Engineering Statistics Handbook Episode 4 Part 6 potx

2.6.1.1.1. Database of resistivity measurements http://www.itl.nist.gov/div898/handbook/mpc/section6/mpc6111.htm (10 of 15) [5/1/2006 10:13:12 AM] 2.6.1.1.1. Database of resistivity measurements http://www.itl.nist.gov/div898/handbook/mpc/section6/mpc6111.htm (11 of 15) [5/1/2006 10:13:12 AM] 2.6.1.1.1. Database of resistivity measurements http://www.itl.nist.gov/div898/handbook/mpc/section6/mpc6111.htm (12 of 15) [5/1/2006 10:13:12 AM] 2.6.1.1.1. Database of resistivity measurements http://www.itl.nist.gov/div898/handbook/mpc/section6/mpc6111.htm (13 of 15) [5/1/2006 10:13:12 AM] 2.6.1.1.1. Database of resistivity measurements http://www.itl.nist.gov/div898/handbook/mpc/section6/mpc6111.htm (14 of 15) [5/1/2006 10:13:12 AM] 2.6.1.1.1. Database of resistivity measurements http://www.itl.nist.gov/div898/handbook/mpc/section6/mpc6111.htm (15 of 15) [5/1/2006 10:13:12 AM] Pooled level-1 standard deviations (ohm.cm) Graphs of reproducibility and stability for probe #2362 Averages of the 6 center measurements on each wafer are plotted on a single graph for each wafer. The points (connected by lines) on the left side of each graph are averages at the wafer center plotted over 5 days; the points on the right are the same measurements repeated after one month as a check on the stability of the measurement process. The plots show day-to-day variability as well as slight variability from run-to-run. Earlier work discounts long-term drift in the gauge as the cause of these changes. A reasonable conclusion is that day-to-day and run-to-run variations come from random fluctuations in the measurement process. Level-2 (reproducibility) standard deviations computed from day averages and pooled over wafers and runs Level-2 standard deviations (with K - 1 = 5 degrees of freedom each) are computed from the daily averages that are recorded in the database. Then the level-2 standard deviations are pooled over: L = 2 runs for L(K - 1) = 10 degrees of freedom ● Q = 5 wafers for QL(K - 1) = 50 degrees of freedom● as shown in the table below. The table shows that the level-2 standard deviations are consistent over wafers and runs. 2.6.1.2. Analysis and interpretation http://www.itl.nist.gov/div898/handbook/mpc/section6/mpc612.htm (2 of 6) [5/1/2006 10:13:13 AM] Level-2 standard deviations (ohm.cm) for 5 wafers Level-3 (stability) standard deviations computed from run averages and pooled over wafers Level-3 standard deviations are computed from the averages of the two runs. Then the level-3 standard deviations are pooled over the five wafers to obtain a standard deviation with 5 degrees of freedom as shown in the table below. 2.6.1.2. Analysis and interpretation http://www.itl.nist.gov/div898/handbook/mpc/section6/mpc612.htm (3 of 6) [5/1/2006 10:13:13 AM] Level-3 standard deviations (ohm.cm) for 5 wafers Graphs of probe biases A graphical analysis shows the relative biases among the 5 probes. For each wafer, differences from the wafer average by probe are plotted versus wafer number. The graphs verify that probe #2362 (coded as 5) is biased low relative to the other probes. The bias shows up more strongly after the probes have been in use (run 2). 2.6.1.2. Analysis and interpretation http://www.itl.nist.gov/div898/handbook/mpc/section6/mpc612.htm (4 of 6) [5/1/2006 10:13:13 AM] [...]... [5/1/20 06 10:13: 14 AM] 2 .6. 1 .4 Effects of days and long-term stability Wafer 139 Wafer 140 http://www.itl.nist.gov/div898 /handbook/ mpc/section6/mpc6 14. htm (2 of 5) [5/1/20 06 10:13:15 AM] 2 .6. 1 .4 Effects of days and long-term stability Wafer 141 http://www.itl.nist.gov/div898 /handbook/ mpc/section6/mpc6 14. htm (3 of 5) [5/1/20 06 10:13:15 AM] 2 .6. 1 .4 Effects of days and long-term stability Wafer 142 http://www.itl.nist.gov/div898 /handbook/ mpc/section6/mpc6 14. htm... 4 = #2 062 ; 5 = #2 362 http://www.itl.nist.gov/div898 /handbook/ mpc/section6/mpc613.htm (3 of 4) [5/1/20 06 10:13: 14 AM] 2 .6. 1.3 Repeatability standard deviations Run 2 Graph showing repeatability standard deviations for 5 probes as a function of wafers and probes Symbols for probes: 1 = #1; 2 = #281; 3 = #283; 4 = #2 062 ; 5 = #2 362 http://www.itl.nist.gov/div898 /handbook/ mpc/section6/mpc613.htm (4 of 4) ... 142 http://www.itl.nist.gov/div898 /handbook/ mpc/section6/mpc6 14. htm (4 of 5) [5/1/20 06 10:13:15 AM] 2 .6. 1 .4 Effects of days and long-term stability http://www.itl.nist.gov/div898 /handbook/ mpc/section6/mpc6 14. htm (5 of 5) [5/1/20 06 10:13:15 AM] 2 .6. 1.5 Differences among 5 probes Run 2 Graph of differences from wafer averages for each of 5 probes showing that probe #2 362 continues to be biased low relative... to the other probes Symbols for probes: 1 = #1; 2 = #281; 3 = #283; 4 = #2 062 ; 5 = #2 362 http://www.itl.nist.gov/div898 /handbook/ mpc/section6/mpc615.htm (2 of 2) [5/1/20 06 10:13:15 AM] 2 .6. 1 .6 Run gauge study example using Dataplot™ 2 Measurement Process Characterization 2 .6 Case studies 2 .6. 1 Gauge study of resistivity probes 2 .6. 1 .6 Run gauge study example using Dataplot View of Dataplot macros for... http://www.itl.nist.gov/div898 /handbook/ mpc/section6/mpc612.htm (6 of 6) [5/1/20 06 10:13:13 AM] 2 .6. 1.3 Repeatability standard deviations Run 2 Graph of repeatability standard deviations for probe #2 362 6 days and 5 wafers showing that repeatability is constant across wafers and days http://www.itl.nist.gov/div898 /handbook/ mpc/section6/mpc613.htm (2 of 4) [5/1/20 06 10:13: 14 AM] 2 .6. 1.3 Repeatability standard deviations Run 1 Graph...2 .6. 1.2 Analysis and interpretation Formulas for computation of biases for probe #2 362 Biases by probe are shown in the following table Differences from the mean for each wafer http://www.itl.nist.gov/div898 /handbook/ mpc/section6/mpc612.htm (5 of 6) [5/1/20 06 10:13:13 AM] 2 .6. 1.2 Analysis and interpretation How to deal with bias due to the probe Probe #2 362 was chosen for the certification... D, E, and F of run 2 are larger in some instances than for the other days 3 and 4 Interpretation: Probe #2 362 appears as #5 in the plots which show that, for both runs, the precision of this probe is better than for the other probes http://www.itl.nist.gov/div898 /handbook/ mpc/section6/mpc6 16. htm (1 of 2) [5/1/20 06 10:13: 16 AM] ... #2 362 to the average of the probes 2 Include the standard deviation for the difference among probes in the uncertainty budget The better choice is (1) if we can assume that the probes in the study represent a random sample of probes of this type This is particularly true when the unit (resistivity) is defined by a test method http://www.itl.nist.gov/div898 /handbook/ mpc/section6/mpc612.htm (6 of 6) ... 2) 3 Probe effect on repeatability (run 1) 4 Probe effect on repeatability (run 2) 5 Reproducibility and stability Results and Conclusions The links in this column will connect you with more detailed information about each analysis step from the case study description 1 and 2 Interpretation: The plots verify that, for both runs, the repeatability of probe #2 362 is not dependent on wafers or days, although . #283; 4 = #2 062 ; 5 = #2 362 2 .6. 1.3. Repeatability standard deviations http://www.itl.nist.gov/div898 /handbook/ mpc/section6/mpc613.htm (4 of 4) [5/1/20 06 10:13: 14 AM] Wafer 139 Wafer 140 2 .6. 1 .4. . stability http://www.itl.nist.gov/div898 /handbook/ mpc/section6/mpc6 14. htm (2 of 5) [5/1/20 06 10:13:15 AM] Wafer 141 2 .6. 1 .4. Effects of days and long-term stability http://www.itl.nist.gov/div898 /handbook/ mpc/section6/mpc6 14. htm. [5/1/20 06 10:13:15 AM] Wafer 142 2 .6. 1 .4. Effects of days and long-term stability http://www.itl.nist.gov/div898 /handbook/ mpc/section6/mpc6 14. htm (4 of 5) [5/1/20 06 10:13:15 AM] 2 .6. 1 .4. Effects