| Statistical process control is an important means to ensure the quality and reliability of the production process,and control charts are the most commonly used tool for monitoring the controlled state of products in statistical process control.The traditional control chart usually assumes that the quality characteristics to be monitored obey the normal distribution and the parameters involved in the process are known,so as to construct the model of test statistics and control chart.However,in the actual production process,the following problems are often faced:(1)The process obeys a non-normal distribution;(2)The process parameters are unknown;(3)The available sample size is small.Inapplicable control charts can lead to underreporting or misreporting signals,leading to ineffective monitoring and a series of unknown risks,especially for life-related products.Regarding control charts suitable for non-normal distributions,in recent years,many scholars have studied control charts suitable for distributions such as exponential distribution,Weibull distribution,and gamma distribution,but few scholars have studied the minimum extreme value distribution.In some events with significant impact and low incidence(such as automobile brake system failure,airbag effectiveness,etc.),analysis with the smallest extreme value distribution can obtain more accurate prediction results.Therefore,this thesis proposes a quantile control chart considering auxiliary variables for the production process that obeys the minimum extreme value distribution.And using the commonly used performance metrics for control charts,the quantile control chart and traditional control charts are compared in simulation data and examples.The design ideas of control charts are mainly elaborated from the following aspects:Firstly,introduce an auxiliary variable that has a regression relationship with the research variable and the auxiliary variable obeys the smallest extreme value distribution.Derive the expressions of the conditional distribution function and quantile statistics of the research variables through the regression relationship between the auxiliary variables and the research variables,and combine the least squares estimation method and the maximum likelihood estimation method to obtain the unknown parameter values involved in the process,Based on the given small sample data,the unknown parameter value is calculated by the Bootstrap method to obtain the control limit.Secondly,the Bootstrap method is used to calculate the average running chain length and standard deviation of the running chain length of the control limit in the controlled state and the out of control state to measure the performance of the control limit.Thirdly,in the simulation data,the quantile control chart proposed in this paper is compared with the traditional mean range control chart for the three dimensions of control limit,average running chain length,and running chain length standard deviation.The simulation results show that the monitoring effect of the quantile control chart proposed in this paper on the minimum extreme value distribution is better than the other two control charts.Among them,the quantile control chart has a better effect on the deviation monitoring of the position parameters,even a weak deviation can be monitored.The monitoring effect of large deviation of the scale parameter is good,and the monitoring effect of small deviation is not good.Finally,the quantile control chart proposed by the text is applied to a set of example data of automobile brake system.The control chart identifies very weak changes in the automobile brake system,while the traditional control charts are completely invalid.Therefore,this article combines the research and theory of domestic and foreign scholars to demonstrate the rationality of the quantile control chart proposed in this article,and then combines simulation and examples to verify that the performance of the quantile control chart is better than traditional control charts. |
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