The long turnaround time (TAT) will prolong the waiting time of patient, increase hospital costs and decrease service satisfaction. None of the studies on control charts and medical care have applied control charts to monitor TAT and proposed a probability function for the distribution of the mean. This study proposed a general formula for the probability function of the distribution of the mean. The control limits of the average chart were determined according to the type I risks (alpha) and the standardized Weibull, lognormal and Burr distributions. Furthermore, compared to control charts that use alpha=0.0027, weighted variance (WV), skewed correction (SC) and traditional Shewhart control charts, the proposed control chart is superior to other control chart, in terms of the as for a skewed process. An example of the TAT of laboratory for the medical center presented to illustrate these findings. Significance: This study proposes a control chart to TAT of complete blood count (CBC) test of laboratory for a medical center. Constants of average control chart are calculated in accordance with fixing type I risks(alpha, 0.0027) with three distributions (Weibull, lognormal and Burr) by using the proposed a general model for the probability density function of the distribution of the mean. Average control chart using the proposed method is superior to other control chart, in terms of the type I risks for a skewed process.