According to a progress of the software process improvement, the time series data on the number of faults detected by the software testing are collected extensively. In this paper, we perform statistical analyses of relationships between the time series data and the field quality of software products. At first, we apply the rank correlation coefficient $\tau$ to the time series data collected from actual software testing in a certain company, and classify these data into four types of trends: strict increasing, almost increasing, almost decreasing, and strict decreasing. We then investigate, for each type of trend, the field quality of software products developed by the corresponding software projects. As a result of statistical analyses, we showed that software projects having trend of almost or strict decreasing in the number of faults detected by the software testing could produce the software products with high quality.