A case study on monitoring polynomial profiles in the automotive industry

In some statistical process control applications, the quality of a process or product can be characterized by a relationship between a response variable and one explanatory variable, which is referred to as profile. We give an example here of a profile that can be described using a polynomial model. This example comes from the automotive industry, where one of the most important quality characteristics of an automobile engine is the relationship between the torque produced by an engine and the engine speed in revolutions per minute. We find for this data set that a second‐order polynomial works well. In addition, we show that there is autocorrelation within each profile, thus an ordinary least‐square method that ignores the autocorrelation is inappropriate. We propose a linear mixed model method as an alternative approach. After the reduction of the data to a series of parameter estimates, we then conduct a step‐by‐step Phase I analysis of the polynomial profiles monitoring using a T²‐based procedure to check the stability of the process and whether or not there are outlying profiles. The remaining profiles are used to form the estimated mean vector and variance–covariance matrix to be used in Phase II studies. Finally, a brief discussion is presented to show how one can use these parameters in Phase II.