On the design of variable sample size and sampling intervals X¯ charts under non-normality

Recent theoretical studies demonstrated the variable sampling rate (variable sample size and/or sampling interval) X¯ charts are quicker than standard Shewhart (SS) X¯ control charts in detecting process mean shifts. The usual assumption for designing a control chart is that the data or measurements are normally distributed. However, this assumption may not be true. The Burr distribution has been used in the literature to represent various non-normal distributions. In this paper, the Burr distribution will be employed to design the variable sample size and sampling intervals (VSSI) X¯ charts under non-normality. Two types of X¯ charts are proposed and studied: the symmetric-limit chart and the asymmetric-limit chart. Based on the study, it is shown that (a) the variable sample size (VSS) and VSSI X¯ charts are more effective than the SS and variable sampling intervals (VSI) X¯ charts in detecting small process mean shifts, (b) the VSS and VSSI X¯ charts are more robust against non-normality. In addition, under consideration of the false alarm rate and detection ability, the asymmetric-limit chart is a better choice.