Practical application of Westgard Sigma rules with run size in analytical biochemistry processes in clinical settings

Abstract Background The performance of 18 routine chemical detection methods was evaluated by the sigma (σ) metric, and Westgard Sigma rules with run size were used to establish internal quality control (IQC) standards to reduce patient risks. Materials and methods External quality assessment (EQA) and internal quality control data from 18 assays in a biochemical laboratory were collected from January to June 2020. The sigma values of each assay were calculated, based on the bias, total error allowable, and coefficient of variation, appropriate quality control rules were selected. According to the quality goal index, the main causes of poor performance were determined to guide quality improvement. Results At IQC material level 1, seven of the 18 assays achieved five sigma (excellent), and five assays (UA, Crea, AMY, TC and Na) showed world‐class performance. At IQC material level 2, 14 of the 18 assays achieved 5 sigma (excellent), and thirteen assays (UA, ALT, CK, Crea, AMY, K, AST, ALP, Na, LDH, Mg, TC and GGT) showed world‐class performance. The quality goal index (QGI) was calculated for items with analysis performance <5 sigma, and the main causes of poor performance were determined to guide quality improvement. Conclusions Westgard sigma rules with run size are an effective tool for evaluating the performance of biochemical assays. These rules can be used to more simply and intuitively select the quality control strategy of related items and reduce the risk to patients.

MaxE (NUF) = 1 as the target to determine run size and established Westgard sigma rules with the run size. 2 Six Sigma is a technology that can improve the quality process management of enterprises, and it was first applied at Motorola. The purpose was to meet the quality requirements of 'zero defects'. Six Sigma indicates the international quality level. A six sigma analysis means that 99.99966% of the results are error free, corresponding to 3.4 defects for every million opportunities. 3 Since the application of six sigma quality management in laboratory medicine in 2000, more and more laboratories in China have begun to apply the six sigma management method in the quality evaluation of detection systems. So far, the sigma methodology has mainly been applied in the evaluation of immunoassay and biochemical tests. 4,5 In this study, Westgard sigma rules with a run size management method were used to evaluate the detection performance of clinical test items in a biochemical laboratory with the objectives of improving the quality level of the clinical biochemical laboratory and reducing the risk to patients.
ALT, AST, GGT, ALP, CK, Urea, UA, Crea, LDH, AMY, Glu, TC and TP were tested with reagents obtained from Meikang, Mg from Woko, Ca from Diasys, and K, Na and Cl from Hitachi. Calibration was performed with reagents from Roche, and IQC products were

| Statistical analysis
The precision is expressed by the coefficient of variation (CV) and calculated by the following formula: CV (%) = [Standard Deviation/ Mean] × 100. 6 The internal quality control data were collected between January and June 2020 at our clinical biochemical laboratory.
The average value of the absolute percentage differences was used to evaluate bias in our laboratory (   Table 1.
Calculate the sigma metric using the following formula 7 : The QGI was calculated using the standard equation: . This indicator can help to identify the main reasons for the lower sigma level in the test performance of clinical chemistry projects and may help to select the best quality improvement plan. [8][9][10] The quality goal index (QGI) was calculated for assays with analysis performance <5 sigma, and the main causes of poor performance were determined to guide quality improvement. When QGI > 1.2, improvement of the accuracy should be prioritized; when 0.8 ≤ QGI ≤ 1.2, both accuracy and precision of the analyte should be improved; When QGI < 0.8, the precision of the analyte needs to be improved.

| RE SULTS
The performances and sigma values of the 18 assays in the Hitachi 7600 analysis system were calculated in our laboratory, and the results are shown in Tables 1 and 2, intuitively assess the performance Note: R, run size of patient samples between QC events, R45 represents a run size of 45 patient samples between QC events, and similar definitions apply to R1000, R450, and R200.
N, total number of control measurements per run, N2 represents two measurements at a single control material level or one measurement at two control material levels, and a similar definition applies to N4.
The IQC procedures for the 18 assays at different IQC material levels are detailed in Table 2 were problems of accuracy and precision at one or more IQC levels; two assays (Cl and GGT) showed low accuracy problems at one or more IQC levels (Table 3). The sigma level of some of the assays, investigated in this study,

| D ISCUSS I ON
show the differences between different research groups. 14-17 There were several main reasons for this phenomenon: the first was source selection of the TEa target; the second was the difference between the algorithms used to evaluate CV and bias; the third was that the different types of reagents, analysers and IQC materials were used.
In addition, there is a difference in the sigma metrics between the two IQC levels in this study (Tables 1 and 2), and this fact is not specific for this study, as it has been found in other studies. 6,[18][19][20] For example, Zhou et al 6  increasing the frequency of QC. However, QC frequency is very difficult to control because different testing items have different QC frequencies. Second, personalized quality control strategies will increase labour volume, and a high QC frequency will increase the related economic burden.

| CON CLUS IONS
The use of Westgard sigma rules with run size is rarely reported in domestic literature. In theory, the Westgard sigma rule with run size can also be used for quality control of other high-throughput continuous work instrument projects, but its practicability needs further clinical verification and discussion.

ACK N OWLED G EM ENTS
None.

CO N FLI C T O F I NTE R E S T
None of the authors have any commercial or other associations that might pose a conflict of interest.

DATA AVA I L A B I L I T Y S TAT E M E N T
The data are available upon reasonable request.