Economic design of a joint X with warning limits- and s-control chart

Abstract

In this thesis, an economic model for designing a joint X with warning limits-and s-control charts is developed. The design parameters are sample size, width of the action limits of $\bar{X}$-control chart, width of the warning limits of $\bar{X}$-control chart, width of the action limits of s-control chart, sampling interval, and significant run length. The production process which is monitored by an economically designed control chart is allowed to be in four states; both the process mean and the process standard deviation in control, only the process mean out of control, only the process standard deviation out of control, and both the process mean and the process standard deviation out of control. The costs of inspection, defective production, and investigation for and correction of assignable causes are considered, and an expression for the average quality cost per good item produced is developed using conditional expectations and a Markov chain. A computer search method is used for solving a numerical example.