Maximum Entropy Method Based On Density Kernel Estimation In Control Chart Design

As statistical quality control technology continues to be promoted,quality control charts are an important means of quality anomaly monitoring.Quality control charts has become a hot spot in quality control research.The traditional quality control charts usually assume that the quality characteristics of the monitored samples are subject to a certain distribution.The chart constructs the test statistic and design models.However,in the actual process,most of the process is not obeying or approximating to a certain distribution.The traditional chart is prone to false negatives or false positives,which leads to in valid monitoring.Therefore,a control chart based on the kernel density estimation maximum entropy method for estimating the population distribution is established.The design ideas are mainly explained from the following aspects:Firstly,the traditional method of solving the maximum entropy model is improved by successive superposition algorithm and density kernel estimation.Using the kernel density estimate to represent the maximum entropy probability density function,and calculating the order origin moments of the sample by given sample data.Based on the idea of the sample estimation population,the original moments are sequentially introduced to optimize the solution,and the probability density function of the variables is estimated.By comparing the probability density chart and the mean square error value,the new method for solving the maximum entropy model has a good fitting effect.Secondly,a control graph based on density kernel estimation maximum entropy method is designed.The goal of the new control chart is to minimize the upper limit of the Type II error rate.The maximum entropy method based on kernel density estimation can solve the distribution of controlled random variables.Solving the control region by minimizing the Lebesgue Measure.For the problem of inaccurate tails of asymmetric distribution,the idea of distribution normalization is proposed,and the control region is effective after transformation.Finally,a Hermite interpolatory non-parametric control chart was designed to be compared with SKDE-MEM control chart.Through random simulation method,the average run length of SKDE-MEM control chart,Hermite interpolatory non-parametric control chart and Shewhart control chart under different process migration was studied and compared.SKDEMEM control chart is more sensitive than Hermite non-parametric interpolation control chart and traditional Shewhart control chart for different deviation of process.In particular,SKDEMEM control chart and Hermite interpolatory non-parametric control chart performed significantly better than Shewhart control chart when computing non-normal distribution samples.Overall,the SKDE-MEM control diagram shows better monitoring performance.