The Economic Statistical Design Of ARMA Control Chart With Variable Sampling Interval

With the improvement of living standards,people are increasingly demanding on the quality of products.Therefore,how to ensure the quality of products and continuous improve it is an important condition for enterprises to maintain their advantages in the market competition.On the other hand,the improvement of quality will inevitably result in the increase of cost.Therefore,how to reduce the cost as much as possible under the premise of ensuring the quality is a subject worthy of study.The economic statistical design of control charts is a way to reduce the cost as much as possible and ensure the quality of monitoring of control charts at the same time.Firstly,the economic design model of ARMA control chart is introduced,and on the basis of the model,the economic design model of ARMA control chart considering quality loss function is established.Secondly,the economic design model of ARMA control chart with variable sampling interval is constructed.Compared with the fixed sampling interval ARMA control chart,the variable sampling interval ARMA control chart has lower cost,and faster to detect the occurrence of special cause.Finally,the economic statistical design model of ARMA control chart with variable sampling interval is established.Compared with the economic design model with the same conditions,the cost of the economic statistical design model will increase slightly,but the statistical performance of the control chart is greatly improved.In this paper,the economic statistical design model of ARMA control chart with variable sampling interval is set up layer upon layer.Case analysis and solution are shown in the end.It provides an effective way and theoretical support for enterprises to improve product quality and reduce production cost.It is difficult to calculate the average run length(ARL)of ARMA control chart with Markov chain method.So we construct a three dimensional vector which satisfies the properties of Markov chain,calculate the state probability matrix,and then calculate the ARL and average time to signal(ATS)of the ARMA control chart.The economic statistical design model of ARMA control chart with variable sampling interval is established.Compared with the economic design of ARMA control chart,the model has lower cost and better statistical performance.