Rotatable designs that are available for process/ product optimization trials are mostly symmetric in nature. In many practical situations, response surface designs (RSDs) with mixed factor (unequal) levels are more suitable as these designs explore more regions in the design space but it is hard to get rotatable designs with a given level of asymmetry. When experimenting with unequal factor levels via asymmetric second order rotatable design (ASORDs), the lack of fit of the model may become significant which ultimately leads to the estimation of parameters based on a higher (or third) order model. Experimenting with a new third order rotatable design (TORD) in such a situation would be expensive as the responses observed from the first stage runs would be kept underutilized. In this paper, we propose a method of constructing asymmetric TORD by sequentially augmenting some additional points to the ASORDs without discarding the runs in the first stage. The proposed designs will be more economical to obtain the optimum response as the design in the first stage can be used to fit the second order model and with some additional runs, third order model can be fitted without discarding the initial design.

可用于工艺/产品优化试验的可旋转设计本质上大多是对称的。在许多实际情况下，具有混合因子（不等）水平的响应面设计 (RSD) 更适合，因为这些设计探索了设计空间中的更多区域，但很难获得具有给定不对称水平的可旋转设计。当通过非对称二阶可旋转设计 (ASORD) 对不等因子水平进行试验时，模型的拟合不足可能会变得很严重，最终导致基于更高（或三阶）模型的参数估计。在这种情况下尝试新的三阶可旋转设计 (TORD) 将是昂贵的，因为从第一阶段运行中观察到的响应将未被充分利用。在本文中，我们提出了一种构建非对称 TORD 的方法，该方法通过在 ASORD 上依次增加一些额外的点而不丢弃第一阶段的运行。所提出的设计将更经济地获得最佳响应，因为第一阶段的设计可用于拟合二阶模型，并且通过一些额外的运行，可以在不丢弃初始设计的情况下拟合三阶模型。