Economic Design of Variable Sampling Interval X Control Chart Using a Surrogate Variable

Abstract

In many cases, an   control chart which is based on the performance variable is used in industrial fields. 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 surrogate variables. In this paper, we propose a model for the economic design of a VSI (Variable Sampling Interval)   control chart using a surrogate variable that is linearly correlated with the performance variable. 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. The VSI   control charts using surrogate variables are expected to be superior to the Shewhart FSI (Fixed Sampling Interval)   control charts using surrogate variables with respect to the expected profit per unit cycle time from economic viewpoint. †

Economic Statistical Design of Variable Sampling Interval X¯ $\overline X $ Control Chart Based on Surrogate Variable Using Genetic Algorithms

“…Thus, the PSA measurement value might be used as a surrogate variable. Lee et al [9] considered an economic design for the X-control chart using a surrogate variable under the assumption that a performance variable might not be used. Additionally, Lee et al [10] proposed an economic design idea for the VSI X control chart using a surrogate variable.…”