Updated Force Measurement Statistical Tool Jason Beardsley and Bob Fox

Background of Issue  Persistent issues over the interpretation of force measurement data taken on parts or fasteners in plants and compared to specifications. –Some Joint Ergonomics Teams look at the mean of measurements, others look at the maximum of the measurements; –Persistent questions on details such as sample size, reliability of measurement process, variation in measurements, etc. –Measurements taken under lab vs. field conditions can be a potential source of conflict.

Background of Issue  While guidelines are available on how to take measurements, there is no consistent guidance on how to analyze the sample measurement data.  A viable statistical tool for consistent force measurement analysis is as much a matter of policy as it is of statistical validity.

Some Basic Terms and Concepts  Population – the large group of parts, etc. that is of interest to you.  Sample – a smaller group of items that is taken from the larger population. There are different ways that samples can be drawn from the population.  Specification – the value that you want to compare the sample to and that the mean of the sample should not exceed.

Some Basic Terms and Concepts  Test statistic – is computed from the sample mean, the specification and the standard error of the sample.  Hypothesis testing – statistically testing how two values compare (e.g., a specification and the mean of a sample). Formulated as a statement. These are embedded in the tool

What Statistical Testing Does The appropriate hypothesis, along with a test statistic, significance value and understanding of probabilities, allows us to make inferences about whether or not the mean of the sample exceeds the specification and should be rejected.

While the statistics may be complex, the goal here is to have a tool that is simple to use and understand.

When to Use the Statistical Tool  You have a given force specification.  You have at least 10 parts or conditions.  The insertion force for each part or condition can be independently measured.

When to Use the Statistical Tool  The force measurements cluster near the specification and may involve measurements both above and below the specification.  Special case - You have fewer than 10 parts.

Using the Statistical Tool  Asks for entry of specification that measurement data is to be compared against.  Request measurements (special tab for smaller than 10 measurements).  Will first test the variation or the spread in the values of the measurements.  If the variation is too great then it will return a message stating that the data variation is excessive.

Using the Statistical Tool  If the variation is acceptable, then the tool performs a one-tailed (right-tail) t-Test at α=0.05 on the data to compare it to the specification (H A : µ > spec., embedded in the tool).  Messages are returned either accepting the sample as being within the spec or rejecting the sample.

Data Scatter Plot  The program returns a scatter plot of the order of the measurements along with a line indicating the entered specification and the mean of the sample and the 10% limit range above the spec.  This is a good visual aid to see how your measurements vary about the specification.

“Upper Limit” represents 10% above the Specification as a reference

Other Tool Features  Also incorporates information or tabs for: –Important Notes; –Check if Reject or Warning; –Compare two samples; –Excessive variation; –Small sample sizes; –Force measurement methodology; –Sample Size Estimator.

Issues With Large Measurement Spreads  There are always concerns with the possibility of a big spread in the sample measurements  The larger the spread in the measurements, the greater is the standard error and the test loses of power to reject the null hypothesis (H o ).  The tool incorporates additional tests to screen measurement data.

How the Tool Tests Measurement Variation  The tool first performs a 75 th Percentile test (or ‘third quartile test’) to compare The 75 th percentile or third quartile of the data set to 1.2 x the spec.  If the 75 th percentile value exceeds 1.2 x spec (i.e., 20% above the spec) then a message is returned indicating that testing cannot be performed due to excessive variation in measurements.

How the Tool Tests Measurement Variation  If the 75 th percentile test passes then the tool performs t-Test and figures the coefficient of variation (COV=StdDev/Mean).  If COV is > 0.20 then message returned warning that the data show relatively high variation regardless of what test results indicate.

IMPORTANT NOTES INTERPRETING RESULTS

Other Important Notes  The Stats Tool is designed to analyze data where measurements are taken once each on from 10 to 30 parts or items. It is not intended to analyze data where repeated measurements are taken on the same part (other statistical tools for that depending on what you are looking at).  Do not use the Stats Tool for dolly force measurements – each dolly is its own sample. Follow UAW-GM Guidelines for the Snook Tool.  Special provisions for special users.  Enhancements to the Stats Tool will continue to be investigated.

Check if Reject or Warning Tab  This page will provide additional information about the sample that you can refer to in case of a warning about the data or a rejection.  It may allow you to make judgments on the practical significance of the variation of the data from the specification.

Check if Reject or Warning Tab

Calculates and gives a range of the percent of data that exceeds specification. Calculates 95 th percentile value of data range Compares 95 th percentile value to force specification for magnitude of difference.

Check if Reject or Warning Tab: Outlier Check  While data outliers (unusually large or small values) are usually checked during the measurement process, there may be outliers in the final data sample that are suspect.  The Outlier Check will allow you to check a measurement to see if it is statistically within the range of the data. If it is not, then you may consider a re-measure or the removal of the outlier from the analysis.

Outlier Check Enter value of suspected outlier Program returns message indicating if value is within or outside of range.

Comparing Two Samples  Use this tab if you have two samples of measurements that you would like to compare against each other.  The samples may be from two different suppliers, batches, plants, etc.  The number of measurements in each sample do not have to be the same.  The test performed is a two-sample t-test that does not assume that the variances of the samples are equal.

Comparing Two Samples

Small Sample Sizes  Less than 10 measurements will constitute a small sample size.  Conventional statistical testing is not reliable for such small samples –a set mathematical approach for drawing good inferences from such data does not exist.

How the Tool Tests Small Sample Sizes  A separate tab contains instructions on what to do about small sample sizes.  Testing criteria for sample samples: –Accept the sample is the mean is ≤ spec and the max measurement is no more than 1.15 x the spec (i.e., 15% above the spec). –Reject the sample if the mean is > the spec or if the max measurement is more than 1.15 times the spec.

Small Sample Size Data Scatter Plot  A data scatter plot is also provided for the small sample size analysis.  The plot shows the specification, the mean of the sample measurements and the value of 1.15 times the specification.

Small Samples – Small Populations  REMEMBER that the testing of a very limited number of items – where the small sample IS the population – must be regarded as tentative.  Testing must be repeated as the item or part reaches its final form.

Further Investigation  In the case of sample rejection due to excessive variation: –Check measurement method and conditions; –Consider more advanced statistical analyses such as Gage Repeatability and Reproducibility; –Depending upon circumstances, call upon your divisional ergonomics support for assistance.

Notes on How to Reduce Variation When Taking Measurements  Work out and use the same measurement technique for each measurement.  Use the same force gage and keep its calibration up to date.  Have the same person take the measurements. If multiple people take the same measurements, make sure that they are trained in taking measurements. Their measurements should largely agree.

Notes on How to Reduce Variation When Taking Measurements  Make sure that the capacity of your gage is suitable for the magnitude of force measured.  Make sure that the end effecter of the gage is appropriate for the contact point on the part. Each force measurement gage kit has a variety of end effectors. Minimize the opportunity for slipping.  Identify any other factors that may influence the measurement and try to control for them.

Remember that the Statistical Tool is NOT designed for testing differences between gages or analysts. Keep the sources of variation minimal. Other statistical techniques can be used to study or compare different gages, analysts or methods.

Sample Size Estimator  In general, for most ergonomics evaluations of acceptable forces compared to specifications, a sample size from 10 to 30 items will be sufficient.  However, for special or more detailed engineering studies it may be a good idea to consider the calculation of a study sample size if sufficient data exists for the calculation.  The Sample Size Estimator has three tabs - a background/Assumptions/How to Use tab; a Sample Size Range tab and an Exact Sample Size Calculator.

Sample Size Estimator

Sample Size Estimator - Range For each estimator, realistically determine what your acceptable precision is as a percent of the mean of the measurements.

Sample Size Estimator - Exact Most typically an alpha of 0.05 is used

For Further Help  More advanced statistical techniques may be used to help with specific problems and questions. –Other problem solving resources may be available to you. –Call Bob Fox for questions as well

Examples

Exercise 1  You are studying insertion forces on a coolant temperature sensor supplied by two different manufacturers.  You are able to measure 15 to 20 different sensors from each.  You’ve been asked to determine is there is a difference between the measured forces of the two samples.  Analyze the data with the Compare Two Samples Stats Tool.

Sample Data – Manufacturer A Sample 1: 10.4 Sample 2: 14.9 Sample 3: 13.3 Sample 4: 11 Sample 5: 11.1 Sample 6: 12.9 Sample 7: 15 Sample 8: 12.4 Sample 9: 13.2 Sample 10: 10.3 Sample 11: 13.6 Sample 12: 11.9 Sample 13: 12.6 Sample 14: 13.1 Sample 15: 11.2 Sample 16: 14.1 Sample 17: 14.3 Sample 18: 12.1 Sample 19: 11.1 Sample 20: 14.1

Sample Data – Manufacturer B Sample 1: 18 Sample 2: 18.4 Sample 3: 18.7 Sample 4: 18.6 Sample 5: 18.9 Sample 6: 19.8 Sample 7: 19.5 Sample 8: 18 Sample 9: 16.5 Sample 10: 14.6 Sample 11: 17.7 Sample 12: 18.5 Sample 13: 18 Sample 14: 19.2 Sample 15: 17.3 Sample 16: 18.3 Sample 17: 18 Sample 18: 17.9 Sample 19: 15.7

Comparing Manufacturer A to Manufacturer B

Exercise 1 Continued  The Stats tool showed that there is a statistically significant difference between Manufacturers A and B with Manufacturer A having the lower mean force.  Suppose that the specification is 13 lb. Does Manufacturer A meet the specification?

Manufacturer A Results

Exercise 2  Suppose that you have a new manually inserted connector for a new program.  The specification is 60 N and you are only able to get six of the connectors for testing.  You get the following insertion force measurements (N): 40; 44; 45; 67; 74; 46.  Run the data and interpret the results.  What questions may you want to ask about the connectors?