The Design And Application Of Synthetic S~2 Chart

Some factors in manufacturing such as faulty raw material or unskilled operators may lead to a change in process dispersion without influencing the process mean. The control limits of X chart will be unreasonable and the output of the process will be more scattered when there is an increase in the process dispersion. And the output of the process will be more concentrated when there is a decrease in the process dispersion. So it is important to monitor the change in the process variance. The Shewhart S2 chart is traditionally used to detect the shifts in the process variance. The chart is quite effective in detecting large shifts in the variance. However, it may become insensitive in detecting small shifts in the process dispersion. In order to improve the performance of the Shewhart S2 chart, this paper proposes a synthetic S2 chart that is an integration of the Shewhart S2 chart and a conforming run length chart to monitor the variance of the process.The main work of this paper is summarized as follows:(1) This paper designs a lower-sided synthetic S2 chart and an upper-sided synthetic S2 chart to monitor the increase in process variance and the decrease in process variance separately when the parameters are known. And the paper designs a two-sided synthetic S2 chart when the direction of the changes in process variance is uncertain. Then the paper compares the performance of the synthetic S2 chart and Shewhart S2 chart. The results show that the synthetic S2 chart is more effective than Shewhart S2 chart.(2) The control chart is usually designed assuming that the parameters of the process are known, however, in most applications, the process parameters are unknown and need to be estimated by the phase-I samples. This paper studies the effects of parameter estimation on the three kinds of synthetic S2 charts. The results show that when the shifts of the variance and the number of the phase-I samples are small, the parameter estimation increase the false alarm rate and reduces the efficiency of the synthetic S2 chart.(3) Considering the serious effect of parameter estimation, this paper designs a new lower-sided synthetic S2 chart, a new upper-sided synthetic S2 chart and a new two-sided synthetic S2 chart with desired in-control ARL when in-control variance is estimated. We also compare them with the corresponding Shewhart S2 charts. The results show that the synthetic S2 charts with new control charts perform better than the corresponding Shewhart S2 charts.