This paper investigates the relation between the Process capability index(PCI) and the quality assurance level under various conditions. The effect of the off-targetness of the process mean, deviation from the nomality, the estimation error, and the measurement error on the quality assurance level is evaluated. Various distributions such as the Student-t, the chi-square, the gamma, the Weibull, and the log-normal distributions are considered to evaluate the deviation from the nomality. The quality levels under abnormal conditions turn out to be severely different from that under the standard condition. We provide tables and graphs of the quality assurance level on various abnormal conditions. In order for the industry users to use the PCI properly, they should refer to the tables and graphs, especially when they are not certain about the standard assumptions on which the PCI depends.