Design Of T_r Control Chart From Conditional Perspective

With the enhancement of the technological production capacity,the traditional counting control charts have been unable to effectively monitor the high-quality production processes.In order to improve the applicability of the counting control charts in the requirements not only on the production capability but also on the production procedure that the modern era has being required.The paper has designed the Shewhart-t_r control chart and the CUSUM-t_r control chart based on the continuous r-event time interval(ie t_r)to achieve an effective monitoring for the production process.Most scholars who have studied the t_r control charts and assumed that the process parameters have been known.However,in the practical applications,the process parameters often need to be estimated from Phase I samples.Different Phase I samples will have different control limits,resulting in the different performance of the control charts.In practice,people usually only can get a set of Phase I samples.The research has been conducted,based on the control chart performance which has been a given set of Phase I samples.It has meant that the conditional performance has been more realistic.In view of the conditional perspective,this paper has applied the Markov chain method to calculate the quantile,the mathematical expectation and standard deviation of the conditional ARL distribution to evaluate the influence of parameter estimation on the performance of the control charts.The results have indicated that parameter estimates can cause the excessive false alarms,resulting in excessive adjustments to the production process.The main research contents of this paper has been as follows:(1)Based on the all-known parameters,this paper has compareed the performances between Shewhart-t_r control charts and CUSUM-t_r control charts according to the equal-tailed and ARL-unbiased concept design.In practice,people sometimes have paid more attention to the drift of process parameters with the trend of the ups and downs.Therefore,this paper has designed a one-sided CUSUM-t_r control charts.(2)According to the conditional perspective,this paper has derived the exact distributions for the conditional ARL of the Shewhart-t_r control charts and the CUSUM-t_r control charts.The Markov chain method has been employed to calculate the percentile,the mathematical expectation and the standard deviation of the conditional ARL distribution to evaluate the influence of parameter estimation in view of the performance of the control charts.The results have shown that without considering the influence of parameter estimates on the Shewhart-t_r control chart and the CUSUM-t_r control chart,a large enough number of Phase I samples have been required.(3)It has been very difficult to achieve such a large number of Phase I samples in the actual operations.Even if it can be realized as a result,it has cost a large quantity of all kinds of expenditure.In order to save production costs,this paper has proposed a Shewhart-t_r control chart and a CUSUM-t_r control chart,using an accurate method to correct the equal-tailed and ARL-unbiased principle based on a set of Phase I samples available,which make the control charts produce more obvious effects in the favorable conditional performance.