Economic design of two-stage non-central chi-square charts for dependent variables

Non-central chi-square charts are more effective than the joint X¯ and R charts in detecting small mean shifts or variance changes of a performance variable. However, the cost may be high to monitor a primary quality characteristic, such as the weight of each bag in a cement filling process. It is more economical to monitor a surrogate variable, for example, the milliampere of the load cell. When the correlation of the performance variable of surrogate variable exists, this article proposes a two-stage charting design to monitor either the performance variable or its surrogate variable in an alternating fashion rather than monitoring the performance variable alone. The proposed method simplifies process monitoring when users only concern about whether a process is in control or not. The application of the proposed method and the advantages of the proposed chart over the existing methods are presented through an example. Numerical results show that the proposed chart is insensitive on the correlation of the performance variable and surrogate variable even when the historical information on the correlation coefficient is not very accurate.

► We propose a two-stage non-central chi-square chart to reduce the overall cost of process monitoring.
► A surrogate variable usually easier and cheaper to observe is under surveillance initially.
► When an out-of-control signal is given, the original performance variable is then examined during a confirmation stage.
► A Markov chain approach is adopted to derive the parameter setting of the proposed chart.
► The proposed chart is insensitive to the correlation changes of the performance variable and surrogate variable.