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YW2017
Level III

Statistical DOE and Modeling for Repeated Measures in Rubber Research (2021-US-EPO-909)

Level: Intermediate

 

Wenzhao Yang, Statistician, Dow Chemical Company

 

EPDM is a synthetic rubber widely used in applications such as transportation, infrastructure, sports, leisure, and appliance. Dow, as a leading manufacturer of EPDM, continuously innovates in the development of EPDM products and applications to achieve superior properties, including color stability property in automotive weatherstrip. In this Dow case study, the color stability properties of different EPDM rubbers were repeatedly measured over time (repeated measures). The objective of this study is to develop fundamental understanding of EPDM weatherstrip discoloration mechanism and validate hypotheses on EPDM microstructure factors. Efficient DOE strategy and proper statistical models are developed for cause and effect conclusion. We analyzed the data using two methods: linear regression and random coefficient regression. Linear regression completely pools the data by assuming a common variance for all samples across time. Random coefficient regression incorporates the sample-specific effects and provides more inference in variability between samples over time. We identified significant structure effects for color stability property by comparing different methods. In this poster, we demonstrate the power of DOE and statistical modeling for research and fundamental study.

 

 

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  Hello everyone, my name is Wenzhao Yang and I'm a statistician at Dow. Today i'm going to talk about statistical DOE and modeling development for repeated measures in rubber research.
  Before we talk about the methods, I just want to add a little background for this talk.
  EPDM is a synthetic rubber, widely used in applications such as transportation, infrastructure, sports, leisure, and appliance.
  Dow is a leading manufacturer of EPDM. We continuously innovate and develop our EPDM products to achieve superior and user properties in various
  applications just mentioned. This talk we're focused on EPDM based automotive weather strip application. One of the key performance metric is called color stability property.
  Color stability property is measured repeatedly over time on the same experimental unit. it is defined as repeated measures in statistics.
  And time dependency may exist between repeated color measures which is known as auto correlation.
  A new technical development in our work is we developed a Monte Carlo simulation based DOE strategy for repeated measures to assess the statistical power of detecting active effects prior to the data collection.
  Let's move on to the objective and the methods.
  The objective in this application is to develop a fundamental understanding of EPDM weather strip discoloration mechanism and validate hypotheses on EPDM polymer macro structure factors for color stability property.
  The color stability test experiments follows the industrial rubber manufacturers standards as shown in the figure one.
  We start with a list of synthesize EPDM polymers with different micro structures. Then we blend them with other consistent formulation ingredients under the same process condition.
  After compounding curing and sample preparation samples are aging in a weathering chamber. Delta E calculated from
  LAB color measurements is a critical performance metric for color stability property. It quantifies difference between the initial color and the color at different aging times of a cured sample.
  We developerd a D-optimal DOE to select a representative subset from our available polymers. We use the Monte Carlo simulation to evaluate number of repeated measures needed to obtain
  80% of statistical power detecting detecting the main and the interaction effects. The collected data has unequal time intervals among repeated color measurements.
  Therefore, we developed a random coefficient model, RCM, to incorporate the sample specific effects and provides more influence in variability between samples over time. We also compared RCM with linear regression model.
  Which completely proves the data by assuming a common variance for all samples across time.
  With the methods described here are the key results for this work.
  Figure two shows a Monte Carlo simulation based power analysis results for main and interaction effects three under different scenarios.
  If we expect medium auto correlation level, which is about .5, it will adjust and time points. Number of repeated measures should be at least nine
  per cured sample. If the autocorrelation between adjacent time points is really high about .9 the
  statistical power drops significantly for most of the effects. Since we selected relatively large time intervals between repeated color measures for all DOE samples we assume that the repeated measures that will have medium level
  autocorrelation there for nine repeated color measures per cured sample are collected for this DOE.
  A general RCM model is showing in Figure three here, where we have a sample specific random intercept and sloping effects.
  In addition to the main and interaction effects of the EPDM structural factors in a linear regression model.
  The random effects covariance parameter estimate table here shows that there are significant difference in starting Delta E
  and changing rate of Delta E among the cured samples. This indicates that is really important to account for variability between samples over time.
  The profile for the RCM model shows that the confidence interval around the prediction line for our input factors are relatively narrow comparing to the scale of the Delta E in our data collection.
  So the figure four shows that if you treating data as independent in a least square model could really see where they inflate degree of freedom as showing the top graph and
  see where they inflate the degree of freedom, so we would be overconfident about our significance results for the model effects in the model compared to RCM models where we assume like the data should be time dependent.
  And the model prediction plot and the residual plot in figure five shows that RCM has good model fit and meets our model assumptions.
  Our conclusion for this work is we identified dominant microstructure factors and significant interaction between two microstructure factors suggesting alternative polymer design we developed
  fundamental understanding of EPDM weatherstrip discoloration mechanism and demonstrate the power of statistical DOE and modeling using JMP to support the development of new EPDM rubbers with superior color stability.