Economic-Statistical Performance of Auxiliary Information-Based Maximum EWMA Charts for Monitoring Manufacturing Processes

Abstract

An auxiliary information-based maximum exponentially weighted moving average chart, namely, the AIB-MaxEWMA chart, is superior to the existing MaxEWMA chart in detecting small process mean and/or variability shifts. To date, AIB-MaxEWMA chart was designed based on the statistical perspective, which ignores the cost of process monitoring. The economic-statistical performance of the AIB-MaxEWMA chart for monitoring process shifts is investigated. The Monte Carlo simulation was conducted to determine the optimal decision variables, such as sample size, sampling interval, control limit constant, and smoothing constant, by minimizing the expected cost function under the statistical constraints. Numerical simulations indicate that when an auxiliary variable is highly related to the study variable, AIB-MaxEWMA charts not only have better statistical performance, but also have lower expected costs than MaxEWMA charts. Sensitivity analyses also show that a larger expected time to sample an auxiliary variable results in larger optimal expected costs and lower optimal sample size and sampling interval. The relationship between optimal decision variables and minimal costs is valuable for reference by researchers or process engineers.

Keywords

• AIB-MaxEWMA chart
• cost model
• economic-statistical design
• loss function