Detecting anomalies is important for reliable operation of several engineering systems. Multivariate statistical monitoring charts are an efficient tool for checking the quality of a process by identifying abnormalities. Principal component analysis (PCA) was shown effective in monitoring processes with highly correlated data. Traditional PCA-based methods, nevertheless, often are relatively inefficient at detecting incipient anomalies. Here, we propose a statistical approach that exploits the advantages of PCA and those of multivariate memory monitoring schemes, like the multivariate cumulative sum (MCUSUM) and multivariate exponentially weighted moving average (MEWMA) monitoring schemes to better detect incipient anomalies. Memory monitoring charts are sensitive to incipient anomalies in process mean, which significantly improve the performance of PCA method and enlarge its profitability, and to utilize these improvements in various applications. The performance of PCA-based MEWMA and MCUSUM control techniques are demonstrated and compared with traditional PCA-based monitoring methods. Using practical data gathered from a heating air-flow system, we demonstrate the greater sensitivity and efficiency of the developed method over the traditional PCA-based methods. Results indicate that the proposed techniques have potential for detecting incipient anomalies in multivariate data.