Guaranteed performance of individual control chart used in gamma passing rate-based patient-specific quality...

To assess the effect of sampling variability on the performance of individual charts (I-charts) for PSQA and provide a robust and reliable method for unknown PSQA processes.

A total of 1327 pretreatment PSQAs were analyzed. Different datasets with samples in the range of 20-1000 were used to estimate the lower control limit (LCL). Based on the iterative "Identify-Eliminate-Recalculate" and direct calculation without any outlier filtering procedures, five I-charts methods, namely the Shewhart, quantile, scaled weighted variance (SWV), weighted standard deviation (WSD), and skewness correction (SC) method, were used to compute the LCL. The average run length (ARL₀) and false alarm rate (FAR₀) were calculated to evaluate the performance of LCL.

The ground truth of the values of LCL, FAR₀, and ARL₀ obtained via in-control PSQAs were 92.31%, 0.135%, and 740.7, respectively. Further, for in-control PSQAs, the width of the 95% confidence interval of LCL values for all methods tended to decrease with the increase in sample size. In all sample ranges of in-control PSQAs, only the median LCL and ARL₀ values obtained via WSD and SWV methods were close to the ground truth. For the actual unknown PSQAs, based on the "Identify-Eliminate-Recalculate" procedure, only the median LCL values obtained by the WSD method were closest to the ground truth.

Sampling variability seriously affected the I-chart performance in PSQA processes, particularly for small samples. For unknown PSQAs, the WSD method based on the implementation of the iterative "Identify-Eliminate-Recalculate" procedure exhibited sufficient robustness and reliability.