The application of moving average control charts for evaluating magnetic field quality on an individual magnet basis

SSC Collider Dipole Magnet field quality specifications define limits of variation for the population mean (Systematic) and standard deviation (RMS deviation) of allowed and unallowed multipole coefficients generated by the full collection of dipole magnets throughout the Collider operating cycle. A fundamental Quality Control issue is how to determine the acceptability of individual magnets during production, in other words taken one at a time and compared to the population parameters. Provided that the normal distribution assumptions hold, the random variation of multipoles for individual magnets may be evaluated by comparing the measured results to +/- 3 x RMS tolerance, centered on the design nominal. To evaluate the local and cumulative systematic variation of the magnets against the distribution tolerance, individual magnet results need to be combined with others that come before it. This paper demonstrates a Statistical Quality Control method (the Unweighted Moving Average control chart) to evaluate individual magnet performance and process stability against population tolerances. The DESY/HERA Dipole cold skew quadrupole measurements for magnets in production order are used to evaluate non-stationarity of the mean over time for the cumulative set of magnets, as well as for a moving sample