Liberty Mutual

Overview / Introduction

The Snook tables (Liberty Mutual Tables) are a collection of data sets compiled from studies based on a psychophysical approach to material-handling tasks.  These tables are used to determine safe loads for lifting, lowering, carrying pulling, and pushing.  The tables take into account different population percentiles, gender, and frequency of activity. The Liberty Mutual tables make some assumptions, such as a standard break schedule is used, work occurs in the horizontal plane, and that all tasks being assessed are 2-handed.  Despite these restrictions, the Liberty Mutual tables have proven useful in automotive assembly in reducing the risk associated with manual material handling tasks.
However, while using these tables to analyze a work place, Ergonomists often have to select from discrete data points closest to the actual work place parameters thereby reducing accuracy of results. To compound the problem further, multiple interrelated variables are involved, making it difficult to analyze parameters intuitively.  For example, it can be difficult to answer questions such as, does reducing the lifting height lower the recommended lifting weight, if the lifting distance is increased?  To resolve such issues, this paper presents a new methodology for implementing the Snook tables using multi variable regression

Objectives / Methods


In this research a method involving multiple linear regressions is used to interpolate between the data points in the tables, thereby adding higher fidelity to the tables. The users are no longer tied down to the fixed values published in the tables. While designing work stations with digital humans, programming regression equations into the digital environment allows designers access to an instantaneous wide range of results. This allows for a range of workplace configurations. The main objectives of the liberty mutual/Snook table module are as follows

  1.  Digitize the existing Snook tables
  2. Perform multiple linear regression between the points to allow designers greater fidelity in using the tables
  3. Allow designers to study the interaction between the different variables that make up the Snook tables


A method involving multiple linear regressions is used to interpolate between the data points from the tables, a summary of the steps involved is illustrated in figure 1. These regression equations model the Liberty Mutual-Snook dataset.

Figure 1: Summary of steps involved in generating regression equations for Liberty Mutual tables

The data available in the Liberty Mutual tables are organized into five basic tables based on task; the tasks are carry, push, pull, lift and lower. There are separate tables for male and female workers. The predictor variable is the maximum acceptable lifting weight (Wt) in kilograms. The data in the tables was rearranged according to percent of the population capable of doing the task. These percents are 10,25,50,75 and 90. Percent of population capable is the percentage of the population capable of doing a particular task. A 75% of population means that 75% of the people in a population group are capable of performing the task; this differs from 75 percentile, which means that only 25% of the population is capable of performing the task. These percents were not used as independent variables in the regression equations. The rationale behind this decision was because no foreseeable use could be seen for interpolation between percentages in a digital human application. With the regression analysis presented here each percent of population capable would yield a regression equation. The complete Snook data set was analyzed and there were 70 individual tables for regression models.


Three kinds of models were analyzed – linear, polynomial and transform models. Linear models are the simplest form of multiple variable regression and is a good starting point for more complex models. P-values of the independent and interactive terms are established to determine the significance of each term in the equation. All the linear models analyzed were nested models since they are derived from the same complete model (model 1). A popular approach to determining the best model from a set of nested models is by means of a F-test. The F-test is performed on the change in R2 values of the models. The F-test is an additional test performed between the adjacent models in order to establish the best linear model with the least complexity. The linear models were found to have curvature in them. In order to fit the curvature to a regression model, higher order terms were added to the linear equations. In addition   logarithmic transformations were also applied to the predictor variable to get the best fit. A transformation using logarithms might result in a better fit. A useful method for such transformations is the Box-Cox method (Box G, Cox, D.R., 1964).

It is not possible to use the F-test to evaluate the best transform model since they are not nested (i.e. they are all not subsets of the same parent complete model). Instead the Akaike Information Criterion (AIC) is used (Akaike.H, 1973). The AIC penalizes models for increased complexity while evaluating the fit (Bozdogan, H, 1987), (Bozdogan, H, 2000). To choose the best model among these   models, essentially the best of the best, the AIC method was used to determine the best model with the least complexity. The simplest model with the best results was chosen.   The lower the AIC value, the less the complexity of the model for the regression fit.


 The newly developed regression equations allow the analyst to use actual job parameters to evaluate the task. The actual job parameters are inserted into the regression equations and the maximum acceptable forces are calculated. In contrast the results from the traditional ergonomic analysis are arrived at by choosing parameter values from the Liberty mutual data set that are closest to the task parameters.

The regression equations were programmed into the digital human environment based on the Santos™ model (figure 2). The regression models have the distinct advantage in allowing the task designer the freedom to vary the task parameters and instantaneously judge the ergonomic feasibility based on the results. The interface also populates the tables based on information available in the software, thereby reducing the number of fields the user is expected to fill. On the side of caution, the regression results are always displayed in conjunction with the results arrived at by the traditional methods in the generated report (figure 3). The regression models and the effect of the individual parameters on the maximum acceptable force will also have to be studied further to increase their accuracy and robustness.



Figure 2: Interface in Santos™ for assessing Liberty Mutual \Snook database regression results


Figure 3: Sample report generated by the Santos Liberty  Mutual\Snook analyzer


Works Cited

 H. Akaike. (1973)  Information theory and an extension of maximum likelihood principle. In B. N. Petrov and F. Csaki (eds),Second International Symposium on Information Theory, Akademiai Kiado, Budapest, 1973, pp. 267–281.

Box, George E. P.; Cox, D. R. (1964). An analysis of transformations. Journal of the Royal Statistical Society, Series B 26: 211-246.

Bozdogan, H  ( 1987) Model selection and Akaike's Information Criterion (AIC): The general theory and its analytical extensions. Psychometrika,  52, 3, 345-370

Bozdogan, H.(2000) Akaike's Information Criterion and Recent Developments in Information Complexity.  Journal of Mathematical Psychology 44, 62-91 

Related Publications

“A Multi-Variable Regression Model for Ergonomic Lifting Analysis with Digital Humans” Anith Mathai, Jinzengh Li, Karim Abdel-Malek, Lindsey Knake, Julie Wisch, The University of Iowa Christina Godin,Sandalwood,Detroit,MI,USA Jim Chiang,Ford Motor Company, Detroit, MI, USA Presented and SAE-DHM 2008, Pittsburgh.

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