This paper aims to solve the problems of fault diagnosis and variation reduction by using multivariate statistical techniques when the quality measurements are scarce. Both single stage process and multi-stage process are considered. For the single stage process, the nonparametric statistical method, Wilcoxon rank-sum test is used to identify the key variable/step that causes the fault of the un-qualified wafers. For the multi-stage process, the most important variables are first picked out by systematic statistical analysis, and the specifications of these key variables are designated using nonparametric method to improve the product yield. Gene map which gives visual images is used to assist the analysis. Industrial examples are given to show the effectiveness of the proposed method.