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Binomial Test for Oscillations

This research paper discusses the use of a binomial test to detect oscillations in SCT barrel modules at high thresholds. The presence of oscillations is quantitatively measured and tested for modules with low occupancy. The study analyzes the residuals, hit distributions, and S-curves to determine the presence and magnitude of oscillations.

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Binomial Test for Oscillations

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  1. Binomial Test for Oscillations SCT Barrel Modules R. Ely LBL CERN SCT week

  2. Motivation • A quantitative measure of the presence of oscillations • Test at high thresholds where the occupancy is less than 5% CERN SCT week

  3. Strategy • Ideal module – strips are independent • If there is no correlation between strips then the probability of n hits on one side when the probability of a hit on a single strip is f is a binomial distribution where g = 1-f and N = 768 strips CERN SCT week

  4. Strategy II • If oscillations are feedback from the output of the comparator coupled into adjacent strips then we do not expect a binomial distribution. • Let Q(n) be the observed distribution of hits • Define Residual as CERN SCT week

  5. Calibrate Test • Module 61 – untrimmed • No oscillation observed in untrimmed module • The fit is superb CERN SCT week

  6. Residuals for Module 61 - untrimmed • The residuals are nearly a chi square and the number of degrees of freedom is close to the number of non zero bins in the hit distributions. • The residuals for module 61 are about equal to the number of non zero bins. CERN SCT week

  7. Hit Plots for Module 61 - trimmed • Link 1 -The distributions for high and low occupancy are very smeared. • Link 0 – No oscillations are visible in the S curves but the distributions are clearly distorted. • The ‘oscillation’ problem can exist even when it is not visible in the S curves. CERN SCT week

  8. Residuals for Module 61 - trimmed • Visible distortions of the S curves cause residuals greater than 20000. • We define the highest threshold at which ‘oscillations’ are observed as the highest threshold where R > 5000. CERN SCT week

  9. None - 0 Weak - 1 Strong - 2 Visual figure of merit CERN SCT week

  10. 0 - None 1 - weak Visual Rating of Oscillation 2 - Strong Barely visible CERN SCT week

  11. Residual vs Visual Rating Strong correlation between R and S curve distortions CERN SCT week

  12. Oscillations on Link 0 • Module LBL 136 • Large residuals and nice S curves • The hit distributions appear to have the same disease as Link 1 CERN SCT week

  13. Residuals for Mod 136 CERN SCT week

  14. Hit distributions – Module 136 Link 0 CERN SCT week

  15. S curves for Module 139 Average over entire link CERN SCT week

  16. Oscillation at High Thresholds • Can we detect oscillations at low occupancy? • We record the highest threshold with residuals greater than 5000 • Module 103 is the only example over .4 fc • Highest thr = 80mv (R = 6600, 106 events) • Occupancy = .074 strips (768 possible) • Data-calc (P(n)<5) = 166 ev, ~ 1/6000 • Are the strips contiguous? • Does this effect hit efficiency? CERN SCT week

  17. Residual Distribution of Module 103 CERN SCT week

  18. Hit distribution CERN SCT week

  19. Conclusions • Binomial test is a sensitive test for ‘oscillations’ • The numerical measure will be useful to establish correlations with temperature and Ish etc. • More experience is necessary to find the most useful parameters. • Care must be used to avoid false signals • Necessary to upgrade the Mustard firmware. CERN SCT week

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