Design Of The Adaptive S₂Control Charts And The S₂Control Charts With Runs Rules

According to the statistics theory and experience, the traditional S2control chart’s parameters are determined. The traditional S2control chart can quickly detect large shifts in the process variance, but it is not effective for detecting small shifts in the parameters. In addition, the fixed control chart parameters reduce the flexibility of control chart, and increase the cost of inspection of the production. This article incorporates the thought of variable sampling intervals、variable sample sizes and the run rules into the traditional S2control chart to improve its performance.The main works and contributions are summarized as follows:(1) Design of the variable sampling intervals S2control charts (VSI-S2control charts) The VSI-S2control charts based on the equal-tail probability limits and the Average Time to Signal (ATS)-unbiased VSI-S2control chart are designed, then the paper compares the performance of two VSI-S2control charts and the Fixed Sampling Intervals S (FSI-S) control chart by ATS and the Adjusted Average Time to Signal (AATS). The results show that VSI-S control charts have better performance than FSI-S control chart. And in line with the characteristics that the larger difference length of sampling interval, the greater performance of control chart. Finally the paper studies the impact of parameter estimation on the performance of the VSI-S2control charts and FSI-S2control chart. The results shows that parameter estimation has large impact on the performance of two VSI-S2control charts, namely it increases the false alarm rate of VSI-S2control charts, and reduces the sensitivity of the control charts to detecting the process changes.(2) Design of the variable sample size S control charts (VSS-S control charts)The VSS-S2control charts based on the equal-tail probability limits and the ARL unbiased concept are designed respectively. Then their performance is evaluated in terms of the Average Run Length (ARL). The results show that VSS-S2control charts find drift faster than the Fixed Sample Size S2(FSS-S2) control chart, and when the process varicance has a small drift, the larger difference between the two sample sizes, the greater performance of the VSS-S2control chart. Finally the paper studies the impact of parameter estimation on the performance of the VSS-S2control charts and FSS-S2control chart. The results show that parameter estimation has large impact on the performance of the VSS-S2charts, namely it increases the false alarm rate of the VSS-S2charts, and reduces the sensitivity of the control charts to detecting the process changes.(3) Design of the S2control chart with runs rulesThis paper firstly gives a design of S2control chart with2-of-2runs rules, an ARL-unbiased design of the S2control chart with2-of-2runs rules and an ARL-unbiased design of the S2control chart with two runs rules. Then their performance is evaluated in terms of the ARL. The results show that for small and medium-sized shifts, these three kinds of S2chart with runs rules have better performance than the conventional S2control chart. Finally the paper respectively studies the impact of parameter estimation on the performance of three kinds of S2chart with runs rules. The results show that parameter estimation has large impact on three kinds of S2chart with runs rules, namely it increases the false alarm rate of VSI-S control charts, and reduces the sensitivity of the control charts to detecting the process changes.