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WEİBULL DAĞILIMININ ÖLÇEK VE BİÇİM PARAMETRELERİ İÇİN İSTATİSTİKSEL TAHMİN YÖNTEMLERİNİN KARŞILAŞTIRILMASI

COMPARISON OF STATISTICAL ESTIMATION METHODS FOR THE SCALE AND SHAPE PARAMETERS OF THE WEIBULL DISTRIBUTION

Journal Name:

  • İstanbul Ticaret Üniversitesi Sosyal Bilimler Dergisi

Publication Year:

  • 2009

Key Words:

Keywords (Original Language):

Author NameUniversity of Author
Abstract (2. Language): 
Weibull probability distribution, which is commonly usedtoday in data analysis in relation with lifetime and failure ratios, mostly includes a logarithmic model with parameters. The parameters of Weibull probability distribution can be predicted through various methods. Out of those methods, the most frequently used ones are graphic method, least squares method, maximum likelihood method and moment method. While a prediction is made through the help of shapes in a totally graphical environment in graphic method, predictions are made by way of employing mathematical equations and statistical functions in other methods. In this study, the methodsused in parameter predictions are briefly covered first. At the end of the study, the parameters of a Weibull probability distribution have been predicted for a data set in respect to the lifetime of a material that is being used as the printing unit of a photocopier through using the said methods and the results ofwhich have been compared respectively.
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Abstract (Original Language): 
Günümüzde yaşam süreli veya başarısızlık oranlarıile ilgili veri analizinde yaygın olarak kullanılan Weibull olasılık dağılımı, çoğunlukla iki parametreli logaritmik bir model içermektedir. Weibull olasılık dağılımının parametreleri, farklıyöntemler ile tahmin edilebilir. Buyöntemler içinde en çok kullanılanlar, grafik yöntemi, en küçük kareler yöntemi, maksimumbenzerlik yöntemi ve moment yöntemidir. Grafik yönteminde, tamamen grafik ortamında şekil yardımıyla bir tahmin yapılırken, diğer yöntemlerde matematiksel eşitlikler ve istatistiksel özellikler kullanılarak tahminler yapılmaktadır. Bu çalışmada öncelikle parametre tahmininde kullanılan yöntemlerden kısaca bahsedilmiştir. Çalışmanın sonunda, bir fotokopi makinesinin baskıünitesi olarak kullanılan bir malzemenin ömürleri ile ilgili veri seti için, Weibull olasılık dağılımının parametreleri, bu bahsedilen yöntemler aracılığıile tahmin edilmişve sonuçlar karşılaştırılmıştır.
FULL TEXT (PDF): 
PDF icon arastirmax-weibull-dagiliminin-olcek-bicim-parametreleri-icin-istatistiksel-tahmin-yontemlerinin-karsilastirilmasi.pdf
  • 15
73-87
  • Turkish

REFERENCES

References: 

AKDAĞ.S.-GÜLER.Ö., (2008) “Weibull Dağılım Parametrelerini Belirleme
Metodlarının Karşılaştırılması”, VII.Ulusal Temiz Enerji Sempozyumu, UTES 17-19 Aralık ,İstanbul, 707-714
BASU.B-TIWARI.D-KUNDU.D-PRASAD.R., (2007), “Is Weibull Distribution the
Most Appropriate Statistical Strength Distribution for Brittle Materials?”, Ceramics
Internatıonal, Volume 35, (Issue 1), 237-246
CARRASCO.J-ORTEGAE.-CORDEİRO.G., (2008) “A Generalized Modified
Weibull Distribution for Lifetime Modeling”, Computational Statistics&Data
Analysis, Vol 53, (İssue 2), 450-462
GRİMMETT.G.R.-STIRZAKER.D.R., (2004) Probability and Random Processes,
New York, Oxford University Press,
GURVİCH.M.R.-DİBENEDETTO.A.T.-RANADE.S.V., (1997) “A New Statistical
Distribution for Characterizing the Random Strength of Brittle Materials”, Journal
of Materials Science , (Issue 32) , 2559-2564
KIM.J.-YUM.B.,(2008) , “Selection Between Weibull and Lognormal Distributions:
A Comparative Simulation Study”, Computational Statistics&Data Analysis,
Volume 53, (Issue 2), 477-485
LİU.J.-CAO.L.-XİE.M.-GOH.T.-TANG.Y.,(2005) ,”A General Weibull Model for
Reliability Analysis Under Different Failure Criteria-Application on Anisotropic
Adhesive Joining Technology”, IEE Transaction on Electronic Packaging
Manufacturing, Vol 28, ( No 4) , 322-327
LOCKHART.R.-STEPHENS.M., (1994), “Estimation and Tests of Fit for the
Three-Parameter Weibull Distribution”, 56, (No 3), 491-500
İstanbul Ticaret Üniversitesi Sosyal Bilimler Dergisi Yıl:8 Sayı:15 Bahar 2009 s.73-87
87
MERT KANTAR,Y-ŞENOĞLU,B.,A Comparative Study for the Location and
Scale Parameters of the Weibull Distribution with Given Shape Parameter,
Computer&Geosciences, Volume 34, İssue 12, December 2008, s.1900
MURTHY.P-BULME.,M.-ECCLESTON.J.,(2004) ,”Weibull Model Selection for
Reliability Modeling”, Reliability Engineering&System Safety, Volume 86, (Issue
3),257-267
PINDER.J.E.-WIENER.J.G.-SMITH M.H., (1979), “The Weibull Distribution: A
New Method of Summarizing Survivorship Data”, Ecological Society of America,
59, (1), 175-179
SMITH.R.-NAYLOR.J.C.,(1987) ,”A Comparison of Maximum Likelihood and
Bayesian Estimators for the three-parameter Weibull Distribution”, Applied
Statistics, 36, (No 3), 358-369
SÜRÜCÜ.B.-SAZAK.H.,(2009), “Robust Control Charts to Monitoring Reliability
for a three-Parameter Weibull Distribtıon”, Reliability Engineering&System Safety,
Vol 94, (Issue 2), 503-508
TAN.Zhibin, (2009), “A New Approach to MLE of Weibull Distribution with
İnterval Data”, Reliability Engineering and System Safety, (94), 394-403
TONY.H.-WANG.Z.,(2009), “Statistical Estimation for the Parameters of Weibull
Distribution Based on Progressively Type-I Interval Censored Sample”, Journal of
Statistical Computation and Simulation, Vol 79, (No 2) ,145-159
TUMIDAJSKİ.P.J.-FİORE.L.-KHODABOCUS.T.-LACHEMİ.M.-PARİ.R., (2006),
“Comparison of Weibull and Normal Distribution for Concrete Compressive
Strengths”, Can.J.Civ.Eng. (33), 1287-1292
ZHANG.T.-XIE.M., (2007), “Failure Data Analysis with Extend Weibull
Distribution”, Comminication in Statistics-Simulation and Computation, (36), 579-592
http://www.itl.nist.gov.7div898/handbook/apr/section1/apr162.htm, [10.06.2008]
http://www.weibull.com/LifeDataWeb, [11.3.2009]
http://weibull.com/LifeDataWeb, [28.01.2009]
http://www.itl.nist.gov.7div898/handbook/apr/section1/apr162.htm, [10.06.2008]

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