Measurement System Analysis

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Measurement System Analysis Section 1: General Guidelines for Measurement Systems. Some knowledge regarding measurement systems is already covered in SPC; the quality of measurement data is an important foundation for process control. The proper selection and use of measurement systems ensure high-quality measurement data at lower measurement costs. I. Several Important Concepts 1. Measurement Process and Measurement Values The process of assigning values to specific entities in order to represent their characteristics is called the measurement process. The measured value, or measurement data, is the output of this process. 2. Measuring tools: Any device used to obtain measurement results, often referring to measuring devices used in workshops, including those that determine whether something passes or fails a test. 3. Measurement system: A collection and process of instruments, equipment, software, programs, operations, and operators used for measurement. 4. Quality of measurement data. The quality of measurement data can be described from the following aspects: ① The quality of measurement data is characterized by the statistical properties of multiple measurement results obtained from a measurement system operating under stable conditions. ② The quality of measurement data is typically expressed in terms of bias and variance; the ideal quality is zero bias and zero variance. ③ The most common reason for low quality of measurement data is data variability. Degradation is the result of the interaction between the measurement system and the environment. The vast majority of variations are undesirable, but those that reflect slight changes in the characteristic being measured are meaningful, as they indicate the sensitivity of the measurement system. II. Statistical Properties of the Measurement System Here, a brief explanation is given of the statistical properties that a measurement system must possess. 1. Statistical stability: The measurement system must be under statistical control, which means that variation can only arise from common causes rather than special causes. 2. The variation of the measurement system is less than that of the manufacturing process. 3. The variation of the measurement system is less than the tolerance band. 4. The increment of the measurement system (which can generally be understood as the scale value) should be less than the smaller of the variation in the manufacturing process or the set limits (tolerance bands), typically 1/10. 5. The statistical characteristics of the measurement system may vary depending on the item being measured; therefore, the maximum variation of the measurement system must be less than the process variation or the smaller of the tolerance bands. III. Standards In the United States, the highest standard for metrology is maintained by the **National Institute of Standards and Technology, NIST**. Standards passed down from NIST are called primary standards. Moving down from the first-level standard is referred to as the second-level standard. Level 1 and Level 2 standards are often owned by private companies, and are maintained and used by the company’s metrology department. The level that follows the second-level standard is called the operational standard. Work standards are typically used to calibrate the measurement systems in the production process. Work standards are often maintained and used by production staff. Appropriate calibration procedures are applied to ensure that a traceability path can be established from the lowest-level standard all the way to NIST. This is called traceability. **Standard, Level 1 Standard, Level 2 Standard, Working Standard (NIST). Private companies, (enterprise metrology departments), (production staff). **Research institutions: When an institution does not have its own metrology department, it can turn to a metrology facility outside the institution; such a facility is called a “calibration laboratory”. For accuracy, the most important factor is the measurement system; using traceable standards is the only way to ensure the accuracy of the system. The use of traceable standards helps reduce conflicts arising from discrepancies in measurements between producers and customers. Difference between calibration and verification: Calibration; Verification. Objects: Measurement equipment; Measuring instruments. Form: An activity carried out by enterprises on their own, with no legal significance; Performed in accordance with the law, and has legal significance. Purpose: Primarily to assess numerical errors; To determine that all metrological characteristics meet legal requirements. Scope of application: Used for quality management; Used for social metrological supervision. IV. General guidelines: 1. Two steps before assessment: ① Verify whether the measurement system is measuring the correct variables; if not, no matter how precise the system is, it is useless. ② Determine what statistical properties the measurement system must have to be considered acceptable. 2. Two stages of the evaluation process ① First stage: Determine whether the measurement system meets the requirements. Two objectives of the first phase: a. Determine through experiments whether the system possesses the required statistical properties ； b. Identify through testing the environmental factors that have a significant impact on the system, in order to determine the requirements for the operating environment. Phase 2: Verify through experiments whether the system can consistently possess the required statistical properties. Bisexuality (R&R) of common measuring tools is a form of testing at this stage. These tests are usually carried out as part of the routine work in an institution’s normal calibration procedures, maintenance procedures, and metrological procedures. 3. The test procedures shall be documented. The documents shall include the following: a. Examples ； b. Select the specifications for the items to be tested and the environment in which the test procedures will be applied. Typically, these specifications should take the form of experimental statistical designs ； c. Detailed instructions on how to collect, record, and analyze data ； d. Operational definitions of key terms and concepts ； e. If the program requires the use of specific standards, such as those from NIST, then the test document should include instructions for storing, maintaining, and using these standards. V. Selection and development of test procedures: The tests referred to here are those used to evaluate the statistical characteristics of a measurement system. The methods and procedures for testing are diverse, and are selected depending on the specific characteristics of the measurement system. When selecting a test evaluation method, the issues to be considered generally include: 1. Which level of measurement standard should be used? Can it be traced back to a **standard? 2. For R&R tests, the use of “blinding” should be considered. Blind testing refers to conducting measurements in an actual measurement environment, where the operator is unaware in advance that the measurement system is being evaluated. 3. Test cost. 4. Time required for the test. 5. Provide clear and actionable definitions for the terms. Such as accuracy, precision, repeatability, reproducibility, etc. 6. Comparison test between the two measurement systems. 7. How often should the second-phase tests be conducted? Section 2: Procedures for Evaluating Measurement Systems I. Introduction 1. Scope of the procedures This measurement system procedure is used to evaluate the following statistical characteristics: repeatability, reproducibility, bias, stability, and linearity. These procedures are sometimes collectively referred to as “gauge R&R” procedures. Because it is often used to evaluate the two statistical properties of reproducibility and repeatability. The evaluation tests of the measurement system should also include an investigation into the effect of other factors (such as temperature and light) on system variability, but this chapter does not cover that. 2. Three basic questions that need to be addressed when evaluating a measurement system are: ① Is there sufficient resolution? ② Does it remain stable over time? ③ Check whether the statistical performance remains within the expected range, to determine if it is acceptable for process control 3. Five forms of measurement system variation. Measurement system errors can be categorized into five types: bias, repeatability, reproducibility, stability, and linearity. One of the purposes of studying a measurement system is to obtain information on the measurement variation and types associated with that system when it interacts with the environment. Applying this research can provide: 1) Criteria for adopting new measurement equipment ； 2) Comparison between one measuring device and another ； 3) Basis for evaluating measuring tools suspected to be defective ； 4) Comparison of the measuring equipment before and after maintenance ； 5) Deterioration of the calculation process, as well as the acceptable level of the production process ； 6) Information necessary to create the gauge characteristic curve (GPC). ① Bias: The difference between the average value obtained through measurement and observation and the standard average value measured using precise instruments for the object. Bias is often referred to as “accuracy”. See MSA manual P16 (Figure 1). ② Repeatability: The variation in the data obtained when the same evaluator uses the same measuring instrument to measure the same characteristic of the same part multiple times. See MSA manual P17 (Figure 2). ③ Reproducibility: The variation in the mean values of data obtained when different evaluators use the same measuring instruments to measure the same characteristic of the same part. See MSA manual P17 (Figure 3). ④ Stability: Also known as drift, it refers to the total variation in the measurement values obtained by a measuring system when it measures the same characteristic of a reference or part over a certain period of time. See MSA manual P17 (Figure 4). ⑤ Linearity: The variation in bias of a measuring instrument within its intended operating range. See MSA manual P18 (Figure 5). II. Measurement System Analysis The purpose of measurement system analysis is to understand the causes of variation. In this section, in addition to analyzing the five types of variation, the resolution of the measurement system is also analyzed. The premise of measurement system analysis is that the part being measured is not altered or damaged by the measurement. 1. Resolution of the measurement system ① The resolution of a measurement system refers to its ability to detect and accurately indicate subtle changes in the characteristic being measured. See MSA manual P20 (Figure 6). ② The resolution that the measurement system can handle is such that it is able to detect variations in the process, including those caused by special causes. ③ Recommended visible resolution: The minimum increment of the measuring instrument is the visible resolution. It is recommended that the visual resolution should be less than or equal to one-tenth of 6 times the process standard deviation σ. That is: the visual resolution ≤ 6σ/10. ④ The manifestation of insufficient resolution on the range chart: within the control limits of the control chart, there are only 1–3 range values, or 4 range values; however, if more than 1/4 of them are 0, then the resolution of the measurement system is insufficient, as shown in Figure 7 of P21. Within the control limits, there are only two range values: 0 and –0.01; clearly, such a range control chart is unable to properly identify special causes of variation. 2. Stability ① Distinguish between two types of stability: a. The total variation in system bias over time. b. Statistical stability, which includes repeatability, bias, general process, etc. We can determine statistical stability using control chart methods. If the measurement process is under statistical control, then it can be confirmed that the measurement system possesses statistical stability. ② Methods for studying the stability of measurement systems: Control chart techniques are applied to examine the stability of measurement systems. Unlike process studies, when studying measurement systems, standards or reference specimens must be used. Moreover, care should be taken to keep the standards or reference specimens in good condition, so as to prevent any bias in the measurement results over time. The techniques and applications of control charts have been introduced in the SPC manual. When analyzing measurement system control charts, it is necessary to apply extensive expertise and experience related to measurement systems in order to avoid taking inappropriate actions that could increase variation. 3. Bias: Bias is measured using the following method: ① Obtain the reference value of the specimen or standard device using precision measurement equipment. ② Measure the sample or standard device using the measured system in question, at least 10 times, and calculate the average value. ③ Bias = Observed mean – Baseline value. ④ Percentage of bias in process variation = Bias/Process variation × 100%. ⑤ See the examples on pages P26 and P27. Note: Process variation = 6σ range. Tolerance: The allowable deviation from the standard, that is, the acceptable range of variation around the nominal value. The allowable tolerance is the difference between the specified upper and lower limits. The specified limits should not be confused with control limits. 4. Reproducibility and repeatability ① Two common causes of repeatability errors are: a. Variations in the instrument itself ； b. The position of the part in the instrument. ② Repeatability determination: When the range chart shows that the process is under control, the standard deviation of repeatability (also known as instrumental variation) is given by σ = R/d. If the 99% points of a normal distribution are used to represent the repeatability error, it can be calculated using the formula 5.15(R/d). If the number of tests is 2 and d = 1.128, then this formula can be simplified to 4.65R. ③ Determination of reproducibility: Reproducibility is expressed by the range R of the evaluators’ averages. Calculate the standard deviation σ: σ = R/d, where R is the difference between the maximum and minimum average values among the different evaluators. ④ The standard deviation of the measurement system, σ = R/d, represents the variability of the measurement system; this is also known as the tool bias R&R. The tool R&R value is 5.15σ, and it indicates the 99% range within a normal distribution. ⑤ If repeatability is higher than reproducibility, the possible reason is: a. The instrument requires maintenance ； b. The measuring tools should be redesigned to improve stiffness ； c. The clamping and inspection points need improvement ； d. Excessive internal variation in the parts exists. ⑥ If reproducibility is higher than repeatability, possible reasons include: a. The evaluators need better training on how to use measuring instruments and read their readings ； b. The markings on the gauge dial are unclear ； c. Some kind of fixture is needed to help evaluators improve the consistency in using measuring tools. ⑦ Examples can be found in manuals P55, 56, 57, 58, 59, 60. ⑧ The acceptable criteria for the repeatability and reproducibility (R&R) of measuring tools are: a. An error of less than 10% – the measurement system is acceptable ； b. 10%～30% error—Depending on the importance of the application, the cost of the measuring instrument, and maintenance expenses, this level of error may be acceptable ； c. Error greater than 30%—the measurement system needs improvement. Various efforts are made to identify problems and make corrections. 5. Linear: Linear research employs linear fitting methods. The process of fitting a straight line with bias and different baseline values, multiplied by the part, yields the linear exponent of the variable gauge. 6. Research on gauge-type measuring tools (sample size method) Part name: GN-125 lock nut Measuring tool name: Thread plug gauge Date: Parameter being measured: Internal thread Measuring tool identifier: 03-Trans-001 6# Operator: Specification: M10×1.25 Type of measuring tool: 7H Avaluator Bvaluator Count 1 2 3 4 1 G G G G 2 G G G G 3 G G G G 4 NG NG NG NG 5 G G G G 6 NG NG NG NG 7 G G G G 8 G G G G 9 G G G G 10 G G G G 11 NG NG NG NG 12 G G G G 13 G G G G 14 G G G G 15 G G G G 16 G G G G 17 NG NG NG NG 18 G G G G 19 G G G G 20 G G G G Remarks: G: Pass ； NG: Not working. 4#, 6#, 11#, and 17# are pre-designated defective parts. Conclusion: This measurement system is qualified. Analyst: Date: 7. Study of Measuring Tools (Repeatability and Reproducibility Analysis Methods) Table of Data on Repeatability and Reproducibility of Tools Evaluator/Number of Trials Part Average Value 1 2 3 4 5 6 7 8 9 10 1. A 1 0.65 1.00 0.85 0.85 0.55 1.00 0.95 0.85 1.00 0.60 0.83 2. 2 0.60 1.00 0.80 0.95 0.45 1.00 0.95 0.80 1.00 0.70 0.825 3. 3 4. Average 0.625 1.00 0.825 0.90 0.50 1.00 0.95 0.825 1.00 0.65 Xa=0.8275 5. Range 0.05 0.00 0.05 0.10 0.10 0.00 0.00 0.05 0.00 0.10 Ra=0.045 6. B 1 0.55 1.05 0.80 0.80 0.40 1.00 0.95 0.75 1.00 0.55 0.785 7. 2 0.55 0.95 0.75 0.75 0.40 1.05 0.90 0.70 0.95 0.50 0.75 8. 3 9. Average 0.55 1.00 0.775 0.775 0.40 1.025 0.925 0.725 0.975 0.525 Xb=0.7675 10. Range 0.00 0.10 0.05 0.05 0.00 0.05 0.05 0.05 0.05 0.05 Rb=0.045 11. C 1 0.50 1.05 0.80 0.80 0.45 1.00 0.95 0.80 1.05 0.85 0.825 12. 2 0.55 1.00 0.80 0.80 0.50 1.05 0.95 0.80 1.05 0.80 0.83 13. 3 14. Average 0.525 1.025 0.80 0.80 0.475 1.025 0.95 0.80 1.05 0.825 Xc=0.8275 15. Range 0.05 0.05 0.00 0.00 0.05 0.05 0.00 0.00 0.00 0.05 Rc=0.030 16. Part Average (Xp) 0.567 1.008 0.80 0.825 0.458 1.017 0.942 0.783 1.008 0.667 X=0.8075 Rp=0.559 17. [Ra=0.045] + [Rb=0.045] + [Rc=0.030] / [# of Evaluators = 3] R=0.04 18. [MaxX=0.8275] – [MinX=0.7675] = XDIFF 0.06 19. R*D4 = UCLR 0.13 20. R*D3 = LCLR 0.00 Note: D4 = 3.27 for 2 trials, and D4 = 2.58 for 3 trials. D3=0 within 7 trials ； UCLR represents the limit of a single R. Circle those values that exceed the limit. Identify the cause and correct it. The same evaluator repeats these readings using the initial instrument, or excludes these values and averages the remaining observations once again to calculate R and the limit values. Report on Gauge Repeatability and Reproducibility
Part Number and Name: Gasket surface
Gauge Name: Thickness gauge
Characteristic: Thickness
Gauge Number:
Date:
Dimension Specification: 0.6–1.0 mm
Gauge Type: 0.0–10.1
Performer: From the data sheet: R=0.04, XDIFF=0.06, Rp=0.559

Analysis of the measurement system
%Total Variation (TV)
Repeatability – Equipment Variation (EV): EV=R*K1; %EV=100(EV/TV)=100(0.18/0.94)=19.1%; EV=0.04*4.56=0.18
Number of tests: K1=23; 4.56, 3.05

Reproducibility – Examiner Variation (AV): AV=√(XDIFF*K2)² – (EV²/nr); AV=√(0.06*2.70)² – (0.18²/10*2); %AV=100(AV/TV)=100(0.16/0.94)=17%; N=number of parts; R=number of tests=0.16; Number of examiners: 2, 3; K2=3.65, 2.70

Repeatability and Reproducibility (R&R): R&R=√(EV²+AV²)=√(0.18²+0.16²)=0.24; %R&R=100(R&R/TV)=100(0.24/0.94)=25.5%

Part variation (PV): PV=RP*K3=0.56*1.62=0.91; %PV=100(PV/TV)=100(0.91/0.94)=96.8%

Number of parts: K3
Total variation (TV): TV=√(R&R²+PV²)=√(0.24²+0.91²)=0.94
2, 3, 4, 5, 6, 7, 8, 9, 10; 3.65, 2.70, 2.30, 2.08, 1.93, 1.82, 1.74, 1.67, 1.62