**3. Results and Discussion**

Based on the test results obtained by each of the participating laboratories, a number of parameters was calculated for the purpose of statistical quality assessment of performed measurements, in compliance with the recommendations of individual industry standards [38–43] and the testing programme designed according to [53,55]. The most important parameters for laboratory assessment are: standard deviation, expanded uncertainty, and *z-score*, ζ-*score* and *En-score*. Calculated values were presented in Tables 3–7 and Figures 2–4.

**Table 3.** Table of obtained values of basic statistical parameters for individual participating laboratories with regard to measurements performed for concrete mix consistency with the use of classical statistical method.



**Table 4.** Table of obtained values of basic statistical parameters for individual participating laboratories with regard to measurements performed for concrete mix air content with the use of classical statistical method.

**Table 5.** Table of obtained values of basic statistical parameters for individual participating laboratories with regard to measurements performed for concrete mix density with the use of classical statistical method.


**Table 6.** Table of obtained values of basic statistical parameters for individual participating laboratories with regard to measurements performed for concrete compressive strength with the use of classical statistical method.



**Table 7.** Values of statistical parameters for individual parameters/properties of concrete mix and hardened concrete according to classical and robust statistics.

> In data analysis and inter-laboratory comparative testing, various statistical tests, e.g., the Grubbs test, are performed to identify and remove outliers. This is appropriate and effective only for large samples. For concrete mix and hardened concrete tests (small samples), removing some data items (from one to three test results) significantly decreases the accuracy of uncertainty estimation, which is why the conducted analyses employed robust statistical methods, designed for robustness against slight deviation from the model (particularly the occurrence of outliers) [56,57]. The calculations were performed in compliance with ISO 13528: 2009-01 "Statistical method for use in proficiency testing by inter-laboratory comparisons", Annex C (normative) Robust Analysis [55]. The values of statistical parameters determined with the use of classical and robust methods were presented in Table 7.

**Figure 2.** The value of z-score based on the results of the tests conducted by the participating laboratories, which performed measurements of density of concrete mix and compressive strength of hardened concrete according to the classical statistical method.

**Figure 3.** The value of *ζ-score* based on the results of the tests conducted by the participating laboratories, which performed measurements of density of concrete mix and compressive strength of hardened concrete according to the classical statistical method.

**Figure 4.** The value of *En*-score based on the results of the tests conducted by the participating laboratories, which performed measurements of density of concrete mix and compressive strength of hardened concrete according to the classical statistical method.

The next step of the calculations was to determine, based on the obtained statistical parameters (Table 6), the values of individual measures that would allow the laboratories' proficiency to be assessed, i.e., the values of *z-score, ζ-score* and *En-score*. On the basis of the inter-laboratory proficiency tests performed, all participating southern Poland-based laboratories which carry out tests of concrete mix and hardened concrete conduct them on a satisfactory level, as confirmed by the obtained *z-score* values |*z*| < 2.0 (Figure 2).

The obtained values of *ζ-score* and *En-score* for seven out of nine laboratories indicate satisfactory proficiency in determining consistency, air content and density of concrete mix, and compressive strength of hardened concrete (Figures 3 and 4).

Only for two laboratories, defined as Lab G and Lab H, the obtained values of *ζ-score* and *En-score* reveal unsatisfactory application by the participants of the methods for testing and consistency determination. The value of *ζ-score* indicates that the results obtained for the consistency parameter are questionable, whereas the value of *En-score* shows the results to be unsatisfactory (Figures 3 and 4).

In both cases, the limit value for *ζ-score* was exceeded by 18.5% → *ζ score* = 2.37, while the limit value for *En-score* was exceeded by 19% →*En-score* = 1.19. This is not a significant exceeding of a satisfactory value, but one that constitutes a questionable result, which suggests undertaking appropriate measures with the aim to establish the causes of incorrect assessment of the consistency of concrete mix. Questionable results might be, in this case, caused by pouring into the cone-shaped form a concrete mixture that is too dry, or incorrect use of a measuring tool. Most tests, such as the slump flow test and the slump test, are carried out by operators by using a ruler or a stopwatch, which is why measurement errors are inherent, and the measured value may vary depending on the operator [58]. There is also a possibility that the obtained value can be wrongly recorded or easily manipulated after measurement. If concrete of insufficient workability is used for construction due to inaccurate measurement results or incorrect data records, it will cause future problems in terms of structural safety [58,59]. Consistency determines the ease of mixing concrete in a form for a given method of laying concrete. Fluidity parameters should comply with the overall plan of the project, as proper concrete consistency allows the durability of a structure to be predicted. Monitoring concrete fluidity [60,61] and durability [62–64] is considered crucial in long-distance transport of concrete required for constructing tower blocks and long-span bridges.

For *z-score* values determined with the use of classical and robust statistical method, regression and correlation analysis was performed. Figure 5 shows graphs of regression functions of *z-score* in classical statistics and *z-score* in robust statistics for various parameters.

**Figure 5.** *Cont*.

**Figure 5.** Regression functions of *z-score* in classical statistics and *z-score* in robust statistics for various parameters: (**a**) consistency; (**b**) air content; (**c**) density; (**d**) compressive strength.

High positive correlation can be observed between *z-score* in classical statistics and *z-score* in robust statistics. Pearson product–moment correlation coefficients for *z-score* in classical statistics versus z-score in robust statistics are presented in Table 8.


**Table 8.** Correlation of *z-score* for the results of two methods: robust and classical statistics.

Combination of classical and robust statistical methods with the use of *z-score* can reduce the risks related to laboratory activities. In classical and robust statistics, *z-score* parameters, based on an assigned value, are more effective in detecting a laboratory having outlier results. *Z-score*, which is based on the difference between the reported result and the assigned value, is particularly useful for detecting discrepancies between laboratories, and may prove helpful in improving their activities. Neither of these methods nor their combination guarantee proper assessment, and they should not be used for the main assessment of laboratory performance in inter-laboratory comparisons. Methods for robust estimation in small samples do not improve the efficiency of the *z-score* parameter in detecting discrepancies of test results. In ISO 13528 [55], Annex D1, it is underscored that some of the procedures for performance evaluation are unreliable when used for too small a number of participants. The conclusions are consistent with the information given in ISO 13528 [55] and in [45]. Assessment of reliability of small sample size tests is a difficult problem to solve in inter-laboratory comparisons of ready-mixed concrete. In such circumstances, it seems justified to refrain from activities aimed at ensuring testing quality by means of inter-laboratory comparisons, and focus on other aspects, such as the personnel's competencies and equipment suitability. However, laboratories, particularly those responsible for carrying out tests of ready mix concrete that affect construction safety and quality, tend to be concerned about the correctness of test results. An interlaboratory comparison could help them assess whether differences between laboratories are significant, and gain more confidence in their results. Such comparisons—as presented in the paper—give both the laboratory and its customer a slightly higher sense of security.

#### **4. Conclusions**

Proper quality control of concrete does not only influence the optimisation and verification of correct functioning of individual stages of the production process, but also directly impacts certification related to factory production control. Quality control is the basis for ensuring that the production plant meets at least the requirements and recommendations set out by EN 206:2014 "Concrete–Specification, performance, production and conformity". The standard introduced a novel approach toward designing the composition and planning the production of concrete mixes, and evaluating concrete with regard to technical parameters. In turn, quality control through laboratory proficiency tests, for instance with regard to testing concrete mix and hardened concrete, allows individual laboratory units' capability to perform specific research to be evaluated. For accredited laboratories, in order to monitor the reliability of the obtained results, participation in inter-laboratory comparison programmes or proficiency testing programmes is required by ISO/IEC 17025:2005. For the remaining research units, participation in such programmes is undoubtedly a means of verifying and improving the quality of conducted analyses, as well

as a platform for exchanging experiences and views (after performing and documenting measurements), both for individual employees and the entire laboratory.

Comparative tests discussed in the present paper, conducted for nine participating laboratories, provided interesting data for scientific consideration. For the purpose of the tests, selected parameters/properties of concrete mix and hardened concrete were analysed. *Z-score* was applied to evaluate laboratory proficiency, whereas *ζ-score* and *En-score* were used for improving the laboratories' performance. For the laboratories defined as Lab G and Lab H, the results obtained provided information about irregularities, which made it possible to take adequate corrective measures with the aim to determine the causes of inappropriate assessment of concrete mix consistency.

Experiences gained from the conducted tests reveal a need to continue this type of project, with the cooperation of both past participants and new laboratory facilities, for the purpose of improving the quality of activities conducted by research units. A tangible aspect of regular participation in comparative tests, with positive results, is an increase in customer trust and the evidence of the laboratory personnel's competencies.

**Author Contributions:** Conceptualization, I.S.; methodology, I.S. and A.L.; validation, I.S., A.L. and P.O.; formal analysis, I.S., A.L., P.O., W.K. and M.G.; investigation, I.S., P.O.; resources, I.S., A.L., W.K., P.O. and M.G.; data curation, I.S., A.L., P.O., W.K. and M.G.; writing—original draft preparation, I.S., A.L., P.O., W.K., M.G. and A.S.; writing—review and editing, I.S., A.L., P.O.,W.K., M.G. and A.S.; visualization, I.S., A.L., P.O., W.K. and M.G.; supervision, I.S., A.L.; project administration, I.S. All authors have read and agreed to the published version of the manuscript.

**Funding:** The research presented in this paper was partly funded by the Ministry of Science and Higher Education within the statutory research at Rzeszow University of Technology (Grant No. PB26.BG.21.001, Grant No. UPB.BG.20.001).

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Data sharing not applicable.

**Acknowledgments:** The authors would like to express their gratitude to Marta Kierni-Hnat from Technological Center for Construction of the Polish Center for Research and Certification (CTB) for providing the access to laboratory test results.

**Conflicts of Interest:** The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.
