Practical application of Six Sigma management in analytical biochemistry processes in clinical settings

Abstract Background Six Sigma methodology with a zero‐defect goal has long been applied in commercial settings and was utilized in this study to assure/improve the quality of various analytes. Methods Daily internal quality control (QC) and external quality assessment data were collected and analyzed by calculating the sigma (σ) values for 19 analytes based on the coefficient of variation, bias, and total error allowable. Standardized QC sigma charts were established with these parameters. Quality goal index (QGI) analysis and root cause analysis (RCA) were used to discover potential problems for the analytes. Results Five analytes with σ ≥ 6 achieved world‐class performance, and only the Westgard rule (13s) with one control measurement at two QC material levels (N2) per QC event and a run size of 1000 patient samples between QC events (R1000) was needed for QC. In contrast, more control rules (22s/R4s/41s) along with high N values and low R values were needed for quality assurance for five analytes with 4 ≤ σ < 6. However, the sigma levels of nine analytes were σ < 4 at one or more QC levels, and a more rigorous QC procedure (13s/22s/R4s/41s/8x with N4 and R45) was implemented. The combination of QGI analysis and RCA further revealed inaccuracy or imprecision problems for these analytes with σ < 4 and discovered five aspects of potential causes considered for quality improvement. Conclusions Six Sigma methodology is an effective tool for evaluating the performance of biochemical analytes and is conducive to quality assurance and improvement.

1999. 1 The Six Sigma management model includes five processes, namely define, measure, analyze, improve, and control (DMAIC).
In mathematical fields, sigma is the symbol for standard deviation (SD). 2 Some studies have shown that sigma metrics can be applied to quantitatively evaluate errors or defects in testing projects in clinical laboratories, and the results are quantified as defects per million (DPMs). 3,4 The Six Sigma metric corresponds to 3.4 DPM opportunities in a clinical process. To date, sigma methodology has mainly been applied in pre-analytical and analytical processes in clinical laboratories, focusing on the evaluation of biochemical and immunoassay tests. [4][5][6][7][8][9][10][11] In this study, the performance of 19 analytes was evaluated by calculating sigma values from the coefficient of variation (CV), bias, and total error allowable (TEa). Moreover, appropriate QC procedures were selected for each analyte using the sigma metrics. In addition, quality goal index (QGI) analyses and root cause analysis (RCA) were further performed to identify problems related to the measurement procedures for analytes with a sigma value below 4.

| Data collection
The internal quality control data required for this study were extracted between January 1 and May 31, 2018, using an AU5800 analyzer (Beckman Coulter) at our clinical biochemical laboratory.
The AU5800 analyzer is a modular combination system that in- data were used to calculate the average value, which was used to evaluate the system error in terms of accuracy for every analyte. In addition, it is worth noting that once the nonconformity of an EQA activity (score < 80%) for an analyte was observed, the bias data for the corresponding analyte in the EQA activity would not be included in the analysis.

| Construction of the standardized QC sigma charts
The frame of the standardized QC sigma charts was constructed by registering a CLInet account in CLInet (http://www.clinet.com.cn) and inputting parameters such as TEa, bias, and CV in the interface of the Six Sigma management menu. The construction of the standardized QC sigma charts obeyed the concept of previously reported studies. 12,13 This approach allows a laboratory to obtain an audiovisual and comprehensive view of the performance of all the analytes in a single graph at every control measurement level and with every instrument module.

| RCA
The RCA method was performed as previously described. 14,15 The cause-effect chart (fishbone diagram) was used as a technical tool for RCA. To date, RCA has been applied to solve problems in the field of medical management. 16

| Statistical analysis
The CV was used to indicate the precision and was calculated with the following formula: CV (%) = Standard Deviation SD ∕Mean × 100.
The following formula was used to calculate every bias value for each EQA activity: Bias (%) = ( | measurement value − target value | ∕target value) × 100.
The median of the EQA results reported by clinical laboratories that used the same type of instrument and method was used as the target value for every analyte.
The TEa was determined according to the proficiency testing criteria of American Clinical Laboratory Improvement Amendment 88 (CLIA88).
Sigma metrics were calculated with the following formula: The QGI was calculated using the formula QGI = Bias∕ 1.5 × CV .
This index can help determine the main reason why the testing performance of a clinical chemistry project yields a lower sigma level and might aid the selection of the best quality improvement plan. 8,9,17 A sigma value less than 4 (σ < 4) was used as the benchmark for the QGI analysis of analytes in this study. A QGI value less than 0.8 (QGI < 0.8) indicates that the precision of the corresponding analyte needs to be improved, whereas a value greater than 1.2 (QGI > 1.2) indicates that the accuracy of the analyte needs to be improved. A QGI value between 0.8 and 1.2 (0.8 ≤ QGI ≤ 1.2) indicates that the accuracy and precision of the analyte need to be simultaneously improved.

| Use of sigma metrics for the evaluation of analyte performance
To understand the performance of the 19 analytes on the AU5800 P1, P2, or ISE modules in our laboratory, the sigma metrics of every analyte at the QC material Levels 1 and 2 were calculated and are summarized in Tables 1 and 2. Furthermore, standardized QC sigma charts were constructed to intuitively evaluate the performance of the analytes at every QC material level and with every module. According to the sigma level, the performance of the analytes was divided into six grades, namely world class (σ ≥ 6), excellent (5 ≤ σ < 6), good (4 ≤ σ < 5), marginal (3 ≤ σ < 4), poor (2 ≤ σ < 3), and unacceptable (σ < 2), as shown in In the P1 and ISE modules, 11 of the 19 analytes showed a performance of at least 4σ (good) at QC material Level 1, and six of these analytes (CK, TG, TBIL, γ-GT, UA, and K) presented worldclass performance (Table 1 and Figure 1). In addition, 12 of the 19 analytes showed a performance of at least 4σ (good) at QC material Level 2, and seven of these analytes (CK, TG, TBIL, γ-GT, UA, ALP, and AST) presented world-class performance (Table 1 and Figure 1). In the P2 module, 10 of 16 analytes showed a performance of at least 4σ (good) at QC material Level 1, and six of these analytes (TG, CK, γ-GT, TBIL, UA, and ALP) presented world-class performance ( Table 2 and Figure 2). Moreover, 11 of 16 analytes showed a performance of at least 4σ (good) at QC material Level 2, and seven of these 11 analytes (TG, CK, γ-GT, TBIL, UA, ALP, and AST) presented world-class performance ( Table 2 and Figure 2).
The data demonstrated that the performance of five analytes (CK, TG, TBIL, γ-GT, and UA) reached the Six Sigma level in both analysis modules and at both QC material levels and that nine analytes (TP, CRE, ALB, GLU, ALT, Ca, BUN, P, and Cl) exhibited σ < 4 at one or both QC material levels.

| Quality control procedures selected by sigma metrics for the analytes
In the daily work of our clinical biochemical laboratory, the QC procedure empirically adopted involves the use of multi-rules 1 2s /2 2s /1 3s with one control measurement at two QC material levels and running these rules once for all the analytes, with the exception of the out-of-control analytes. To investigate the appropriate QC procedures for these analytes with a high probability of error detection (P ed ) and a low probability of false rejection (P fr ), the concept of the statistical QC (SQC) procedure based on sigma metrics was introduced and adopted in this study according to the new guidance CLSI C24-Ed4 18 and novel studies on SQC. 19,20 The design of the SQC procedure adopted in this study included the following three parameters: the selection of

| Combination of QGI analysis and RCA for the analytes with σ < 4
According to the new guideline CLSI C24-Ed4, the SQC procedures with P ed ≥ 90% and P fr ≤ 5% are recommended for analytes. 18 However, nine analytes with σ < 4 under the SQC procedure consisting of the full multi-rules 1 3s /2 2s /R 4s /4 1s /8 x with N4 and R45 could not meet this requirement. Thus, to assure quality and determine why these analytes did not reach the 4σ level or above, the QGI ra-  (Table 4).
To further detect the root causes of the problems with these analytes, a cause-effect chart was used as a technical tool for RCA. As shown in Figure 3, five aspects of potential root causes, including aspects related to methodology, materials, personnel, equipment, and working conditions, were investigated. For example, to analyze the methodology and personnel factors, 14 analytes (nine analytes with σ < 4 and five analytes with world-class performance) investigated by six staff members were evaluated based on sigma metrics (Table S1).
The same staff members worked under the same conditions using the same QC material level, the same domestic brand of reagents (with the exception of the electrolytes using the original reagents), and the same module. As a result, five analytes (CK, TG, TBIL, γ-GT, and UA) with world-class performance could generally reach at least the 5σ level, whereas P exhibited a performance of σ < 4 regardless of the personnel factor, as shown in Table S1. This finding demonstrated that the performance of these analytes showed differences related to the methodology, which revealed that some methods were favorable and others were not appropriate. Therefore, reevaluating and improving the methodology used for the analytes would improve the quality. In addition, the performance of the same Note: 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; R, run size of patient samples between QC events, R1000 represents a run size of 1000 patient samples between QC events, and similar definitions apply to R450, R200, and R45. a Not applicable.
analyte obtained with different staff members presented different sigma levels, as observed with TP, CRE, ALB, GLU, ALT, Ca, BUN, P, and Cl (Table S1). The potential reason for this finding might be that staff members exhibit different degrees of conscientiousness, attitude, theoretical knowledge, and seniority, which demonstrated that the personnel factor plays a role in the performance of the analytes. Thus, personnel retraining as well as a review of the standard operating procedures (particularly those used for reagent addition) and a reevaluation of the competency of some staff members might be favorable for improving quality.
Together, combining imprecision or inaccuracy problems with the potential five aspects of root causes might constitute a strategy for solving problems related to these nine analytes and improving their quality.

| D ISCUSS I ON
In this study, we analyzed 19 biochemical analytes using sigma methodology. The Six Sigma management workflow for quality assurance and improvement is summarized in Figure 4. First, each analyte was effectively evaluated according to the sigma value. Second, the QC procedures were optimized and individualized for the analytes with different sigma grades. Third, the detected QGI ratios and RCA further revealed that the accuracy or precision of the analytes with performance below the 4σ level needed to be improved and revealed five aspects of potential root causes.
In clinical settings, the credibility of clinical reports relies on two items: precision and accuracy. Sigma metrics reveal errors or defects in precision and accuracy that can be used to evaluate quantitative projects. Thus, the Six Sigma methodology was evaluated in our work.  (Tables 1 and 2). However, this situation was not particular to this study because it was also discovered in other studies. [6][7][8][9][10][11] The two analysis modules could be considered two separate analyzers, and differences in performance could not be avoidable.
However, the sigma levels obtained with these two analysis modules were generally comparable. The discrepancy between the two material levels was partly attributed to the methodology used for some analytes, which might present better performance with normal or abnormal concentrations of the QC materials. Thus, as suggested by a previous study, stricter QC procedures should be followed under these conditions to abolish this discrepancy. 11 Various corrective actions were performed in this study for these analytes, as shown in Table 3.
The IQC procedure is an important stage in the daily work performed in clinical settings. As previously reported, appropriate QC procedures might not only decrease the P fr and increase the P ed but also avoid economic costs and improve efficiency. 21,22 For example, compared with the previous procedures adopted in our laboratory, only one QC rule, 1 3s , needed to be used for TG, CK, γ-GT, TBIL, and UA, which decreased economic costs and increased the working efficiency. However, for the analytes with σ < 6, more rigorous QC procedures were implemented in this study compared with those used analytes was a major problem that needed to be addressed.
To improve the quality of these analytes, a strategy that combines QGI analysis with RCA for problem discovery was proposed in this study. QGI provided robust directions for solving only the problems associated with the analytes, such as inaccuracy or imprecision.
However, the shortcomings of the QGI analysis could be compensated with RCA. In the analytical process, the observed problems belonged to five factors, as shown in Figure 3. Of course, the potential root causes included in the figure are only based on the situation in our laboratory, and other undiscovered problems might also exist. As shown in a previous study in a veterinary laboratory, methodology improvements (reagent substitution) and personnel training can improve the quality of analytes. 23 Therefore, addressing the method and personnel factors could improve the quality of some analytes with low sigma values, such as P and Cl. In addition, quality problems remained due to failures at multiple levels of the measurement processes, indicating the existence of multiple root causes, which is consistent with the adverse events observed in health care. 15 The problems associated with working conditions and instrument proficiency could also affect measurement quality, and these problems cannot be ignored (Figure 3). For example, the analyzer sometimes emits a high-temperature alarm once in summer, which is inevitably linked to the environmental temperature due to the lack of a constant indoor temperature. This situation would impact not only the instrument proficiency but also the enzymatic methods used for the analytes. Thus, designing a constant-temperature system for use in a laboratory would help resolve this problem. To address fluctuations in instrument proficiency and thus improve quality, the frequency of calibrating these analytes could be increased from once a week to every 2 days in our laboratory. The degree of improvement in the quality of these analytes will be investigated in our future work. Certainly, if the performance of an analyte cannot be improved by implementation of all the proposed actions, nonstatistical QC procedures, including repeated tests for a patient and comparability testing, could be adopted for QA, as suggested by previous studies. 18,24 Overall, the Six Sigma methodology provides a useful evaluation system for the biochemical projects considered in this study, optimizes the QC procedures for every item, and supplies a problem-solving strategy for analytes with σ < 4. This method has great practical value in clinical biochemical laboratories.

ACK N OWLED G M ENT
The project was financially supported by the Open Research Fund

AUTH O R CO NTR I B UTI O N S
BZ, YC, and YW conceived and designed the approach of this study; HH collected the 5-month daily quality data; BZ analyzed data and wrote the article; and YC, CL, and LT supervised this study and reviewed and edited this article. All authors have read and approved the final manuscript.