在線試驗或是多變量實驗是一種在網路世界快速成長的方法，在網路世界用於各種應用上，像是網站或是郵件的最佳化。隨著科技快速成長，在線測試常常使用在許多平台上，像是筆記型電腦、智慧型手機與智慧型手錶。因此設計在多個平台上有效的在線測試是非常緊迫的問題。Sadeghi et al. (2016) 與 Sadeghi et al.(2017) 分別對於兩個水準與四個水準的多平台實驗提出挑選設計的準則。然而，這種修改的準則缺乏強力的統計理由。在這篇論文中，我們通過兩種方法研究這樣的設計問題，稱為貝氏方法與泰勒級數方法。我們也針對各種因子個數以及水準組合個數提供了使用我們方法找出來的最佳設計。;Online testing or multivariate experiment is a method that grows rapidly in the digital world for various applications, such as website and email optimization. Due to the highly development of technology, online testings are more often conducted on other platforms, such as laptops, smartphones, and smart watches. Thus, designing efficient online testings across multiple platforms is an urgent issue. Sadeghi et al. (2016) proposed a design selection criterion for two-level multiple-platform experiments. Sadeghi et al. (2017) further extended Sadeghi et al. (2016) to fourlevel factors. However, such naive modifications lack strong statistical justifications. In this thesis, we study such design problem through two approaches, referred to as Bayesian method and Taylor Series method. We also provide optimal designs based on our methods for various run sizes and numbers of factors.
