如何推估產品在保固期內的退貨率是廠商需考慮的重要決策問題。文獻上有多位學者針對多個類別且具有 “通過/不通過” 屬性的實驗室測試資料及現場退貨資料，分別探討如何建立參數化 “層狀結構” 模型及 limited failure population (LFP) 模型，並藉由連結函數來預測保固期內退貨率。然而上述參數化模型對實際實驗室測試資料的配適不甚理想，且 LFP 模型對現場資料的配適亦有整體低估現象。為克服此問題，本研究採用無參數化的singular value decomposition (SVD) 方法來克服此困難。具體做法是分別對實驗室測試資料與現場退貨資料進行SVD分解後，再透過適當的連結函數來進行現場退貨率預測分析。此無參數化模型之優點是此方法操作上十分簡便且可避免前述參數化模型的選模及模型配適等問題。唯SVD方法的預測能力與實驗室測試樣本數息息相關，故本研究在退貨率的預測值之總變異控制在給定的臨界值下，亦探討如何決定適當的測試樣本數。最後透過模擬實驗來比較此方法與現存方法之預測績效，整體而言，在測試樣本數足夠大 (大於15以上) 下，本方法之預測績效優於現存方法。

Nowadays, the manufacturers usually provide a warranty policy to attract their potential customers, under which a failed item can be replaced for free during the warranty period. For the purpose of inventory and management, the manufacturers need to estimate the product's field return rate accurately within the warranty period. For this challenging problem, several research works have been proposed in the literature, but these methods are applicable case by case and only for a single product. Recently, for the case with multiple products, an empirical Bayes (EB) parametric model has been proposed. This approach, however, does not have a good prediction performance in practical applications. To handle this problem, this study adopts the singular value decomposition method to construct a prediction model for the field return rate based on data available for multiple products. The proposed method is a semiparametric approach and therefore has the advantage of avoiding the issue of model selection, which is crucial in the EB parametric approach. In addition, the implementation of the proposed methodology is very easy and fast. Finally, we make comparisons on the prediction performance of this method to EB parametric approach via simulations. The results demonstrate that the prediction performance of the proposed methodology outperforms the existing methods.

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