On the conditional performance of the synthetic chart with unknown process parameters using the exceedance probability criterion.

Recent researches on the control charts with unknown process parameters have noticed the large variability in the conditional in-control average run length (ARL) performance of control charts, especially when a small number of Phase I samples is used to estimate the process parameters. Some research works have been conducted on the conditional ARL performance of different types of control charts. In this paper, by simulating the empirical distribution of the conditional ARL and especially using the exceedance probability criterion (EPC), we study the conditional ARL performance of the synthetic [Formula: see text] chart. Our results show that a large amount of Phase I samples is needed to obtain a specified EPC of the synthetic chart. For the available number of Phase I samples, the control limits of the synthetic chart are adjusted using the EPC method to improve its conditional in-control performance. It is shown that, for small mean shift sizes, a tradeoff should be made between the conditional in-control and out-of-control performances. For moderate to large shifts, the conditional performance of the synthetic chart using the adjusted control limits is generally satisfied. By comparing the results with the ones using the bootstrap approach, it can also be concluded that the conditional performances of both approaches are comparable. While the method proposed in this paper requires much less computation work than the bootstrap approach.

TNM staging of colorectal cancer should be reconsidered by T stage weighting.

AIM: To verify that the T stage has greater weight than the N stage in the staging of colorectal cancer. METHODS: Open data from the Surveillance, Epidemiology, and End Results program were reviewed and analyzed according to the T stage, N stage, and patients' observed survival (OS). The relative weights of the T and N stages were calculated by multiple linear regressions based on their impact on survival. Risk scores for 25 TN categories were then calculated from the T and N stage relative weights, and a rearranged tumor node metastasis (TNM) staging system was proposed via a cluster analysis of the TN scores. RESULTS: Both T and N stages significantly affect the OS of patients with colorectal cancer. Moreover, the T stage has greater weight than the N stage in the TNM staging system of colorectal cancer. For colon cancer, the relative T and N stage weights were 0.58 and 0.42, respectively, and for rectal cancer, the relative T and N stage weights were 0.61 and 0.39, respectively. On the basis of cluster analysis of the TN scores, T1N1a was classified to stage I, and T2N1a-1b and T1N1b-2a were classified to stage II in our revised TNM staging system for both colon and rectal cancer. For colon cancer, T4bN0 was classified to stage IIIa, but for rectal cancer, it was classified to stage IIIb. CONCLUSION: As the T stage affects colorectal cancer survival more significantly than the N stage, the TNM staging should be revised by relative T stage weight.