A wavelet-based procedure for process fault detection

To detect faults in a time-dependent process, we apply a discrete wavelet transform (DWT) to several independently replicated data sets generated by that process. The DWT can capture irregular data patterns such as sharp "jumps" better than the Fourier transform and standard statistical procedures without adding much computational complexity. Our wavelet coefficient selection method effectively balances model parsimony against data reconstruction error. The few selected wavelet coefficients serve as the "reduced-size" data set to facilitate an efficient decision-making method in situations with potentially large-volume data sets. We develop a general procedure to detect process faults based on differences between the reduced-size data sets obtained from the nominal (in-control) process and from a new instance of the target process that must be tested for an out-of-control condition. The distribution of the test statistic is constructed first using normal distribution theory and then with a new resampling procedure called "reversed jackknifing" that does not require any restrictive distributional assumptions. A Monte Carlo study demonstrates the effectiveness of these procedures. Our methods successfully detect process faults for quadrupole mass spectrometry samples collected from a rapid thermal chemical vapor deposition process.