Msa manual aiag

Order Now. Achieve Certification. MSA Certification Exam. Upcoming Quality Events. Department of Commerce. NIST provides these services directly to many types of industries, but primarily to those industries that require the highest level of accuracy for their products and that incorporate state-of-the-art measurements in their processes. Most of the industrialized countries throughout the world maintain their own NMIs and similar to NIST, they also provide a high level of metrology standards or measurement services for their respective countries.

NIST works collaboratively with these other NMIs to assure measurements made in one country do not differ from those made in another. One thing to note is that the capabilities of these NMIs will vary from country to country and not all types of measurements are compared on a regular basis, so differences can exist.

This is why it is important to understand to whom measurements are traceable and how traceable they are. Traceability is an important concept in the trade of goods and services. Measurements that are traceable to the same or similar standards will agree more closely than those that are not traceable. This helps reduce the need for re-test, rejection of good product, and acceptance of bad product.

The traceability linkage of these consensus standards to the NMI may not always be clearly understood, so ultimately it is critical that the measurements are traceable to the extent that satisfies customer needs.

With the advancement in measurement technologies and the usage of state-of-the- art measurement systems in industry, the definition as to where and how a measurement is traceable is an ever-evolving concept.

This linkage or chain of events ultimately finds its way onto the factory floor and then provides the basis for measurement traceability. A calibration system is a set of operations that establish, under specified conditions, the relationship between a measuring device and a traceable standard of known reference value and uncertainty.

Calibration may also include steps to detect, correlate, report, or eliminate by adjustment any discrepancy in accuracy of the measuring device being compared. The calibration system determines measurement traceability to the measurement systems through the use of calibration methods and standards. Traceability is the chain of calibration events originating with the calibration standards of appropriate metrological capability or measurement uncertainty.

Each calibration event includes all of the elements necessary including standards, measurement and test equipment being verified, calibration methods and procedures, records, and qualified personnel.

Chapter I — Section A Introduction, Purpose and Terminology 11 True Value An organization may have an internal calibration laboratory or organization which controls and maintains the elements of the calibration events.

Measurement Assurance Programs MAPs can be used to verify the acceptability of the measurement processes used throughout the calibration system. Independent measurements imply that the traceability of the secondary measurement process is derived from a separate chain of calibration events from those used for the initial measurement. MAPs may also include the use of statistical process control SPC to track the long-term stability of a measurement process. When a qualified laboratory is not available for a given piece of equipment, calibration services may be performed by the equipment manufacturer.

It is desired that any individual reading be as close to this value as economically possible. Unfortunately, the true value can never be known with certainty. However, uncertainty can be minimized by using a reference value based on a well defined operational definition of the characteristic, and using the results of a measurement system that has higher order discrimination and traceable to NIST.

Because the reference value is used as a surrogate for the true value, these terms are commonly used interchangeably. This usage is not recommended. Knowledge is gained of what the process is doing by evaluating the parameters or results of the process. This activity, often called inspection, is the act of examining process parameters, in-process parts, assembled subsystems, or complete end products with the aid of suitable standards and measuring devices which enable the observer to confirm or deny the premise that the process is operating in a stable manner with acceptable variation to a customer designated target.

But this examination activity is itself a process. Equipment was the major focus — the more "important" the characteristic, the more expensive the gage. Gruska and M. Heaphy, The Third Generation, , OperationInput Output Chapter I — Section B The Measurement Process 14 usefulness of the instrument, its compatibility with the process and environment, and its usability was rarely questioned.

Consequently these gages were often not used properly or simply not used. The measurement and analysis activity is a process — a measurement process. Any and all of the management, statistical, and logical techniques of process control can be applied to it. This means that the customers and their needs must first be identified. The customer, the owner of the process, wants to make a correct decision with minimum effort. Management must provide the resources to purchase equipment which is necessary and sufficient to do this.

But purchasing the best or the latest measurement technology will not necessarily guarantee correct production process control decisions. Equipment is only one part of the measurement process.

The owner of the process must know how to correctly use this equipment and how to analyze and interpret the results. Management must therefore also provide clear operational definitions and standards as well as training and support. The owner of the process has, in turn, the obligation to monitor and control the measurement process to assure stable and correct results which includes a total measurement systems analysis perspective — the study of the gage, procedure, user, and environment; i.

Each measurement would always agree with a standard. P 5 F A measurement system that could produce measurements like that would be said to have the statistical properties of zero variance, zero bias, and zero probability of misclassifying any product it measured.

Unfortunately, measurement systems with such desirable statistical properties seldom exist, and so process managers are typically forced to use measurement systems that have less desirable statistical properties. The quality of a measurement system is usually determined solely by the statistical properties of the data it produces over time.

Other properties, such as cost, ease of use, etc. But it is the statistical properties of the data produced that determine the quality of the measurement system.

Statistical properties that are most important for one use are not necessarily the most important properties for another use. Data obtained from such a machine can be very useful for analyzing a manufacturing process. Edwards Deming, , , p. Statistical Properties of Measurement Systems Chapter I — Section B The Measurement Process 15 Management has the responsibility for identifying the statistical properties that are the most important for the ultimate use of the data.

Management is also responsible for ensuring that those properties are used as the basis for selecting a measurement system. To accomplish this, operational definitions of the statistical properties, as well as acceptable methods of measuring them, are required. These include: 1 Adequate discrimination and sensitivity. The increments of measure should be small relative to the process variation or specification limits for the purpose of measurement.

The commonly known Rule of Tens, or to-1 Rule, states that instrument discrimination should divide the tolerance or process variation into ten parts or more. This rule of thumb was intended as a practical minimum starting point for gage selection. FP6PF This means that under repeatable conditions, the variation in the measurement system is due to common causes only and not due to special causes.

This can be referred to as statistical stability and is best evaluated by graphical methods. Assess the measurement system to the feature tolerance. The statistical properties of the measurement system may change as the items being measured vary. If so, then the largest worst variation of the measurement system is small relative to the smaller of either the process variation or the specification limits. Similar to all processes, the measurement system is impacted by both random and systematic sources of variation.

These sources of variation are due to common and special causes. In order to control the measurement system variation: 1 Identify the potential sources of variation. Although the specific causes will depend on the situation, some typical sources of variation can be identified. There are various methods of 6 The measurement analyst must always consider practical and statistical significance. Sources of Variation Chapter I — Section B The Measurement Process 16 presenting and categorizing these sources of variation such as cause-effect diagrams, fault tree diagrams, etc.

The acronym S. P 7 F is used to represent the six essential elements of a generalized measuring system to assure attainment of required objectives. This may be thought of as an error model for a complete measurement system. P 8 Factors affecting those six areas need to be understood so they can be controlled or eliminated. Figure I-B 1 displays a cause and effect diagram showing some of the potential sources of variation.

T 8 See Appendix F for an alternate error model, P. S Standard W Workpiece i. Chapter I — Section B The Measurement Process 17 Figure I-B 1: Measurement System Variability Cause and Effect Diagram MeasurementSystem VariabilityStandard Workpiece Part Instrument Gage EnvironmentPerson Appraiser geometric compatibility coefofthermal expansion elasticproperties calibration stability elastic deformation supporting features elastic properties mass cleanliness interrelated characteristics hidden geometry operational definition adequate datums skill limitations experience training understanding training experience attitude physical educational vibration temperature standard vsambient equalization-- systemcomponents traceability airpollution ergonomics lighting stress cycles thermal expansion sun components airdrafts people lights artificial designamplification contact geometry deformation effects build maintenance bias variability stability linearity repeatability reproducibility sensitivity consistency uniformity calibration p.

Chapter I — Section B The Measurement Process 18 The Effects of Measurement System Variability Because the measurement system can be affected by various sources of variation, repeated readings on the same part do not yield the same, identical result. Readings vary from each other due to common and special causes. The effects of the various sources of variation on the measurement system should be evaluated over a short and long period of time.

The measurement system capability is the measurement system random error over a short period of time. It is the combination of errors quantified by linearity, uniformity, repeatability and reproducibility. The measurement system performance, as with process performance, is the effect of all sources of variation over time.

This is accomplished by determining whether our process is in statistical control i. This adds stability and consistency to the measurement system capability. Historically, it would be determined if the part were acceptable within specification or unacceptable outside specification. Another common scenario is the classification of parts into specific categories e. This does not restrict the application of the discussion to other categorization activities.

Further classifications may be reworkable, salvageable or scrap. Under a product control philosophy this classification activity would be the primary reason for measuring a part. But, with a process control philosophy, interest is focused on whether the part variation is due to common causes or special causes in the process. Philosophy Interest Product control Is the part in a specific category? Process control Is the process variation stable and acceptable?

Verify fixturing and clamping if applicable Also if there are any critical environmental issues that are interdependent with the measurement. Additionally, the variation attributable to the bias and linearity of the measurement device should be small compared with the repeatability and reproducibility components. The knowledge gained during Phase 1 testing should be used as input to the development of the measurement system maintenance program as well as the type of testing which should be used during Phase 2.

Environmental issues may drive a change in location or a controlled environment for the measurement device. For example, if there is a significant impact of repeatability and reproducibility on the total measurement system variation, a simple two- factor statistical experiment could be performed periodically as a Phase 2 test. The choice of which procedure to use depends on many factors, most of which need to be determined on a case-by-case basis for each measurement system to be assessed.

In some cases, preliminary testing may be required to determine if a procedure is appropriate for a particular measurement system or not. Such preliminary testing ought to be an integral part of the Phase 1 testing discussed in the previous section.

Standards are frequently essential for assessing the accuracy of a measurement system. If standards are not used, the variability of the measurement system can still be assessed, but it may not be possible to assess its accuracy with reasonable credibility.

Blind measurements are measurements obtained in the actual measurement environment by an operator who does not know that an assessment of the measurement system is being conducted.

Properly administered, tests based on blind measurements are usually not contaminated by the well-known Hawthorne effect. Examples of such terms include accuracy, precision, repeatability, reproducibility, etc. In the experiments, the researchers systematically modified working conditions of five assemblers and monitored the results. As the conditions improved, production rose. However, when working conditions were degraded, production continued to improve.

This was thought to be the results of the workers having developed a more positive attitude toward the work solely as a result of them being part of the study, rather than as a result of the changed working conditions. If so, one should consider using test procedures that rely on the use of standards such as those discussed in Phase 1 above. If standards are not used, it may still be possible to determine whether or not the two measurement systems are working well together.

However, if the systems are not working well together, then it may not be possible, without the use of standards, to determine which system needs improvement.

In addition to these general issues, other issues that are specific to the particular measurement system being tested may also be important. Finding the specific issues that are important to a particular measurement system is one of the two objectives of the Phase 1 testing.

Typical preparation prior to conducting the study is as follows: 1 The approach to be used should be planned. For instance, determine by using engineering judgment, visual observations, or a gage study, if there is an appraiser influence in calibrating or using the instrument. There are some measurement systems where the effect of reproducibility can be considered negligible; for example, when a button is pushed and a number is printed out.

The reason being the degree of confidence desired for the gage study estimations. The assessment of the measurement system is based on the feature tolerance i. An independent estimate of process variation process capability study is recommended when assessing the adequacy of the measurement system for process control i.

The TV index i. Ignoring TV does not affect assessments using tolerance product control or an independent estimate of process variation process control. Samples can be selected by taking one sample per day for several days. Again, this is necessary because the parts will be treated in the analysis as if they represent the range of production variation in the process.

Since each part will be measured several times, each part must be numbered for identification. The manner in which a study is conducted is very important. All analyses presented in this manual assume statistical independence 27 of the individual P F readings. To minimize the likelihood of misleading results, the following steps need to be taken: 1 The measurements should be made in a random order 28 to P F ensure that any drift or changes that could occur will be spread randomly throughout the study.

The appraisers should be unaware of which numbered part is being checked in order to avoid any possible knowledge bias. However, the person conducting the study should know which numbered part is being checked and record the data accordingly, that is Appraiser A, Part 1, first trial; Appraiser B, Part 4, second trial, etc. Mechanical devices must be read and recorded to the smallest unit of scale discrimination. For electronic readouts, the measurement plan must establish a common policy for recording the right-most significant digit of display.

Analog devices should 27 There is no correlation between readings. For analog devices, if the smallest scale graduation is 0. If possible, the appraisers who normally use the measurement device should be included in the study. Each appraiser should use the procedure — including all steps — they normally use to obtain readings.

The effect of any differences between methods the appraisers use will be reflected in the Reproducibility of the measurement system.

If so, the appraisers should recalibrate the equipment before each group of readings. The number of parts required will depend upon the significance of the characteristic being measured and upon the level of confidence required in the estimate of measurement system variation. Although the number of appraisers, trials and parts may be varied when using the recommended practices discussed in this manual, the number of appraisers, trials and parts should remain constant between Phase 1 and Phase 2 test programs or between sequential Phase 2 tests for common measurement systems.

Maintaining commonality between test programs and sequential tests will improve comparisons between the various test results. A measurement system should be stable before any additional analysis is valid.

Acceptability Criteria — Gage Assembly and Fixture Error Assembly or An improperly designed fixture or poorly assembled gage will increase Fixture Error measurement error.

This is normally found when the measurements indicate or display process instability or out-of-control conditions. This may be due to excessive gage variation or poor repeatability and poor GRR values. Also, for automated measurement, verify the program follows required or expected protocol. If problems are found in any of these areas, reset or repair the gage and fixtures, then rerun the measurement evaluation. Acceptability Criteria — Location Error Location Error Location error is normally defined by analyzing bias and linearity.

In general, the bias or linearity error of a measurement system is unacceptable if it is significantly different from zero or exceeds the maximum permissible error established by the gage calibration procedure.

In such cases, the measurement system should be recalibrated or an offset correction applied to minimize this error. If an out-of-control condition or nonconformance is P F found in this situation, the first thing that should be done is to evaluate the measurement system. For measurement systems whose purpose is to analyze a process, a general guidelines for measurement system acceptability is as follows: GRR Decision Comments Under 10 Generally considered to be an Recommended, especially useful when trying to sort or percent acceptable measurement system.

Should be approved by the customer. Over 30 Considered to be unacceptable Every effort should be made to improve the measurement percent system. This condition may be addressed by the use of an appropriate measurement strategy; for example, using the average result of several readings of the same part characteristic in order to reduce final measurement variation.

This statistic indicates the number of categories P F into which the measurement process can be divided. This value should be greater than or equal to 5. Caution: The use of the GRR guidelines as threshold criteria alone is NOT an acceptable practice for determining the acceptability of a measurement system.

In either case the process is producing acceptable product. In case 2 the existence of a nonconformance or out of control condition could be a false alarm i. Specifying the guidelines as the threshold criteria can drive the wrong behavior. For example, the supplier may be creative in achieving a low GRR by eliminating real life sources of variation e.

Comments on the Application and Gage Acceptability When looking at GRR and measurement variation it is important to look at each application individually, to see what is required and how the measurement is going to be used.

For example: the required precision of temperature measurement may be different for dissimilar applications. It is acceptable for this application. But in a laboratory, where small variations in temperature can impact test results, a more sophisticated temperature measurement and control is required.

This thermostat will be more expensive and is required to have less variability i. The final acceptance of a measurement system should not come down to a single set of indices. The long-term performance of the measurement system should also be reviewed, for example, using graphical analysis over time. The procedures are simple to use and can be readily applied in a production environment.

As discussed previously, the test procedure which should be used to understand a measurement system and to quantify its variability depends on the sources of variation which may affect the measurement system. The test procedures in this chapter are sufficient for this type of measurement system analysis.

A thorough review of Chapter I, Section E is recommended to ensure proper application of these guidelines. Guidelines for Determining Stability Conducting the Study 1 Obtain a sample and establish its reference value s relative to a traceable standard.

If one is not available, select a production part 31 that falls in the mid-range of the production measurements P F and designate it as the master sample for stability analysis. The known reference value is not required for tracking measurement system stability. Time It may be desirable to have master samples for the low end, the high end, and the mid-range of the expected measurements. Separate measurements and control charts are recommended for each.

The sample size and frequency should be based on knowledge of the measurement system. Factors could include how often recalibration or repair has been required, how frequently the measurement system is used, and how stressful the operating conditions are.

The readings need to be taken at differing times to represent when the measurement system is Reference Value actually being used. This will account for warm-up, ambient or other factors that may change during the day. Analysis of Results — Graphical 4 Establish control limits and evaluate for out-of-control or unstable conditions using standard control chart analysis.

This may require modifying the production part, such as plating, to extend the life of the master. This can be compared with that of the process to determine if the measurement system repeatability is suitable for the application. Design of Experiments or other analytical problem solving techniques may be required to determine the prime contributors to the lack of measurement system stability.

Example — Stability To determine if the stability of a new measurement instrument was acceptable, the process team selected a part near the middle of the range of the production process.

This part was sent to the measurement lab to determine the reference value which is 6. The team measured this part 5 times once a shift for four weeks 20 subgroups. In general, the bias or linearity error of a measurement system is acceptable if it is not statistically significantly different from zero when compared to the repeatability.

Consequently, the repeatability must be acceptable when compared to the process variation in order for this analysis to be useful. If one is not available, select a production part that falls in the mid-range of the production measurements and designate it as the master sample for bias analysis.

If this is done, analyze the data using a linearity study. Review the histogram, using subject matter knowledge, to determine if any special causes or anomalies are present. If not, continue with the analysis. Example — Bias A manufacturing engineer was evaluating a new measurement system for monitoring a process.

An analysis of the measurement equipment indicated that there should be no linearity concerns, so the engineer had only the bias of the measurement system evaluated. A single part was chosen within the operating range of the measurement system based upon documented process variation. The part was measured by layout inspection to determine its reference value. The part was then measured fifteen times by the lead operator. The repeatability of 0. Since zero falls within the confidence interval of the bias — 0.

The control chart analysis should indicate that the measurement system is stable before the bias is evaluated. Analysis of Results — Numerical 5 Obtain the X from the control chart 6 Compute the bias by subtracting the reference value from X.

The calculated bias is therefore 0. Using a spreadsheet and statistical software, the supervisor generated the numerical analysis Table III-B 3. Since zero falls within the confidence interval of the bias Check mastering procedure. This can show up in the stability analysis and will suggest the maintenance or refurbishment schedule.

Review calibration procedure. Review measurement instructions. If the measurement system has non-zero bias, where possible it should be recalibrated to achieve zero bias through the modification of the hardware, software or both.

If the bias cannot be adjusted to zero, it still can be used through a change in procedure e. Since this has a high risk of appraiser error, it should be used only with the concurrence of the customer. Analysis of Results — Graphical 4 Calculate the part bias for each measurement and the bias average for each part.

For the linearity to be acceptable this bias must be zero. Five parts were chosen throughout the operating range of the measurement system based upon documented process variation. Each part was measured by layout inspection to determine its reference value.

Each part was then measured twelve times by the lead operator. The parts were selected at random during the study. Part 1 2 3 4 5 Reference Value 2. The data for reference value 4 appear to be bimodal. Even if the data for reference value 4 were not considered, the graphical analysis clearly shows that this measurement system has a linearity problem.

The R2 value indicates that a linear model may not be an appropriate model for these data. At this point, the supervisor ought to begin problem analysis and resolution on the measurement system, since the numerical analysis will not provide any additional insights.

In this case, it does not matter what relation tb has to t58,. Three acceptable methods will be discussed in detail in this section. The ANOVA method is preferred because it measures the operator to part interaction gauge error, whereas the Range and the Average and Range methods does not include this variation. As presented, all methods ignore within-part variation such as roundness, diametric taper, flatness, etc. The ANOVA approach can identify appraiser-part interaction but it can also evaluate other sources of variation which is the reason why it was included.

Historically, the assumption is made that the interaction is zero, in which case the results of both approaches are equivalent.

With that said, the ANOVA approach is preferred because of its flexibility if the user has access to a appropriate computer program. If not, the X bar and R approach is appropriate and can be done manually or via a computer program. The determination of how to handle within-part variation needs to be based on a rational understanding of the intended use of the part and the purpose of the measurement.

Finally, all of the techniques in this section are subject to the prerequisite of statistical stability. Although reproducibility is usually interpreted as appraiser variation, there are situations when this variation is due to other sources of variation. For example, with some in-process measurement systems there are no human appraisers. If all the parts are handled, fixtured and measured by the same equipment, then reproducibility is zero; i.

If, however, multiple fixtures are used, then the reproducibility is the between-fixture variation. Range Method The Range method is a modified variable gage study which will provide a quick approximation of measurement variability.

This method will provide only the overall picture of the measurement system. It does not decompose the variability into repeatability and reproducibility. It is typically used as a quick check to verify that the GRR has not changed. The Range method typically uses two appraisers and five parts for the study. In this study, both appraisers measure each part once.

The range for each part is the absolute difference between the measurement obtained by appraiser A and the measurement obtained by appraiser B. The sum of the ranges is found and the average range R is calculated.

Let appraiser A measure n parts in a random order 45 and P F enter the results in row 1. Enter data in rows 2, 7 and Record the data in the appropriate column. For example if the first piece measured is part 7 then record the result in the column labeled part 7. If three trials are needed, repeat the cycle and enter data in rows 3, 8 and Let appraiser B measure the first part and record the reading in row 6. Let appraiser C measure the first part and record the reading in row Repeat this cycle and enter the results in rows 3, 8, and 13, if three trials are to be used.

Let appraiser A measure all 10 parts and enter the reading in row 1. Then have appraiser A repeat the reading in a different order and enter the results in rows 2 and 3. Do the same with appraisers B and C. Although the form was designed with a maximum of 10 parts, this approach is not limited by that number. As with any statistical technique, the larger the sample size, the less sampling variation and less resultant risk will be present.

Circle those that are beyond this limit. Identify the cause and correct. Repeat these readings using the same appraiser and unit as originally used or discard values and re-average and recompute R and the limiting value from the remaining observations.

The specific graphical tools used depend on the experimental design employed to collect the data. A systematic screening of the data for apparent special causes of variations by using graphical tools should precede any other statistical analysis. The following are some of the techniques which have proven to be useful. See also the Analysis of Variance Method. The data from the measurement system analysis can be displayed graphically by control charts.

The averages of the multiple readings by each appraiser on each part are Average plotted by appraiser with part number as an index. This can assist in Chart determining consistency between appraisers. The grand average and control limits determined by using the average range are also plotted. Since the group of parts used in the study represents the process variation, approximately one half or more of the averages should fall outside the control limits.

If the data show this pattern, then the measurement system should be adequate to detect part-to-part variation and the measurement system can provide useful information for analyzing and controlling the process. If less than half fall outside the control limits then either the measurement system lacks adequate effective resolution or the sample does not represent the expected process variation. No appraiser-to-appraiser differences are readily apparent. The reason being that no matter how large the measurement error Chart may be, the control limits will allow for that error.

That is why the special causes need to be identified and removed before a measurement study can be relevant. The ranges of the multiple readings by each appraiser on each part are plotted on a standard range chart including the average range and control limit s. From the analysis of the data that are being plotted, several useful interpretations can be made. If all ranges are in control, all appraisers are doing the same job. If one appraiser is out-of-control, the method used differs from the others.

If all appraisers have some out of control ranges, the measurement system is sensitive to appraiser technique and needs improvement to obtain useful data. Neither chart should display patterns in the data relative to the appraisers or parts. The ranges are not ordered data. Normal control chart trend analysis must not be used even if the plotted points are connected by lines. Stability is determined by a point or points beyond the control limit; within-appraiser or within-part patterns.

Analysis for stability ought to consider practical and statistical significance. It Histogram also shows their combined frequency distribution. Issues such as whether bias or lack of consistency exists in 7 the measurements taken by the 6 appraisers, can be identified even 5 before the data are analyzed.

They also indicate that only 0 appraiser B has a symmetric form. Appr A 1. Figure III-B 15 shows the data collection sheet Calculations on which all study results are recorded. Figure III-B 16 displays a report sheet on which all identifying information is to be recorded and all calculations made according to the prescribed formula. Reproducible blank forms are available in the Sample Forms section.

The procedure for doing the calculations after data have been collected is as follows: The following refers to Figure III-B 15 1 Subtract the smallest reading from the largest reading in rows 1, 2 and 3; enter the result in row 5. Do the same for rows 6, 7, and 8; and 11, 12, and 13 and enter results in rows 10 and 15, respectively. Do the same for rows 10 and 15 to obtain Rb and Rc. Add them together and divide by the number of appraisers and enter results R average of all ranges.

Note: D 4 is 3. Correct the special cause that produced the out-of-control condition. If the data were plotted and analyzed using a control chart as discussed previously, this condition would have already been corrected and would not occur here. Repeat this for rows 6, 7 and 8; and 11, 12 and 13, and enter the results in the blocks for X b and X c in rows 9 and 14, respectively. Enter the results in row 16 in the spaces provided for part average.

R p is the range of part averages. The analysis will estimate the P F variation and percent of process variation for the total measurement system and its components repeatability, reproducibility, and part variation. This information needs to be compared to and complement the results of the graphical analysis. Since the appraiser variation is contaminated by the equipment variation, it must be adjusted by subtracting a fraction of the equipment variation. If a negative value is calculated under the square root sign, the appraiser variation AV defaults to zero.

The results from a valid computer program may differ from the example results in the second or greater decimal place but the final analysis will remain the same. When comparing measurement error from a GRR study to a tolerance, this is the same as comparing it to a production process with a Pp of 1.

OEM customers rarely expect process variation to have as low a Pp k as 1. It may make more sense to compare the measurement variation to a target production process performance level which meets the customer requirement.

The results of this percent total variation need to be evaluated to determine if the measurement system is acceptable for its intended application. Either or both approaches can be taken depending on the intended use of the measurement system and the desires of the customer. The final step in the numerical analysis is to determine the number of distinct categories that can be reliably distinguished by the measurement system. If the reader chooses to increase the coverage level, or spread, of the total measurement variation to Note: The approach used in the 4th Edition is to compare standard deviations.

This is equivalent to using the multiplier of 6 in the historical approach. Awareness of which multiplying factor is used is crucial to the integrity of the equations and resultant calculations.

This is especially important if a comparison is to be made between measurement system variability and the tolerance.