**1. Introduction**

Modern structures must meet various design standards concerning durability, ergonomics, safety and quality; furthermore, construction has to be executed without harm

**Citation:** Skrzypczak, I.; Le´sniak, A.; Ochab, P.; Górka, M.; Kokoszka, W.; Sikora, A. Interlaboratory Comparative Tests in Ready-Mixed Concrete Quality Assessment. *Materials* **2021**, *14*, 3475. https:// doi.org/10.3390/ma14133475

Academic Editors: Dolores Eliche Quesada and Krzysztof Schabowicz

Received: 27 May 2021 Accepted: 18 June 2021 Published: 22 June 2021

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**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

to the environment and natural resources. With the development of technology and advanced construction materials, increasingly more requirements are being imposed. Modern construction consists of structures of possibly minimal impact on the environment [1–3], which is achieved through proper architectural design, use of proper construction materials characterised, among other things, by low CO2 emission [4–6], low energy consumption during operation and construction [7–9], and the possibility of renovation following extensive use [10,11] or potential malfunction [12,13]. Not without significance is also the use of construction materials that can be recycled or utilised [14,15]. Hence, both the design and execution of modern structures requires undertaking measures that involve employing appropriate quality assessment processes. Assessment is conducted with regard to both the production of construction materials, and the process of design, execution and completion of construction works or entire structures. Each of these procedures is of different character. Quality control of construction materials delivered to the market is limited by legal provisions, whereas the remaining measures related to the execution of construction objects can be approached optionally while remaining within the framework of internal, domestic procedures [16]. Concrete is undoubtedly one of the most frequently used construction materials [17]. According to a Chatham House report [18], the world produces 4.4 billion tons of concrete annually, but that amount is expected to rise to over 5.5 billion tons by 2050. Ready-mixed concrete (RMC) is the principal construction material for civil engineering infrastructure [19]. It should be noted that construction concrete that is subject to quality control constitutes circa 70% of total concrete production [20]. Quality assessment may be carried out on various stages of production, delivery, and before and after laying concrete mix. The intended concrete quality is achieved owing to the selection of appropriate formulas (ingredients, strength class, exposure class etc.) [21–26], a production process that is compliant with the procedures [27–29], the mode of transport and laying of fresh concrete mix, and the proper maintenance of hardened concrete [30,31]. Quality assessment involves the control of conformity and uniformity in compliance with the recommended criteria. Not without significance for the quality of modern concretes remains the development of innovative research methods that aid concrete design aimed at obtaining appropriate properties and durability [32–35], and the development of methods for the evaluation of the results [16,36].

Concrete testing procedures and quality assurance criteria for ready-mixed concrete delivered to the construction site are fairly well-established under law, especially under industry standards. It is also important to underscore the significance and role of technical specification for execution and completion of construction works. Although appropriate industry standards contain conformity and uniformity criteria related to concrete production control, technical specifications contain, in particular, sets of requirements that are necessary for determining the standard and quality of works with regard to the manner of execution of construction works and the evaluation of correctness of execution of individual stages; these elaborations are custom-developed for each construction project [37].

Industry standards require that the concrete supplier implement a production and quality control plan—a set of quality requirements with regard to the products and their production. The plan contains a detailed description of the manufacturing process which includes stages, organisation, methods and standards of production as well as procedures and instructions, and the testing and quality control programme [38–43]. For the readymixed concrete supplier, quality assessment involves pro-active measures that allow for maintaining the quality of concrete by ensuring the cohesion of properties of concrete mix and hardened concrete between the batches and for the entire duration of the project; quality assessment also includes appropriate actions and measures taken in the case when the supplied product does not meet the requirements [38]. In construction practice, in the execution of concrete works, concrete quality is usually verified by the investor by commissioning an independent laboratory unit to carry out the tests, which is a guarantee for quality control of both concrete mix and hardened concrete. As set out by ISO/IEC 17000:2020, "Conformity assessment–Vocabulary and general principles" [44], accreditation

is "attestation by a third party, related to the unit assessing conformity, providing formal evidence of its competence for executing defined tasks within the scope of conformity assessment". The IOS 17000:2020 standard contains a requirement that the laboratories have quality control procedures and plan their actions, which would subsequently be subject to monitoring. The actions should ensure the reliability of test results delivered to the customer. One of the essential tools for ensuring the quality of test results is the laboratories' participation in proficiency testing (PT) or inter-laboratory comparison (ILC) programmes [45]. In accordance with EN ISO/IEC 17025 [46] and EA-4/18 [47], accredited laboratories should ensure the quality of the results through participation in proficiency testing programmes. Involvement in PT/ILC programmes is, on the one hand, a tool for demonstrating the laboratory's performance, and on the other hand an aid for maintaining the quality of available tests and validating test methods. Participation in comparative PT/ILC programmes is usually paid for, and the services are provided by domestic and international organisers of PT/ILC programmes. Laboratories may, however, organise inter-laboratory comparisons with other laboratories on their own behalf. Such activity is not aimed at qualifying or evaluating the operation of participating laboratories, yet it allows the obtained results to be analysed individually and used to improve testing quality. In practice, inter-laboratory testing is most frequently organised for one of the three following purposes [48–50]: assessment of laboratory proficiency, certification of reference material, evaluation (validation) of analysis method. Participation in inter-laboratory comparisons undoubtedly contributes to improving quality systems in laboratories. This directly translates into the quality of assessment, for instance of concrete, in the monitored facilities.

The aim of the present paper is the evaluation of laboratory performance by means of inter-laboratory proficiency tests as carried out for ready-mixed concrete quality assessment, for nine participating laboratory units. The most innovative element of the study was the simultaneous use of classical and robust statistical methods. In practice, the most common procedures employ classical statistical analysis, which is optimal under the assumption of normality of data distribution and large sample size. Classical statistical procedures involve, as a first step, the verification of questionable results, e.g., by applying the Grubbs test, which allows us to identify and remove abnormal values, i.e., outliers. This is only effective for large data sets, whereas for small-sized samples, removing one or several significant outliers may greatly alter the classical statistical parameters. In many fields of experimental research, particularly in destructive testing, the tests are limited to small-sized samples due to high cost intensity of the testing process. In such circumstances, it is necessary to make use of all the obtained measurement results, as removing outliers/questionable results from the sample diminishes the reliability of statistical assessment. Employing robust statistical methods is recommended, as, in comparison with classical statistical methods, they ensure a smaller impact of outliers and other anomalies on the measurement results. Quality assessment of concrete is generally carried out on the basis of small-sized samples, by means of destructive testing, without the possibility to repeat or complement the measurements. This is why iterative robust statistical methods, rarely used in concrete quality control, were proposed for the analysis of inter-laboratory comparative tests. Southern Poland-based laboratories participated in the programme voluntarily. Concrete tests and analyses were performed from June to July 2020.

#### **2. Materials and Methods**

#### *2.1. Laboratory Proficiency Testing/Interlaboratory Comparison*

According to ISO/IEC 17043:2010 [51], laboratory proficiency testing involves the evaluation of a participant's performance against pre-established criteria by means of inter-laboratory comparisons. This allows the laboratory's capability for conducting concrete tests to be assessed, and thus the reliability of the obtained results to be evaluated. In proficiency testing, the results of the analyses of the same object, obtained in a given laboratory, are compared with the results obtained independently in one or several different laboratories. The basic tool for carrying out proficiency testing is inter-laboratory comparison, which involves the organised conduct and evaluation of testing of the same or similar objects by at least two laboratories, in accordance with previously determined conditions [52]. Furthermore, inter-laboratory comparisons can be used for different, indirect purposes, as shown in Figure 1.

**Figure 1.** Goals of inter-laboratory comparisons. Source: own elaboration based on [53,54].

Participation in proficiency testing programmes constitutes, therefore, an evaluation of a laboratory's testing capabilities. It provides an independent, external assessment, which complements the laboratory's internal quality control procedures. Participation in a proficiency testing programme may be a basis for self-evaluation, and contribute to improving the laboratory's proficiency; it is, thus, an important, often obligatory element of the laboratory's quality control system.

Prior to proceeding with the testing, an appropriately designed and organised programme must be prepared in order to determine the type of analytical methods, the type of test object, and the number of participating laboratories.

While preparing the test object, one should take into consideration all factors that may influence the reliability of inter-laboratory testing, such as the object's homogeneity, the method of sample collection, the object's stability over time, and the impact of environmental conditions (during transport and storage) on the test object's properties. It is crucial that the material used in proficiency testing is homogenous, and that all participants are provided with test objects which do not significantly differ in terms of tested parameters. The material's uniformity should be documented, and the conditions of its transportation

and storage, and the timeframe of the testing, should be clearly defined. Test methods should be unambiguously determined and based on normalised and validated methods.

#### *2.2. Evaluation of Comparative Test Results*

The results obtained by the participants are subject to statistical analysis and evaluation. The methods for statistical evaluation of inter-laboratory comparison results are described in the following standards:


Most of the methods are based on a known assigned value (value attributed to a particular quantity and accepted [55] and its uncertainty. Assigned value (*xpt*) is the value agreed on the basis of the participants' results in the way described in ISO/IEC 17043 (2010) [51], Annex B.2.1 e) and ISO 13528:2015 [55], Annex C, Algorithm A p.C.3.1.

Assigned value is calculated as arithmetic mean from the participants' results, having considered the influences of outliers, with the use of robust statistical methods.

Standard uncertainty of assigned value *u*(*xpt*) is determined with the application of statistical method as described in ISO 13528: 2015 p.7.7.3 [55] and calculated by Equation (1):

$$
\mu \left( x\_{pt} \right) = 1.25 \cdot \frac{S^\*}{\sqrt{\mathcal{P}}} \tag{1}
$$

where: *p*—number of participants,

*S\**—strong (solid) standard deviation calculated by Equation (2):

$$S^\* = 1.134\sqrt{\frac{\sum \left(\mathbf{x}\_i^\* - \mathbf{x}\_{pt}\right)^2}{p-1}}\tag{2}$$

where: *xi\**—results obtained by the participants after applying robust statistics,

*xpt*—assigned value, calculated as strong (solid) mean from the participants' results. Expanded uncertainty (*Ur*) of the assigned value, with expansion coefficient k = 2 and confidence level circa 95%, is calculated by Equation (3):

$$
\mathcal{U}I\_r = 2 \cdot \mathcal{U}(\mathbf{x}\_{pt}) \tag{3}
$$

#### *2.3. Means of Proficiency Assessment and Evaluation Criteria for Laboratory Activity Results*

Laboratory activity results are usually presented with the use of *z-score, ζ-score* and *En-score,* which are determined in accordance with ISO/IEC 17043: 2011 [51], Annex B, B.3.1.3 c) and d), and calculated by Equations (4)–(6):

• *z-score* (4):

$$z = \frac{\mathbf{x}\_i - \mathbf{x}^\*}{SD} \tag{4}$$

where: *SD*—standard deviation for proficiency test assessment, determined considering the results of all participants,

*xi*—result reported by the participant,

*x\**—assigned value, determined as strong (robust) mean from the participants' results.

• *ζ-score* (5):

$$\mathcal{Z} = \frac{\mathbf{x}\_i - \mathbf{x}^\*}{\sqrt{\mu\_{x\_i}\mathbf{z}^2 + \mu\_{x^\*}\mathbf{z}^2}}\tag{5}$$

where: *xi*—result reported by the participant,

*x*∗—assigned value, determined as strong (robust) mean from the participants' results, *μxi* —standard uncertainty estimated by the participant,

*μx*∗—standard uncertainty of assigned value x∗.

• *En-score* (6):

$$E\_n = \frac{\mathbf{x}\_i - \mathbf{x}^\*}{\sqrt{\|\mathbf{U}\_{\mathbf{x}\_i}\|^2 + \|\mathbf{U}\_{\mathbf{x}^\*}\|^2}}\tag{6}$$

where: *xi* —result reported by the participant,

*x*∗—assigned value, determined as strong (solid) mean from the participants' results,

*Uxi* —measurement uncertainty estimated by the participant,

*Ux*∗—measurement uncertainty of assigned value *x*∗.

The results of the laboratories' activity are evaluated with the use of *z-score*. By assessing a participant's performance by means of *z-score*, both the trueness and precision of the obtained result are addressed [52]. *ζ-score* and *En-score* can be applied in combination with *z-score* as an aid for improving the laboratories' activity [56,57]. *ζ-score and En-score* depend on the participants submitting accurate measurement uncertainty estimates along with their result, a procedure not easily adhered to [52].

Assessment according to *z-score*, *ζ-score* and *En-score* is applied to all results, including those which, as outliers, were not considered in statistical calculations of the assigned value and its standard deviation. The results of actions of the programme's participants were evaluated according to the following criteria (Table 1):

**Table 1.** Assessment of results according to the values of individual scores [52].


\* Assessment according to z-score is not performed when the number of results for the tested parameter is lower than 8.

Is it worth mentioning that the paper [45] presented an approach toward the analysis of inter-laboratory comparison results for a small number of laboratories (2) and small number of samples (3), which can apply for e.g., a construction product for which tests and test elements are very expensive.

#### *2.4. Laboratory Proficiency Tests with Regard to Testing Concrete Mix and Hardened Concrete*

The tests involved the participation of nine southern Poland-based laboratory units. For confidentiality reasons, the present elaboration did not include the names or addresses of the laboratories. The proficiency testing programme considered test objects, measured parameters, and methods of testing concrete mix and hardened concrete as shown in Table 2.

**Table 2.** Test objects, measured parameters and recommended standard test methods.


The laboratory proficiency testing programme was designed following the guidelines set out by ISO 13528:2015 [55], Annex B, and consisted in the collection of samples of concrete mix, and the preparation and maintenance of concrete samples by each of the participating laboratories. This is why the concrete mix was the only area of uniformity and stability control of the test object. For concrete sample testing, together with sample collection, inter-laboratory assessment involves the preparation and maintenance of concrete samples, and all related measures, including the transport of samples to the participants' laboratories. For concrete samples, the test object's instability effects were eliminated, as the testing programme assumed that the preparation, maintenance and assessment of concrete samples should be carried out by each participant at the same time (concrete compressive strength test—28 days after preparing test forms).

As the properties of concrete mix change over time, the quickest possible method was adopted for collecting samples. It was assumed that all samples would be collected within circa 15 min, in a single place.

Due to the availability, universality and cost-efficacy of testing methods, immediate tests of consistency and/or air content were employed to determine uniformity and stability of concrete mixes. For all participants, the manner of sample collection, preparation, testing and transportation complied with the recommendations set out by the relevant industry standards (Table 1) and programme-specific guidelines. Comparative tests were performed for concrete of the following parameters: strength class C30/37, consistency S3, frost resistance degree F150 and water resistance degree W8.
