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

Purpose: 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.

Materials And Methods: 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 (ARL) and false alarm rate (FAR) were calculated to evaluate the performance of LCL.

Results: The ground truth of the values of LCL, FAR, and ARL 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 ARL 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.

Conclusions: 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.