Reliabilitas Stress-Strength dengan Distribusi Weibull

Nina Permatasari, Sutawanir Darwis, Abdul Kudus

Abstract


Abstract. Random variable stress Y and random variable strength X along with estimate parameter reliability. The model which is used in order to distribution model Weilbull with the shape of parameter  same that is α but have different scale parameter that is  and  . Reliability parameter R definition as a opportunity from strength more large from stress, that is R = P( X > Y). Based on distribution of model which assumption resulted that reliabilty parameter R = . With used all of the real data did it estimation parameter  the method of  maximum likelihood . there is estimate parameter stages with method of maximum likelihood and formed confidence interval with bootstrap-persentile. In this minithesis application for the data fatigue with specimen diameter 21 mm (strength) and diameter 50 mm (stress), which is for strength variable form estimate parameter α = 0,93308 and estimate parameter scale q1  =  1088102 and for variable stress form estimate α = 0,83361 and estimate parameter q2  = 335326, and estimate value reliability  = 0,7479541119. And confidence interval bootstrap-persentile resulting under value limit persentile going 25 that is 0.5545906 and limit persentile upper going to 975 that is 0.8961282.

 

Abstrak. Variabel acakstrengthX dan variabel acak stress Y beserta penaksiran parameter keandalan (reliability)-nya. Model yang digunakan adalah model distribusi Weibull dengan parameter bentuk (shape) yang sama yakni α tetapi memiliki parameter skala (scale) yang berbeda yakni  dan  . Parameter keandalan R  didefinisikan  sebagai  peluang  dari  strength  lebih   besar   dari  stress, yakni R = P( X >Y). Berdasarkan model distribusi yang diasumsikan diperoleh bahwa parameter keandalan Dengan menggunakan data riil akan dilakukan penaksiran semua parameter tersebut dengan menggunakan metode kemungkinan maksimum. Adapun tahapan penaksiran parameter dengan metode kemungkinan maksimum dan membentuk selang kepercayaan dengan bootstrap-persentil. Dalam penelitian ini diaplikasikan untuk data fatigue dengan specimen diameter 21 mm (strength) dan diameter 50 mm (stress), dimana  untuk variabel strength membentuk taksiran paramater bentuk α =0,93308 dan taskiran parameter skala q1  =  1088102 dan untuk variabel stress  membentuk taksiran parameter bentuk α = 0,83361  dan taskiran parameter skala q2  = 335326 , dan nilai taksiran reliabilitas . dan selang kepercayaan bootstrap-persentil menghasilkan nilai batas bawah persentil yang ke 25 yaitu 0.5545906 dan batas atas persentil yang ke 975 yaitu  0.8961282.


Keywords


Reliability, Stress-Strength, Maximum Likelihood Estimation, Bootstrap-Percentil.

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DOI: http://dx.doi.org/10.29313/.v0i0.4401

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