Summary: Although the normality is a usual assumption for quality measurements, it may be erroneous and misleading in many industrial applications of quality control online models. In addition, incorporating Taguchi’s loss function to these inspection activities leads the management to better decisions. In this paper, the integrated model of Taguchi’s loss function and the economic statistical design of \(\bar{X}\)-control charts are investigated under both normal and non normal quality data. This purpose has been achieved by modifying the cost model of P. K. Banerjee and M. A. Rahim [Technometrics 30, No. 4, 407–414 (1988; Zbl 0721.62101)] in which a non uniform sampling scheme is utilized for systems with increasing failure rate and Weibull shock model. For the same values of time and cost quantities and Weibull distribution parameters, the effects of three most popular quality characteristic distributions (Normal, Burr, and Johnson) that are fitted on a case study data in [M. A. Rahim, “Economic design of control charts assuming Weibull distribution in-control times”, J. Quality Tech. 25, No. 4, 296–305 (1993; doi:10.1080/00224065.1993.11979475)] are studied and compared. The optimal parameters of both economic and economic statistical designs reveal that there is an insignificant difference between Normal and Burr distributions, whereas a relative difference can be observed in the case of Johnson distribution.