The evaluation of MS and process capability in engineering is crucial for ensuring production accuracy and quality. One of the key methods is Measurement System Analysis (MSA), which focuses on the analysis and evaluation of MS variability. MSA includes repeatability and reproducibility (R&R) studies, which analyze the variation caused by measurement instruments and operators, without explicitly taking measurement uncertainty into account. VDA 5 and ISO 22514-7:2021 share common elements, particularly regarding statistical methods for evaluating the capability of MSs and processes. Both methods use similar calculations and approaches to determine measurement uncertainty and capability, which explains their interrelation. VDA 5, developed specifically for the automotive industry, provides guidelines for the systematic evaluation of MS capability. It focuses on measurement accuracy and includes methods for analyzing measurement uncertainty. VDA 5 contains procedures for quantifying the uncertainty and the capability of MSs, which is crucial for ensuring high-quality and reliable results in the highly regulated automotive industry. ISO 22514-7:2021 focuses on statistical methods for evaluating process capability and performance. This standard provides a framework for the use of various statistical techniques to improve and maintain process quality, including capability analysis. ISO 22514-7:2021 also incorporates measurement uncertainty into capability assessments, allowing for a comprehensive view of the performance of MSs and processes. Both methods utilize similar statistical tools, such as control charts, process capability analysis (
Cp,
Cpk), and analysis of variance (ANOVA). These tools are used to evaluate the variability and capability of MSs and processes. Both VDA 5 and ISO 22514-7:2021 include procedures for quantifying and analyzing measurement uncertainty. This ensures that capability evaluation is not just about measuring the average values, but also about understanding and managing the variability and uncertainty that can affect results. Both methods provide a systematic approach to evaluating MSs and processes, including defining criteria, collecting data, analyzing results, and implementing corrective actions based on the findings. ISO 14253-1:2017 primarily focuses on verifying the conformity with technical specifications and details procedures for incorporating the measurement uncertainty into this process. While not primarily intended for assessing MS capability, its principles and methods can be effectively applied for applicability evaluations by providing clear guidelines for incorporating measurement uncertainty. This ensures that MSs can accurately and reliably measure the required parameters, contributing to the overall capability assessment. It is important to note that while MSA focuses primarily on repeatability and reproducibility, standards such as VDA 5, ISO 22514-7:2021, and ISO 14253-1:2017 include measurement uncertainty, providing a more comprehensive and accurate view of the capability and applicability of MSs. The chronological development of these methods and standards reflects the increasing demands for measurement accuracy and reliability, corresponding to the needs of modern industry for detailed and systematic evaluation of MS and process capability. The capability evaluation procedures for the assessed MSs presented in the following chapters are consistent with the articles by Blecha et al. [
8,
12] and the relevant standards [
31,
32,
33].
4.3.1. Procedure for Evaluating MS Capability According to ISO 22514-7:2021
The ISO 22514-7:2021 standard defines the procedure for evaluating the capability of measurement systems (MSs) and measurement processes (MPs) based on the theory of combined measurement uncertainty and clarifies whether a given measurement process meets the requirements for a specific measurement task.
Resolution
RE is a key factor that affects the system’s ability to detect small changes in measured values. The standard specifies that the resolution of the MS should be less than 5% of the tolerance (
TOL), ensuring accurate detection of deviations within the measured tolerance. If the resolution is insufficient, it can negatively impact the overall capability of the system. In such cases, the capability evaluation should be suspended, as inadequate resolution calls into question the reliability of further calculations, such as the
QMS and
CMS indicators.
The MS performance ratio (
QMS) indicator evaluates the ratio between the expanded measurement uncertainty (
UMS) and the tolerance size
TOL. The
QMS value should not exceed 15%, i.e., the expanded measurement uncertainty should not be more than 15% of the total tolerance.
The MS capability index (
CMS) monitors how many combined measurement uncertainties can fit within the given tolerance. The standard requires the
CMS to be at least 1.33, i.e., that at least 5.32 combined measurement uncertainties must fit within one-fifth of the tolerance.
UMS in Equation (4) represents the expanded measurement uncertainty and can be expressed by the equation:
In Equations (4) and (5), uMS is the combined standard uncertainty, and the expansion coefficient k = 2, as the approximately 95.45% coverage interval is used in accordance with the standard.
The relationship between the
QMS and
CMS indicators is such that if
QMS meets the required criterion (i.e.,
QMS ≤ 15%), the
CMS indicator will also always be compliant. This relationship stems from the fact that both indicators are based on the same parameters—specifically, the combined uncertainty of the MS (
uMS) and the size of the tolerance range (
TOL). Both indicators share the same goal: to determine whether the MS is capable.
QMS expresses the ratio of the expanded uncertainty to the tolerance range and ensures that the expanded uncertainty of the MS does not exceed 15% of the tolerance.
CMS, on the other hand, follows a similar goal but works with combined measurement uncertainty (
uMS) and focuses on how many of these uncertainties can fit within the given tolerance. Since both indicators are based on combined measurement uncertainty, if
QMS meets the requirement, it means that the MS occupies less than 15% of the tolerance, which automatically guarantees that
CMS will also fall within the required range (greater than 1.33). Therefore, if the
QMS indicator is within the required range, the
CMS indicator will also be compliant. This makes
CMS redundant in this context if
QMS is used as the primary criterion for assessing capability. This may explain why some standards, such as VDA 5, do not include the
CMS indicator, considering
QMS sufficient for evaluating the MS’s capability.
Figure 6 illustrates the individual steps of the MS capability evaluation process according to ISO 22514-7:2021. First, the resolution of the MS is verified, ensuring the ability to detect small deviations within the given tolerance. Next, the MS performance ratio is evaluated to determine whether the expanded measurement uncertainty, multiplied by two, occupies less than 15% of the tolerance. If both criteria are met, the test is successful. The diagram suggests that the capability indicator criterion is supplementary to this concept. The capability evaluation process in this article complies with the provisions of ISO 22514-7:2021; therefore, the
CMS capability index was evaluated in the standard manner.
The combined standard uncertainty of the MS
uMS (see Equations (4) and (5)) is determined using the following Equation (6)
where the individual components from Equation (6) are calculated step by step according to the equations in
Table 3.
The release of ISO 22514-7:2021 is stricter in several respects compared to the 2012 version, particularly in the area of MS capability evaluation. One of the key changes is the refinement of the requirements for the use of Maximum Permissible Error (MPE) values. While the previous version relied more on experimental methods for capability evaluation, the new version clearly states that the MPE value can be used, which simplifies calculations but also requires strict adherence to the procedure for correctly calculating the combined uncertainty. The calculation of combined uncertainty incorporating MPE provides a standardized way of assessing the system capability, allowing for quicker implementation in the production process without the need for repeated experiments. The equation for calculating MPE is as follows:
If the MS is characterized by multiple MPE values, the calculation is carried out according to Equation (8).
Another tightening concerns the QMS indicator, where ISO 22514-7:2021 specifies that QMS shall not exceed 15%, i.e., that the combined measurement uncertainty shall not exceed 15% of the total tolerance, thereby increasing the requirements for the accuracy of MSs. Along with this, the definition of the CMS indicator has also been refined, with the standard requiring CMS to be at least 1.33, which means that at least 5.32 combined uncertainties must fit within one-fifth of the tolerance range.
These stricter requirements put pressure on manufacturers to ensure that their MSs can meet these demands and potentially invest in more advanced and accurate measuring equipment that complies with the stringent requirements of ISO 22514-7:2021 [
8].
If we designate the maximum allowable performance ratio for the MS as
QMSmax = 15%, we can also calculate the minimum tolerance
TOLMIN, for which, given the calculated expanded uncertainty
UMS, the specified condition (as well as
CMS = 1.33) is met:
4.3.2. Verifying the Conformity with the Specification According to ISO 14253-1:2017
According to ISO 14253-1:2017, conformity with the specification is verified when the measured value falls within the acceptance zone. The acceptance zone is the specification range reduced by guarding bands, taking into account the probability limit of compliance (see
Figure 7).
If the probability density of the measured values follows a normal distribution with a standard deviation significantly smaller than the specification range, then the standard probability limit of compliance of 95% corresponds to a guarding band factor value of g
A = 1.65, i.e., the width of the guarding band is equal to 1.65 times the combined standard uncertainty uc. The width of the guarding band is given by the Equation (10):
To determine the value of
gA, we calculate the ratio of tolerance
TOL to the combined measurement uncertainty
uc using Equation (11):
The value of the guarding band factor
gA is then calculated so that the probability of conformity with the specification is exactly 95%. The maximum value of the guarding band factor is
gA = 1.96, which applies when the ratio (11) is exactly 3.92.
Figure 8 shows the graph of the guarding band factor
gA values depending on the size of the
RATIO according to Equation (11).
Let us further assume that the value of the combined measurement uncertainty is estimated using the maximum permissible measurement error (MPE) according to the previous Equation (7).