Good quality products are the key to success in business. In the past few years, process capability analysis have been introduce and used to characterize process performance. One of the methods for process capability analysis is indices. Process capability indices have been proposed to provide numerical measures on process performance. Extensive researches have been done on the univariate process capability indices. However in modern manufacturing process, often there is more than one quality characteristic for a product. For this reason, multivariate method for assessing process capability are proposed. When these characteristics are related variables, principal component analysis can be used as a multivariate statistical technique. Furthermore, the measurement errors has an important effect on the determining process capability. Analyzing process capability without considering gauge capability may often lead to unreliable decisions. Although an extensive study have been done for the case of univariate process capability with considering the measurement error; but this effect on the multivariate quality characteristics has received little attention. Shishebori and Hamadani considered the measurement error to compute MCp index for the first time. In this thesis, we discuss various multivariate capability indices and introduce the multivariate index based on principal component analysis. Also, we use another approach to consider MCp when the measurement errors are unavoidable and then we investigate the statistical properties of this index at the mentioned state. Since the gauge capability has a significant impact on the estimating and testing process capability, thus we present adjusted confidence interval bounds and critical values for capability testing purpose of MCp with unavoidable measurement errors. Keywords: process capability analysis, multivariate analysis, principal component analysis, gauge measurement error.