A Control Chart Based On Likelihood Ratio Test For Monitoring Logarithmic Normal Distribution

Most traditional control charts assume that the process quality characteristics are subject to normal distribution,and the corresponding control charts are established to monitor the production process.If the distribution of the production process data deviates from this basic assumption,the performance of the control chart designed according to the normal assumption will be affected,such as increasing the false alarm rate and so on.Therefore,it is necessary to make full use of historical data to estimate the distribution characteristics of the process before using the control chart.In many practical problems,the data distribution may be non-normal,but biased,such as obeying logarithmic normal distribution(The process data is carried out,log transformation follows normal distribu-tion.).In reality,there are many examples of obeying logarithmic normal distribution,For example,to estimate the quality of engine oil in automobile industry.According to the experience of the engineer,the quality data of the engine oil can be determined ac-cording to the logarithmic normal distribution.In geological problems,The composition of the rare metallic ore deposits and the trace elements in the rock ore are approximate to the logarithmic normal distribution.In addition,the number of biological populations,population problems,survival analysis and reliability analysis and other issues,in the problems of reliability analysis,lognormal distribution can be used to depict.Therefore,it is very important to construct the control chart of lognormal distribution.The likelihood ratio test is widely used because the probability distribution of the unknown population does not need to be too restrictive.This paper is based on the idea of likelihood ratio test,and combining with exponential weighted moving average(EWMA)method,put forward a kind of method that used to detect parameters of the lognormal distribution process control chart.According to the test,the purpose of considering three kind of design scheme of control chart,including only monitoring lognormal distribution parameter?of the control chart,separate monitoring lognormal distribution parameter?~2of the control chart and at the same time detection of lognormal distribution parameter?and?~2of the control chart.According to the average run length(ARL)and the run length standard deviation(SDRL),the performance of each control chart is investigated.The Shewhart control chart and another four charts are compared with the new chart.The simulation results show that the control charts proposed in this paper have good detection capability for all kinds of drift of parameters,and its detection effect is far greater than that of Shewhart control chart and another four charts.In the end,the actual application of the control chart presented in this paper is illustrated with the actual data of a production process.The example shows that the control chart presented in this paper can quickly detect the change of production process,which is an efficient detection method.