The quality and loss of products are crucial factors separating competitive companies in many industries. Firms widely employ a loss function to measure the loss caused by a deviation of the quality variable from the target value. Monitoring this deviation from the process target value is important from the view of Taguchi's philosophy. In reality, the distribution of the quality variable may be skewed and not normal, and the in-control process mean may not be the target. We propose a median loss control chart to detect the changes in the process loss center or equivalently the shifts in the process deviation from the mean and target and/or variance for the quality variable with a skewed distribution. We also derive the median loss control chart with variable sampling intervals to detect small shifts in the process loss center. The out-of-control detection performance of the proposed median loss control chart and the median loss chart with variable sampling intervals are illustrated and compared for the process variable with a left-skewed, symmetric or right-skewed distribution. Numerical results show that the median loss chart with variable sampling intervals performs better than the median loss chart in detecting small to moderate shifts in the process loss center or in the difference of mean and target and/or variance of a process variable. The median loss chart and the median loss chart with variable sampling intervals also illustrate the best performance in detection out-of-control process for a process quality variable with a left-skewed distribution.