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

Guangjun Li · Qing Xiao · Guyu Dai · Qiang Wang · Xiangbin Zhang · Xiangyu Zhang +3 more

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Advanced Statistical Process Monitoring Advanced Radiotherapy Techniques Healthcare Quality and Management

Abstract

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 0 ) and false alarm rate (FAR 0 ) were calculated to evaluate the performance of LCL. Results The ground truth of the values of LCL, FAR 0 , and ARL 0 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 0 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.

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References

1998Transforming Non-Normal Data to Normality in Statistical Process Control 2014An Overview of Phase I Analysis for Process Improvement and Monitoring 2015The Difficulty in Designing Shewhart X and X Control Charts with Estimated Parameters 2001Control charts for positively‐skewed populations with weighted standard deviations 2003Skewness correction X and R charts for skewed distributions 2019Two perspectives for designing a phase II control chart with estimated parameters: The case of the Shewhart X¯ Chart 2017Guaranteed In-Control Performance for the Shewhart X and X Control Charts 2013Retrospective analysis of linear accelerator output constancy checks using process control techniques

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