Economic-statistical design of the X¯ chart used to control a wandering process mean using genetic algorithm

This research considers the process mean wanders according to a first-order autoregressive model. During the in-control period the process mean wanders around its target value, and after the assignable cause occurrence, around an off-target value. The cost model proposed by Duncan was used to select the X bar chart’s parameters and the genetic algorithm to meet their optimum values. The wandering movement required a Markov chain to obtain the properties of the control chart. The autocorrelation among mean values increases the monitoring costs and reduces significantly the chart’s efficiency.

► The process mean is supposed to wander according to a first-order autoregressive model.
► Considers the cost model proposed by Duncan to select the X¯ chart’s parameters.
► The alternative to obtain the average run length and the rate of false alarms consists of building a Markov chain.
► The genetic algorithm is used to find the optimum parameter values.
► The autocorrelation among mean values increases the monitoring costs and reduces significantly the chart’s efficiency.