Effects of heterogeneous variance on X̄ chart

This research investigated the performance of the X̄ chart when the heterogeneous variation occurs. Machines are regarded as another source of variations with an assumption that the expectation of the quality characteristics produced by each machine is normally distributed. This study report the derivations of the computation of an effect of false alarm, and/or in different way the computation of an efficiency of X̄ chart in detecting change of process, due to heterogeneous variation. This research study was divided into two cases. If the extra variation is not accounted for during control chart setup, only part of within variation is used, the misplace control limits will be narrower since the variation are under-estimated leading to significant false alarm rate. When the extra variation is accounted for, the methodology to determine the control chart is provided. The result shows that the probability of detection and ARLs of the chart has increasing power of detection regardless of the sample size as the extra variation gets larger.