Yıl 2019, Cilt 31 , Sayı 3, Sayfalar 214 - 222 2019-09-01

I.Tip Uçdeğer Dağılımından Gelen Rekor Değerler İçin Stres Dayanıklılık Modelinin Güvenilirliğinin Tahmini
Stress-Strength Reliability Estimation for the Type I Extreme-Value Distribution Based on Records

Fatih KIZILASLAN [1]


Bu çalışmada, stres Y ve dayanıklılık X rastgele değişkenleri I. Tip uçdeğer dağılımına sahip olduğunda rekor değerler için stres dayanıklılık modelinin güvenilirliği ele alınmıştır. İlk olarak  için klasik yaklaşım yani değişmez en küçük varyanslı yansz minimum varyans tahmin edici ve en çok olabilirlik tahmin edicisi kullanılmıştır. Sonra, önsellerin gamma dağılımına sahip olması varsayımı altın  için Bayes yaklaşımı ele alınmıştır. Stres ve dayanıklılık değişkenlerinin ortak parametresi biliniyorken,  nin kesin Bayes tahmin edicisi ve Bayes güven aralığı elde edilmiştir. Stres ve dayanıklılık değişkenlerinin ortak parametresi bilinmiyorken, ’nin Bayes tahmin edicisi ve en yüksek olasılık yoğunluklu Bayes güven aralığı Markov Zinciri Monte Carlo (MCMC) metodu ile elde edilmiştir. Son olarak elde edilen tahmin edicilerin performanslarını karşılaştırmak için Monte Carlo simülasyonu gerçekleştirildi. Elde edilen tahmin edicilerin performanslarını göstermek için hava sıcaklıkları ile ilgili gerçek veri seti analiz edilmiştir.

In this paper, we consider the stress-strength reliability  for record data when the distribution of random stress  and strength  have the type I extreme-value distribution. First, classical inference methods, namely uniformly minimum variance unbiased estimate (UMVUE) and maximum likelihood estimate (MLE), are used for . Second, Bayesian inference of  are considered for gamma priors assumption. When the common parameter of stress and strength variables is known, the exact Bayes estimate and Bayesian credible interval of  are obtained. Markov Chain Monte Carlo (MCMC) method are used to derive the Bayes estimate and highest probability density (HPD) credible interval of  when the common parameter is unknown. Finally, Monte Carlo simulations are performed to compare the performance of the obtained estimates. A real data set about the weather temperature is analyzed to illustrate the performances of the derived estimators in the paper.

  • Referenc1: Murthy, D.N.P, Xie, M, Jiang R. (2003). Weibull Models. Wiley. New York.
  • Referenc2: Lai, C.D., Xie, M. (2003). A modified Weibull distribution. IEEE Transactions on Reliability, 52, 33-37.
  • Referenc3: Chandler, K.N. (1952). The distribution and frequency of record values. Journal of the Royal Statistical Society, Series B, 14, 220-228.
  • Referenc4: Arnold, B.C., Balakrishnan, N., Nagaraja, H.N. (1998). Records. John Wiley & Sons, New York.
  • Referenc5: Ahsanullah, M., Nevzorov, V. (2015). Records via probability theory. Atlantis Press.
  • Referenc6: Birnbaum, Z.W. (1956). On a use of Mann-Whitney statistics. In Proceedings of 3rd Berkeley Symposium on Mathematical Statistics and Probability, 1, 13-17.
  • Referenc7: Kotz, S., Lumelskii, Y., Pensky, M. (2003). The Stress-Strength Model and its Generalizations: Theory and Applications. World Scientific, Singapore.
  • Referenc8: Tarvirdizade, B., Gharehchobogh, H.K. (2015). Inference on Pr⁡(X>Y) based on record values from the Burr Type X distribution. Hacettepe Journal of Mathematics and Statistics, 45, 267-278.
  • Referenc9: Basirat, M., Baratpour, S., Ahmadi , J. (2016). On estimation of stress–strength parameter using record values from proportional hazard rate models. Communications in Statistics - Theory and Methods, 45, 5787-5801.
  • Referenc10: Kızılaslan, F., Nadar, M. (2017). Statistical inference of P(X<Y) for the Burr Type XII distribution based on records. Hacettepe Journal of Mathematics and Statistics, 46, 713-742.
  • Referenc11:Rasethuntsa, T. R., Nadar, M. (2018). Stress–strength reliability of a non-identical-component-strengths system based on upper record values from the family of Kumaraswamy generalized distributions. Statistics, 52, 684-716.
  • Referenc12: Çetinkaya, Ç., Genç, A.İ. (2019). Stress–strength reliability estimation under the standard two-sided power distribution. Applied Mathematical Modelling, 65, 72-88.
  • Referenc13: Basirat, M., Baratpour, S., Ahmadi, J. (2015). Statistical inferences for stress-strength in the proportional hazard models based on progressive type-ii censored samples. Journal of Statistical Computational and Simulation, 85, 431-449.
  • Referenc14: Gelman, A., Carlin, J.B., Stern, H.S., Rubin, D.B. (2003). Bayesian Data Analysis. Chapman & Hall, London.
  • Referenc15: Chen, M.H., Shao, Q.M. (1999). Monte carlo estimation of Bayesian credible and hpd intervals. Journal of Computational Graphical and Statistics, 8, 69-92.
Birincil Dil en
Konular Fen
Bölüm Araştırma Makaleleri
Yazarlar

Orcid: 0000-0001-6457-0967
Yazar: Fatih KIZILASLAN (Sorumlu Yazar)
Kurum: Marmara University, Faculty of Arts and Sciences, Department of Statistics
Ülke: Turkey


Tarihler

Yayımlanma Tarihi : 1 Eylül 2019

Bibtex @araştırma makalesi { jeps512278, journal = {International Journal of Advances in Engineering and Pure Sciences}, issn = {}, eissn = {2636-8277}, address = {fbedergi@marmara.edu.tr}, publisher = {Marmara Üniversitesi}, year = {2019}, volume = {31}, pages = {214 - 222}, doi = {10.7240/jeps.512278}, title = {Stress-Strength Reliability Estimation for the Type I Extreme-Value Distribution Based on Records}, key = {cite}, author = {KIZILASLAN, Fatih} }
APA KIZILASLAN, F . (2019). Stress-Strength Reliability Estimation for the Type I Extreme-Value Distribution Based on Records. International Journal of Advances in Engineering and Pure Sciences , 31 (3) , 214-222 . DOI: 10.7240/jeps.512278
MLA KIZILASLAN, F . "Stress-Strength Reliability Estimation for the Type I Extreme-Value Distribution Based on Records". International Journal of Advances in Engineering and Pure Sciences 31 (2019 ): 214-222 <https://dergipark.org.tr/tr/pub/jeps/issue/48917/512278>
Chicago KIZILASLAN, F . "Stress-Strength Reliability Estimation for the Type I Extreme-Value Distribution Based on Records". International Journal of Advances in Engineering and Pure Sciences 31 (2019 ): 214-222
RIS TY - JOUR T1 - Stress-Strength Reliability Estimation for the Type I Extreme-Value Distribution Based on Records AU - Fatih KIZILASLAN Y1 - 2019 PY - 2019 N1 - doi: 10.7240/jeps.512278 DO - 10.7240/jeps.512278 T2 - International Journal of Advances in Engineering and Pure Sciences JF - Journal JO - JOR SP - 214 EP - 222 VL - 31 IS - 3 SN - -2636-8277 M3 - doi: 10.7240/jeps.512278 UR - https://doi.org/10.7240/jeps.512278 Y2 - 2019 ER -
EndNote %0 International Journal of Advances in Engineering and Pure Sciences Stress-Strength Reliability Estimation for the Type I Extreme-Value Distribution Based on Records %A Fatih KIZILASLAN %T Stress-Strength Reliability Estimation for the Type I Extreme-Value Distribution Based on Records %D 2019 %J International Journal of Advances in Engineering and Pure Sciences %P -2636-8277 %V 31 %N 3 %R doi: 10.7240/jeps.512278 %U 10.7240/jeps.512278
ISNAD KIZILASLAN, Fatih . "Stress-Strength Reliability Estimation for the Type I Extreme-Value Distribution Based on Records". International Journal of Advances in Engineering and Pure Sciences 31 / 3 (Eylül 2019): 214-222 . https://doi.org/10.7240/jeps.512278
AMA KIZILASLAN F . Stress-Strength Reliability Estimation for the Type I Extreme-Value Distribution Based on Records. JEPS. 2019; 31(3): 214-222.
Vancouver KIZILASLAN F . Stress-Strength Reliability Estimation for the Type I Extreme-Value Distribution Based on Records. International Journal of Advances in Engineering and Pure Sciences. 2019; 31(3): 222-214.