Improvement Of Standard Deviation Control Chart

Control chart is seen as one of the most effective tools in statistical process control(SPC),used to monitor process parameters and test the production process is in control or out of control.Monitoring process standard deviation is as important as process mean.The increasing of the process standard deviation can reduce the quality of products,and the decreasing the process standard deviation may signal the raise of product quality level in the future.The most common used to monitor process standard deviation is Shewhart R and Standard Deviation control chart(Shewhart S control chart).Actually,it is well known that traditional Shewhart R control chart can estimate the population standard deviation,but the efficiency is very low and need to use S control chart to replace it.While,there are many defects in traditional S control chart,such as sensitive to large offsets but not sensitive to small and medium offsets.Moreover,when the sample size is very small,the detection efficiency is very low.Thus,this paper proposed several improved methods of the Shewhart S control chart,and it has important practical significance in monitoring the deviation of process standard deviation.Firstly,this paper designed the tail probability S chart with variable sampling interval.We used markov chain method to construct the transition probability matrix of the control chart and obtain the ATS.Comparing the ATS of new control chart with original control chart with fixed sampling interval,we found that new control chart has a higher efficiency in monitoring the deviation of process standard deviation.In addition,the ATS curve of the tail probability S chart with variable sampling interval is biased,which causes the ATS value in out of control is larger than that of in control,then we used ATS unbiased concept to modify the upper and lower limit of control chart,so ATS unbiased S chart with variable sampling interval is obtained,and the monitoring efficiency has improved.Secondly,according to the variable sampling interval and variable sample size thoughts,the paper discussed one-sided chart with variable sampling interval and variable sample size.According to the state space of control chart,we constructed the state transition probability matrix and calculated ATS.Comparing the ATS of new control chart with the ATS of ATS unbiased S chart with variable sampling interval,the results showed that the new chart is more efficient in monitoring process standard deviation.Finally,according to the two-sided zone control charts,we designed the one-sided cumulative score S control charts with joining negative score for monitoring the process variability.We used markov chain method to study the ARL of control chart.Comparing new control chart with CUSUM control chart for testing process variability,we found that its ARL performance has no obvious advantage.Then we added the initial response to control chart,numerical results proved that the test efficiency is probably same as CUSUM control chart.Finally,we studied the effect of different initial response values to the ARL of one-sided cumulative score S chart.