Tip-I sansürleme ve Tip-I hibrit sansürleme altında bileşik Weibull dağılımı parametrelerinin tahmini

Abstract

Yaşam süresi deneylerinde kullanılan çeşitli sansürleme yöntemleri mevcuttur. Yaşam süresinin testi deneylerinde en yaygın kullanılan iki sansürleme yöntemi, Tip-I ve Tip-II sansürleme yöntemleridir. Hibrit sansürleme yöntemi ise Tip-I ve Tip-II sansürleme yöntemlerinin bir karışımıdır. Bu çalışmada, Tip-I ve Tip-I hibrit sansürlü verilere dayalı olarak bileşik Weibull dağılımının parametrelerinin tahmini ele alınmaktadır. Parametreler, en çok olabilirlik yöntemiyle tahmin edilmiştir. En çok olabilirlik tahminlerinin kapalı bir formda elde edilemediği görülmüştür. Bilinmeyen parametrelerin en çok olabilirlik tahminleri, beklenti-maksimizasyon algoritması kullanılarak elde edilmiştir. Ayrıca, parametrelerin asimptotik güven aralığı tahminleri da hesaplanmıştır. Sansürleme yöntemlerinin karşılaştırması ele alınmış ve örnek teşkil etmesi amacıyla bir veri seti analiz edilmiştir.

Keywords

• : En çok olabilirlik tahmin edicileri
• EM algoritması
• Tip I sansürleme
• Tip I hibrit sansürleme
• bileşik Weibull dağılımı

Estimation of the compound Weibull distribution parameters under type-I censoring and type-I hybrid censoring

Abstract

There are various censorship schemes used in lifetime experiments. The two most common censoring schemes used in life testing experiments are Type-I and Type-II censoring schemes. Hybrid censoring scheme is mixture of Type-I and Type-II censoring scheme. In this study, we considered the estimation of parameters of compound Weibull distribution based on Type I and Type I hybrid censored data. The parameters were estimated by the maximum likelihood method. It was observed that the maximum likelihood estimates could not be obtained in closed form. We obtained the maximum likelihood estimates of the unknown parameters using expectation maximization (EM) algorithm. We also obtained asymptotic confidence interval estimations of the parameters. The comparison of these censorship schemes was discussed and one data set was analysed for illustrative purposes.

Keywords

• Maximum likelihood estimators
• EM algorithm
• Type-I censoring
• Type-I hybrid censoring
• Compound Weibull distribution

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