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Abstrak :
Pada perusahaan asuransi bisnis long-tail (penyelesaian klaim ≥ 1 tahun), perusahaan harus memiliki cadangan klaim untuk membayar klaim pada masa yang akan datang. Metode yang sering digunakan untuk perhitungan prediksi cadangan klaim adalah Chain Ladder (CL) yang dihitung berdasarkan pola dari klaim yang sudah dibayarkan. Namun, CL tidak dapat memberikan hasil prediksi cadangan klaim yang akurat, karena dari pendefinisiannya CL sangat bergantung dengan data. Padahal, data tersebut dapat mengandung outlier, atau tidak memadai. Ketika hal ini terjadi, maka aktuaris seringkali menggunakan penilaian subyektif mereka dengan menyesuaikan perhitungan dan dapat memberikan hasil yang berbeda-beda. Hasil yang berbeda-beda menyebabkan adanya ketidakpastian akan hasil yang didapat. Pada skripsi ini, dikenalkan metode Fuzzy Chain Ladder (FCL) yang menggabungkan metode CL dengan triangular fuzzy number (TFN) agar dapat mempertimbangkan ketidakpastian terhadap perhitungan. Berbeda dengan CL yang menghasilkan satu nilai cadangan klaim, FCL menerapkan TFN pada perhitungannya sehingga menghasilkan besar cadangan klaim dalam bentuk kisaran atau range. Dalam range tersebut, aktuaris dapat memilih nilai cadangan klaim berdasarkan penilaian subyektif mereka sehingga diharapkan metode FCL dapat mempertimbangkan adanya ketidakpastian tersebut. Selanjutnya, dilakukan analisis perhitungan prediksi cadangan klaim dari data klaim asuransi umum kelautan menggunakan FCL dibandingkan dengan metode CL.

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In long-tail business insurance (settlement period ≥ 1 year), companies must have claim reserve to pay claims in the future. The method often used for calculating claims reserve is Chain Ladder (CL) that is calculated based on the pattern of paid claims. However, CL cannot provide accurate claims reserve predictions, because the definition of CL is dependent on data. In fact, these data can contain outliers, inadequate. When this happens, actuaries often use their subjective judgment by adjusting calculations and can produce different results. Different results cause uncertainty about the obtained results. In this thesis, a method called Fuzzy Chain Ladder (FCL) is introduced which combines CL with triangular fuzzy number (TFN) to consider uncertainty regarding calculations. In contrast to CL which produces a single value of claim reserves, FCL applies TFN to its calculation to produce many claims reserves in the form of ranges. Within that range, actuaries can choose the value of claims reserves based on their subjective judgement so that the FCL method can be expected to consider the existence of these uncertainties. Furthermore, an analysis of the prediction of claim reserves from the general marine insurance claim data is analyzed using FCL compared to the CL method.

Abstrak :
The Westinghouse AP1000 is a new design nuclear power plant which has implemented the concept of passive system. Even though a passive system may be more reliable than an active one, the possibility of the passive system to fail still exists. In line with this possibility, generic database have been used to study the reliability of the AP1000 passive safety system. However, since the used data are not specific to the AP1000, the results of the analysis will not show its real performance. This study proposes a fuzzy reliability approach to overcome this problem. The proposed fuzzy reliability approach utilizes the concept of failure possibility to qualitatively describe basic event likely occurences and membership functions of triangular fuzzy numbers to quantitatively represent qualitative failure possibilities. A case-based experiment on reliability study of the AP1000 passive safety system involved to mitigate a large break loss of collant accident is used to validate the feasibility of the proposed approach. By comparisons, probabilities of basic events generated by the proposed approach are very close to the ones which have been used by previous reliability studies. This can be observed from the small numbers of relative errors, i.e. between 0.004125 and 0.079635. These results confirm that the fuzzy reliability approach offers a more realistic technique to study the reliability of the AP1000 passive safety system without the need to engage to precise probability distributions of its components which are currently unavailable.