An X-bar control chart has been widely used for process monitoring in industrial fields. Typically, the control chart monitors the measurements of a performance variable. However, if the performance variable is too costly or impossible to measure and a less expensive surrogate variable is available, the process may be more efficiently controlled using a surrogate variable.
This dissertation is concerned with the statistical and economic designs of a VSI(Variable Sampling Interval) and VSS (Variable Sample Size) X-bar control chart using a surrogate variable that is linearly correlated with the performance variable. These control charts with a surrogate variable are based on the idea of a statistical model constrained with an ARL (Average Run Length) and an economic model with the total average profit per cycle time. The total average profit model is constructed, which involves the profit per cycle time, the cost of sampling and testing, the cost of detecting and eliminating an assignable cause, and the cost associated with production during out-of-control state.
This dissertation is divided into the following three parts.
(1) VSI X-bar control charts using a surrogate variable are proposed.
(2) VSS X-bar control charts using a surrogate variable are proposed.
(3) The two proposed X-bar control charts are applied to a nuclear fuel measurement system to compute the amount of reduction in cost compared with the current control procedure.
The VSI and VSS control charts using surrogate variables are compared to the Shewhart FSSI (Fixed Sampling Interval and Sample Size) X-bar control charts using surrogate variables with respect to the expected profit per unit cycle time.
Computational experiments and extensive sensitivity analyses show that the VSI X-bar control chart and VSS X-bar control charts using surrogate variables are superior to the Shewhart X-bar chart using performance variables from the statistical and economic-statistical viewpoints.