The Economic Design of a Dynamic X-Control Chart

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Abstract
The most prominently used statistical process control tool is the X¯-chart. Duncan's economic model of Shewhart's original X¯-chart has established its optimal economic application for processes with a Markovian process failure mechanism. However, there are practical situations in which the distribution of the time to failure of the process is not exponential. This paper extends the state of the art in control charting by providing: (1) a generalized dynamic (sample size, sampling frequency, and control limit spread allowed to vary over time) version of Duncan's X¯-chart model and (2) the adoption of the rich Weibull distribution for the failure mechanism. This paper also discusses: (3) a methodology under which control chart parameters may change over time, (4) computational aspects of model implementation, (5) model optimization, and (6) some economic comparisons between the dynamic design and Duncan's design. It is concluded that the choice of process failure mechanism in the cost model is significant; substantial cost savings can result from the use of the dynamic design as compared to Duncan's design.