 okuma veya hatal1 giri_ yapma gibi durumlarla kar_1 kar_1ya kalmaktad1r. Bu gibi hatal1 faturaland1rma i_lemlerinde ise çounlukla faturaland1r1lm1_ fazla miktar aboneden tahsil edilmekte, daha sonraki tahsilat dönemlerinde ödeme emri olu_turulmayarak hata telafi edilmektedir. Tahsilat1 yap1lan ürünlere ait abonelerin tüketim rejimleri konusunda asl1nda çe_itli tahmin ve hatal1 giri_leri önleme usülleri geli_tirilebilir. Bunlardan bir tanesi Zaman Serisi Analizi olabilecei gibi bir tanesi de tüketim miktar1n1n normal da1l1m gösterdii varsay1m1 ile Ortalama ve Standart sapma deerlerini kullanarak belirli güvenirlik aral11nda tahminlerde bulunmak ve bu güvenlik aral11 d1_1nda kalan deerler için uyar1 sinyali vermek ve görevliyi yeniden okuma ve veri giri_i yapmaya yönlendirmek _eklinde olabilir. Bu çal1_mada 0stanbul Büyük_ehir Belediyesi ne ait ^ebeke Suyu harcamalar1n1n Ev, 0_yeri, Hastane, Fabrika ve imalathane s1n1fland1rmalar1na göre çözümlemesi yap1lm1_ ve Normal Da1l1m çerçevesinde güvenirlik Aral11 yakla_1m1n1n tutarl1l11 sorgulanm1_t1r. Sorgulaman1n doruluu ölçüsünde de hatal1 veri okuma / giri_lerini önleyecek bir algoritma geli_tirilmi_tir. 2. MODEL Doada dei_kenlik içeren ve olas1l1k kuram1 içinde incelenebilen bir çok olguda Normal Da1l1m 1n geçerli olduu gözlenmektedir. Normal da1l1m, sürekli bir fonksiyon için tan1mlanm1_ olsa da sonlu say1da tekrar eden ölçümler için de kullan1labilir baz1 özelliklere sahiptir. Normal da1l1m1 tan1mlamadan önce k1saca ortalama ve standart sapma ifadelerinin verilmesi gerekmektedir. Ölçüm say1s1 n olan bir olguda i ninci ölçülen deer xi olmak üzere  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 gösteren bir fonksiyonda ortalama, ortanca ve mod deerleri ayn1 olmaktad1r. Standart sapma ne kadar küçük ise ölçülen deerlerin ortalama civar1na yak1n olduu anla_1lmaktad1r. 0deal normal da1l1m gösteren fonksiyonlar için 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 endüstri içinde uygulamalarda 6 Sigma ( EMBED Equation.3 ) düzenlemeleri ile s1f1r hatay1 amaçlayan uygulamalarda milyonda 2 hataya izin veren üretim süreçleri gerçekle_tirilmi_tir [4]. Tablo 1. Standart Sapmaya Göre Deer Kümesi içinde Olma Olas1l1k Deerleri [3]  EMBED Equation.3 Olas1l1k (%)168.27295.45399.73499.9937599.999943699.9999998 Çal1_man1n konusu olan sayaç okuma sürecinde ele al1nan tüketicilerin tüketim miktarlar1n1n öncelikle normal da1l1m varsay1m1na uyumluluu incelenecektir. Eer normal da1l1m varsay1m1na uygunluk tespit edilirse veri giri_inin belirli bir güvenirlik s1n1r1nda tahmin edilen deer aral11 içinde olmamas1 durumunda veri okuma ve faturalama i_lemini yapan personel için dorulama yap1lmas1n1 öneren bir uyar1 sinyalinin etkinle_tirilmesi salanacakt1r. Çal1_ma için incelemek üzere 0stanbul Büyük_ehir belediyesi ne ait da1t1m sorumluluunda olan _ebeke suyu harcama miktarlar1 ev i_yeri fabrika imalathane hastane _eklinde s1n1fland1r1lm1_ yakla_1k 20 _er örnek kullan1c1 için 15 ila 40 periyotluk bir aral1kta çözümlenmi_tir [5]. Çözümleme s1ras1nda s1ras1 ile her kullan1c1 için 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  üst s1n1r1 ( EMBED Equation.3  + EMBED Equation.3 ) 2  EMBED Equation.3  alt s1n1r1 ( EMBED Equation.3  - 2 EMBED Equation.3 ) 2  EMBED Equation.3  üst 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 ölçüm deerinin aral1klar1n içinde olup olmad11 sorgulanm1_t1r Toplam ölçüm içinde aral1kta olan ölçüm say1s1n1n oran1 1 EMBED Equation.3  aral11 için %68 civar1nda 2 EMBED Equation.3  aral11 için ise %95 civar1nda olmas1 beklenmektedir. Sorgulama bir hesaplama tablosu için =EER(xi< EMBED Equation.3  -  EMBED Equation.3 ;"";EER(xi> EMBED Equation.3 + EMBED Equation.3 ;"";1))(5) tarz1nda bir komut ile gerçekle_tirilebilir. 3. ÇÖZÜMLEME SONUÇLARI Önerilen algoritman1n geçerliliini kan1tlamak için öncelikle tüketim miktarlar1n1n normal da1l1ma uygunluu çözümlenmelidir. Bu amaçla tüketiciler Ev, 0_yeri, Fabrika, 0malathane, Hastane olarak s1n1fland1r1lm1_ ve herkullan1c1n1n tüketim miktarlar1na göre ortalama ve standart sapma deeri hesaplanm1_t1r. Ard1ndan her kullan1c1da periyotlara göre ayl1k tüketim miktar1n1n 1 EMBED Equation.3  ve 2 EMBED Equation.3  aral11nda olup olmad11 incelenmi_tir. Aral1k içinde olan periyot say1s1n1n toplam periyot say1s1na oran1n1n 1 EMBED Equation.3  için % 68, 2 EMBED Equation.3 için de % 95 civar1nda olup olmad11 ara_t1r1lm1_t1r. Ev Kullan1c1lar1 Çözümleme için öncelikli olarak ev kullan1c1lar1n1n durumu 19 ayr1 abone için incelenmi_tir. 0ncelemede en az 15 en fazla 21 periyot için abonelerin durumu ele al1nm1_t1r. ^ekil 1 de örnek bir ev kullan1c1s1n1n zamana göre tüketim miktar1 görülmektedir. Ayn1 grafikte ayr1ca ortalama ve 1 EMBED Equation.3  ve 2 EMBED Equation.3  için deer aral1klar1 da gösterilmektedir..  ^ekil 1. Bir ev kullan1c1s1 için kullan1m grafii ve deer aral1klar1 (1 EMBED Equation.3  için % 62, 2 EMBED Equation.3  için % 95 doruluk) 0ncelenen 19 abone için 1 EMBED Equation.3  ve 2 EMBED Equation.3  deer aral11 (menzil) içinde bulunma yüzdeleri ise Tablo 2 de sunulmaktad1r. Tablo 2. 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analizinde yaln1zca 2., 4., ve 14. kullan1c1lar için aral1kta bulunma yüzdesi aral11n çok alt1nda kalmaktad1r. Bu analiz, 2 EMBED Equation.3  için yap1ld11nda ise yaln1zca 19. kullan1c1n1n teorinin d1_1nda kald11 görülmektedir. Tablo 2 de sunulan veriler ^ekil 2 de grafik olarak verilmektedir.  ^ekil 2. Ev Kullan1c1lar1 için 1 EMBED Equation.3  ve 2 EMBED Equation.3  deer aral11 içinde bulunma yüzdeleri Ev kullan1c1lar1n1n tüketimlerinin 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 için bu deerlerin dei_imlerini göstermektedir.  ^ekil 3. Ev Kullan1c1lar1 için Menzil Tutarl1l11 (xmaks - xmin)/ EMBED Equation.3  ve Da1l1m Tutarl1l11 ( EMBED Equation.3 / EMBED Equation.3 ) deerleri ^ekil 2 ve ^ekil 3 incelendiinde tüketim miktarlar1n1n normal da1l1ma genel olarak uyduu, ancak menzil tutarl11n1n 4.0  5.0 aral11 d1_1na ç1k1nca küçük sapmalar meydana getirdii, ayn1 sapmalar1n Da1l1m tutarl1l11 için büyük deerlere ula_t1kça yeniden ortaya ç1kt11 gözlenmi_tir. 0_yerleri 0_yerleri için yap1lan çal1_mada da benzer sonuçlar elde edilmi_tir. ^ekil 4 te da1l1mlar1n deer aral1klar1ndaki yüzdeleri, ^ekil 5 te da Menzil tutarl1l11 (xmaks - xmin)/ EMBED Equation.3 ), ve Da1l1m Tutarl1l11 ( EMBED Equation.3 / EMBED Equation.3 ) deerleri gösterilmektedir.  ^ekil 4. 0_yeri Kullan1c1lar1 için 1 EMBED Equation.3  ve 2 EMBED Equation.3  deer aral11 içinde bulunma yüzdeleri  ^ekil 5. 0_yeri Kullan1c1lar1 için Menzil Tutarl1l11 (xmaks - xmin)/ EMBED Equation.3  ve Da1l1m Tutarl1l11 ( EMBED Equation.3 / EMBED Equation.3 ) deerleri 0_yerlerinde de ev kullan1c1lar1na benzer özellikte bir tüketim olduu gözlenmektedir. Fabrikalar Fabrikalar bu ara_t1rmada vardiyal1 çal1_man1n getirdii süreklilik nedeniyle ev ve i_yerlerinden fakl1 sonuçlar1n beklendii bir kullan1c1 s1n1f1 olarak ele al1nm1_t1r. Analiz sonuçlar1na bak1ld11nda gerçekten de tüketimdeki sürekliliin Menzil Tutarl1l11 n1 ve Da1l1m Tutarl1l11n1 art1rd11 sonucunu ortaya ç1karm1_t1r. ^ekil 6 da da1l1mlar1n deer aral1klar1ndaki yüzdeleri, ^ekil 7 de de Menzil tutarl1l11 (xmaks - xmin)/ EMBED Equation.3 ), ve Da1l1m Tutarl1l11 ( EMBED Equation.3 / EMBED Equation.3 ) deerleri gösterilmektedir.  ^ekil 6. Fabrika Kullan1c1lar1 için 1 EMBED Equation.3  ve 2 EMBED Equation.3  deer aral11 içinde bulunma yüzdeleri  ^ekil 7. Fabrika Kullan1c1lar1 için Menzil Tutarl1l11 (xmaks - xmin)/ EMBED Equation.3  ve Da1l1m Tutarl1l11 ( EMBED Equation.3 / EMBED Equation.3 ) deerleri 0malathaneler 0malathanelerde üretimin ve dolay1s1 ile ürüt tüketiminin çok olmamas1 nedeniyle ev kullan1c1lar kadar olmasa da Menzil Tutarl1l11 nda ve Da1l1m Tutarl1l11 nda bir düzensizlik ortaya ç1km1_t1r. Ancak yine de incelenen 19 kullan1c1dan 17 sinde kuram a uygun yüzdeler elde edilmi_tir. Sapma görülen 18. ve 19. kullan1c1larda gerçekten Menzil Tutarl1l11 ve Da1l1m Tutarl1l11 sorunlar1 olduu göze çarpm1_t1r. 0malathaneler için Deer Aral11nda Bulunma Yüzdeleri ^ekil 8 de, Menzil Tutarl1l11 ve Da1l1m Tutarl1l11 Deerleri de ^ekil 9 da sunulmaktad1r.  ^ekil 8. 0malathane Kullan1c1lar1 için 1 EMBED Equation.3  ve 2 EMBED Equation.3  deer aral11 içinde bulunma yüzdeler i  ^ekil 9. 0malathane Kullan1c1lar1 için Menzil Tutarl1l11 (xmaks - xmin)/ EMBED Equation.3  ve Da1l1m Tutarl1l11 ( EMBED Equation.3 / EMBED Equation.3 ) deerleri Hastaneler Hastane kullan1c1lar1 nda tüketim miktarlar1 fabrika kullan1c1lar1 ile ayn1 büyüklük mertebesine ula_abilmektedir. Bu benzerlik kendini Menzil Tutarl1l11 ve Da1l1m Tutarl1l11 nda da kendini göstermektedir. Hastane kullan1c1lar1 için de normal da1l1m varsay1m1n1n geçerlilii ^ekil 10 da gözlenmektedir. Hastaneler için Menzil Tutarl1l11 ve Da1l1m Tutarl1l11 Deerleri de ^ekil 11 de sunulmaktad1r.  ^ekil 10. Hastane Kullan1c1lar1 için 1 EMBED Equation.3  ve 2 EMBED Equation.3  deer aral11 içinde bulunma yüzdeleri  ^ekil 11. Hastane Kullan1c1lar1 için için Menzil Tutarl1l11 (xmaks - xmin)/ EMBED Equation.3  ve Da1l1m Tutarl1l11 ( EMBED Equation.3 / EMBED Equation.3 ) deerleri 3.6 Kullan1c1 Türlerine Göre Yakla_1mlar Önerilen algoritman1n kullan1c1lar1n tüketim rejimini tahmin etme konusunda ba_lang1ç için yeterli olabilecei dü_ünülmektedir. Ancak, yazl1k evlerdeki kullan1m ve _imdiden öngörülmemi_ durumlar1n da göz önüne al1nmas1 için Menzil Tutarl1l11 ve Da1l1m Tutarl1l11 parametrelerini de göz önüne alan, hatta zaman serisine göre mevsimsel veya dönemsel (Ramazan ay1 gibi) durumlar1 da inceleyen bir model geli_tirilebilir. Ayr1ca kurulu_lar kendi kullan1c1lar1n1n özelliklerine göre standart sapma düzeylerini 1 ve 2 d1_1nda bir ba_ka say1 ile düzenleyebilirler. Algoritmada bu say1 k ile simgelenmi_tir. Ba_lang1ç için k=2 al1nmas1 önerilmektedir. 4. ALGOR0TMA Algoritma veritaban1n bulunduu bilgisayarda ve faturalaman1n yap1ld11 bilgisayarda olmak üzere iki ayr1 modülden olu_maktad1r. Modül 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  ) üst 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. Modül 2. Sayaç okuma ve faturalama yap1lan ayg1tta olu_turulmu_ bir politika çerçevesinde saptanan standart sapma deeri  EMBED Equation.3  ya göre her kullanc1lar için hesaplanan alt s1n1r xmin ve üst s1n1r xmax deeri faturalama döneminde güncellenerek yüklenir. Tüketim miktar1 x olmak üzere  EMBED Equation.3  veya  EMBED Equation.3 durumunda ayg1t yeniden okuma ve veri giri_i konusunda personeli uyar1r. 5. SONUÇ ve ÖNER0LER Büyük_ehirlerdeki _ebeke suyu tüketim miktarlar1n1n çe_itli kullan1c1 türleri için normal da1l1ma uyduu gözlenmi_tir. Normal da1l1ma uyum için Menzil Tutarl1l11 ve Da1l1m Tutarl1l11 aral1klar1na göre daha ayr1nt1l1 bir ara_t1rma yap1lmas1n1n uygun olduu gözlenmi_tir. Hatal1 faturalaman1n önüne geçmek için faturalama ayg1tlar1nda belirtilen algoritmaya uygun bir yaz1l1m tadilat1 ile bu tür hatalar1n önüne geçilebilecei dü_ünülmektedir. TE^EKKÜR Yazar, ara_t1rmada çözümlemesi yap1lan verinin elde edilmesi konusundaki i_birlii nedeniyle 0stanbul Büyük_ehir Belediyesi ne, 0stanbul Su ve Kanalizasyon 0daresi ne ve say1n Salih ÇAKIROLU na te_ekkürü bir borç 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. KUL, Akademik Bili_im 2008 Çanakkale, Bildiri Özetleri  HYPERLINK "http://ozgur.beykent.edu.tr/~hkul/ab08/" http://ozgur.beykent.edu.tr/~hkul/ab08/     Akademik Bili_im Kongresi Bildiri Yaz1m Kurallar1  Akademik Bili_im 2008 Çanakkale Onsekiz Mart Üniversitesi, Çanakkale, 30 Ocak - 01 ^ubat 2007   PAGE 6 ˜˜˜&˜0˜…www $$*$Ifa$gdì)ÑzkdL{$$IfT–F”ÿÖFöÿÊž^ 'Ôÿÿÿÿ'ÔÿÿÿÿÿÿÿÿÀÿÿÿÿÿÿÿÿöh 6ööÖ ÿÿÿÿÿÿÿÿÿÿÿÿÖ ÿÿÿÿÿÿÿÿÿÖ ÿÿÿÖ ÿÿÿ4Ö4Ö Faö<pÖÿÿÿÿÿÿŠT0˜2˜6˜@˜J˜…www $$*$Ifa$gdì)ÑzkdD|$$IfT–F”ÿÖFöÿÊž^ 'Ôÿÿÿÿ'ÔÿÿÿÿÿÿÿÿÀÿÿÿÿÿÿÿÿöh 6ööÖ ÿÿÿÿÿÿÿÿÿÿÿÿÖ ÿÿÿÿÿÿÿÿÿÖ ÿÿÿÖ ÿÿÿ4Ö4Ö Faö<pÖÿÿÿÿÿÿŠTJ˜L˜P˜Z˜d˜…www $$*$Ifa$gdì)Ñzkd<}$$IfT–F”ÿÖFöÿÊž^ 'Ôÿÿÿÿ'ÔÿÿÿÿÿÿÿÿÀÿÿÿÿÿÿÿÿöh 6ööÖ ÿÿÿÿÿÿÿÿÿÿÿÿÖ ÿÿÿÿÿÿÿÿÿÖ ÿÿÿÖ ÿÿÿ4Ö4Ö Faö<pÖÿÿÿÿÿÿŠTd˜f˜j˜t˜~˜…www $$*$Ifa$gdì)Ñzkd4~$$IfT–F”ÿÖFöÿÊž^ 'Ôÿÿÿÿ'ÔÿÿÿÿÿÿÿÿÀÿÿÿÿÿÿÿÿöh 6ööÖ ÿÿÿÿÿÿÿÿÿÿÿÿÖ ÿÿÿÿÿÿÿÿÿÖ ÿÿÿÖ ÿÿÿ4Ö4Ö Faö<pÖÿÿÿÿÿÿŠT~˜€˜„˜Ž˜˜˜…www $$*$Ifa$gdì)Ñzkd,$$IfT–F”ÿÖFöÿÊž^ 'Ôÿÿÿÿ'ÔÿÿÿÿÿÿÿÿÀÿÿÿÿÿÿÿÿöh 6ööÖ ÿÿÿÿÿÿÿÿÿÿÿÿÖ ÿÿÿÿÿÿÿÿÿÖ ÿÿÿÖ ÿÿÿ4Ö4Ö Faö<pÖÿÿÿÿÿÿŠT˜˜š˜ž˜¨˜²˜…www 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yapabilmektedir. Eðer sayaç deðeri %&!&!&&!%&& &%&&6!!!&.&!& &!&!&!L2 ½Å+`gokunan abonenin genel kullaným tarzý konusu &!&%&%%&%&!&%& &!!&&&5&!%&&%2 ½;`gnda&%&2 ½¬`gki!z2 ½âJ`g önceden edinilen istatistiksel veriler kullanýlýrsa belli bir güvenirlik &&!!&!%!&%!&&!!!!!!&&%&&!%%&!!&!¬2 Åk`garalýðýnda olmasý gereken harcama miktarý tahmin edilebilir. Faturalandýrma personelinin yanlýþ okuma veya h&&&%&%2&5&2&!!!!&2%&!&6&26!&1%&6&2 &!&2.&&&&%&6&1&!&&!&%2!&&1&!&6%2!!!%_2 jÅ8`gbasamaklarýn yerini deðiþtirme gibi yapýlabilecek hatala&&&5&!&& !!% &!&6!&& &&&&!!!! &&&& 2 j² `gýÝ2 jÇ `gr algýlanýp u &&&&& &S2 jY 0`gyarý sinyali gönderilebilir. Bu çalýþmada uyarý !& &!&&%&&!!& .& !&6%&&&!&­2 ÀÅl`gsistemi için abonenin mevcut ortalama aylýk tüketim deðerleri ve bu deðerlerin standart sapma deðerine göre !6!&&&&&!%&6!!!&&&&6&&!!&!!6&!&!!!"&&&!&!!&%&%&&&6&& &!&!&&!2 À`g1 Sigma &&&5%2  Å`g(%<2  `g68&&�2  gX`g )ve 2 Sigma(%95) aralýðýnda tüketim deðerleri sorgulanmýþ ve buna göre güvenirlik aral!"&&&6&;&&&&&&&&&!!6&!&!!&&&%&6!"&&&&%&!&&!!&!&%/2  L`gýðý dýþýnda kalan deðer &&&%&!&%&&!&!e2 l Å<`ggirildiðinde uyarý sinyali veren bir algoritma önerilmiþtir.&&&&&!&!&& &!!!&%&%&6&&&!6 2 l ™ `g Ý 2 l ¬ `g Ý& 2 à Å`g Ý' 2  Å`g Ý'ûµÿ¼¢@Times New Roman-%2 o Å`gAnahtar Kelimeler 2*&*&2!<!!2 o `g: -2 o 3`gHata6%&- 2 o É`g Ý-12 o Ü`gUyarý Sistemi,Sayaç Okuma6!&%!6&&!&!6!&5&2 o ' `g Hatalarý6&&&J2 o < *`g, Ortalama, Standart Sapma, Normal Daðýlým6&&5&&%&%&&%&6&1&6&6&&6- 2 o  `g Ý- 2 o ³`g Ý&- 2 Ô Å`g Ý)-[2 P 5`gA SOFTWARE ALGHORITHM for PREVENTING THE READING AND aN<TBIlNNHNHUTTN*HUf$60CNINHNH*OTHUHNHON*NTNON2 Ì  `gBILLING ERROH*HH*OTHNOT22 Ì A`gRS in HAND HELD COMPUTERS N<<TNNNTHHONUfBNHHO< 2 Ì Ó`g Ý;- 2 7 Å`g Ý)- 2 ¢ ò`gABSTRACTB>3=BBB= 2 ¢ å `g Ý2- 2 Å`g Ý)-Ç2 d Å}`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 º Å]`gthe Personal Digital Assistance Computer systems. If some statistical information about the ci&!".!&&%"6&&!.&&! "2&6&%!"!!6""&6!"&!&"&&6%%&"%&%&"&!"!,2 º q`gonsumer is used it is &&&6!""&!&!"U2 Å1`gpossible to forecast the conmsumption amount withA&&& %&!!&&!!%&6&5&%&&6%&&2%72 î`gin a certain confidence level&&!!&& %&& &!!!!!I2 V )`g. By this way it is possible to recognizem.!%2&!&&& %!!&&%! 2 `g Ý2 gÅ`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 Ý& 2 ½Å`g Ý'2 Å`gIn thisT&&³2 …p`g study, different type of consumers’ consumptions are analyzed and these consumption values are compared with a %&!&!!&!&!&!&%&6!!&&&6&%&&!%&&!!&&%&&!!!&&&6%%&!&&!&!!&6&&!&2&%°2 jÅn`grange of 1 Sigma (%68) and 2 Sigma (%95). If the input data about consumption amount is out of the range, the &&&! & & &&5&!;&&!&&%!%!&&5&!<&&!!&! %&&!%&%!&%&&!!%&&6&&%!&5&%&! && & &!!%&&!!% >2 ÀÅ"`galghoritm proposed creates a warni&%&&6&%&&!&!!&!&2&&.2 Àý`gng signal to the staff.%&%&%%&!& 2 Àu `g Ý&- 2 Å`g Ý&-2 lÅ`gKeywords2!!2&&-�2 lña`g: Error Warning Systems, Counter Reading Errors, Average, Standard Deviation, Normal Distributions.&>&&&&&!!62&%&!.!%&%&.&.!!&&!&&%&&&6!!&&&2&6&6&&&& 2 l`g Ý&- 2 ÙÅ`g Ý-- 2 EÅ`g Ý)ûßÿ�¢@Times New Roman- 2 yÅ`g Ý- 2 ÖÅ`g1. 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