Improvement Of R Chart And S Chart Based On ARL

Statistical process control is used to monitor the production process by using the statistical analysis techniques,to analyze and evaluate the production process by the utilization of control charts.In Shewhart control chart,ensemble mean and variance are inferred by mainly utilizing the mean and range of the sample and standard deviation;in the control chart,because of the nonuniformity of population distribution and the existence of sampling error,the average run length of the control chart is not completely the same as the change of the ensemble variance.In the range R chart,when the process variance change is monitored through the utilization of the small sample in practice,the standard deviation S chart is needed to replace the range R chart.But in conventional S control chart,there also exists flaws: the center line of the control chart is the unbiased estimation of the standard deviation in the actual process;when the sample size is smaller,the curve of the average run length in the S chart based on the 3? control limit present the skewed distribution.This paper studies the control chart to improve its performance from three aspects.Fristly,the range R control chart and the standard deviation S control chart are designed by using the concept of the tail probability.The parameters of the control chart are solved by the means of the order statistic distribution function so that the skewed situation of the average run length curve in the two charts is fixed.And the Type II error is used to compare the two control charts in variance migration to monitor their stability.Secondly,the range R control chart and the standard deviation S control chart are designed in the way of using the concept of the average run length unbiased.The parameters of the control chart are solved by the means of the order statistic distribution function so that the average run length unbiased control chart is established.In the case of the Type I error being the same,the average run length is used to compare the tail probability limit and the performance of its unbiased control chart.Finally,conventional control chart R and S chart is not sensitive to small scale variance changes.The S~2 control chart is introduced to design the S~2 control chart of the average run length unbiased.Constant parameters in control chart in practical production reduce its flexibility and increase the cost of inspection in production.So the introduction of idea of variable sample size into S~2 chart strengthens the performance of the control chart.The method of the Markov chain is used to calculate the average run length of the control chart on the basis of which the average run length of unbiased variable sample size S~2 control diagram and the control variable sample size S~2 tail probability limit are compared.This leads to the conclusion that the unbiased control chart performs well in the process of being monitored with the parameters known.