Recently, several micro electro-mechanical systems (MEMS) such as a MEMS gyroscope have been developed by using micro manufacturing technologies. Micro scale products, however, usually have a relatively large manufacturing uncertainty compared to normal macro scale products. It is quite expensive to lower the variance of material properties as well as the geometric properties of a micro scale product. The material and geometric uncertainties caused by a micro manufacturing process inevitably lead to the uncertainty of the product performance. Therefore, to achieve a reliable design of a product, the performance uncertainty of the product, which is often expressed by the variance or the standard deviation, needs to be estimated in a reliable way. In this paper, the equations of motion of a MEMS gyroscope model are derived to analyze the system performance indices (sensitivity and bandwidth). The mean values of the design variables are determined from the requirements of product size, maximum vibration amplitude, and driving frequency. Then the standard deviation of some critical design variables is determined from the performance requirements. Finally, a statistical analysis procedure based on sample statistics is proposed to estimate the confidence interval of the performance index statistics.