Abstract
Analysis of footprint data is important in the tire industry. Estimation procedures for multiple change points and unknown parameters in a segmented regression model with unknown heteroscedastic variances are developed for analyzing such data. Our approaches include both likelihood and Bayesian, with and without continuity constraints at the change points. A model selection procedure is also proposed to choose among competing models for fitting a middle segment of the data between change points. We study the performance of the two approaches and apply them to actual tire data examples. Our Maximization－Maximization－Posterior (MMP) algorithm and the likelihood－based estimation are found to be complimentary to each other.
Highlights
Footprint data in the tire industry is important to engineers in ascertaining many important features of the tire that affect its performance and endurance
A significant change in the ratio of the footprint width to footprint length of a newly designed tire after testing for say 1,000 hours at 28 per square inch (PSI) inflation and at a constant load indicates that the tire is wearing unevenly, which will lead to safety and performance issues
The change point analysis methodology we develop will be limited to that relevant to our footprint data analysis, the methodology should be applicable to data from other application fields
Summary
Footprint data in the tire industry is important to engineers in ascertaining many important features of the tire that affect its performance and endurance. In our case of the footprint data (see Figures 2 and 3), the number of interesting change points are known to be two, the location of changes are unknown and to be estimated, the errors are independent to each other but are heteroscedastic from one segment to the another, the reasonable regression functions are segmented polynomials with unknown coefficients in which the polynomial order in the middle segment may need to be determined (based on the data or the type of tires under study), the changes can be in both the parameters of the regression function and the error variances while the change type appears to be continuous ( we shall develop estimation procedures with and without continuity, under the likelihood approach), and the detection process is the “looking-back” process (i.e. not those used in sequential analysis). They include process control in engineering, disease outbreaks studied in epidemiology, the effects of an intervention that is of interest in medicine, and the behavior of an economical indicator over time in finance
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