Economic statistical design of adaptive $$\bar{X}$$ X ¯ control charts based on quality loss functions

An economic-statistical model is developed for variable parameters $$(VP){\bar{X}}$$ ( V P ) X ¯ control chart is developed in which the constraints are imposed on the expected times to signal when the process is out of control and the expected number of false alarms per cycle. To improve chart effectiveness, the cost function is extended based upon the Taguchi philosophy of social loss of quality using the common loss functions including the linear, quadratic, exponential, and Linex. All of the loss functions that have been used up so far are symmetric, but what actually happens is that the imposed costs are not the same for over estimation and under estimation of the target value. For this reason, in this paper for the first time in the literature we use the Linex asymmetric loss functions, that results in the least average cost in all adaptive designs, compared to other symmetric loss functions. Using numerical example, we compare the performances of the $$VP{\bar{X}}$$ V P X ¯ control charts with the others adaptive charts based on the loss function, and investigate the sensitivity of the chart parameters to changes in process parameters and loss functions. Results indicate a satisfactory performance for the proposed models.