of System due to the Hot Electron Effect 1 * exresist; 2 option ls=120 ps=75 nocenter nodate; 3 title of System due to the Hot Electron Effect ; 4 * TIME = failure time (hours) of a system due to drift caused by hot electrons; 5 * RESIST = resistance (micro ohms) of a key resistor; 6 7 data CIRCUIT; input RESIST TIME @@; RESIST2=RESIST*RESIST; 8 RESIST3=RESIST*RESIST2; RESIST4=RESIST2*RESIST2; 9 R1=RESIST-9.889; R2=R1*R1; R3=R1*R2; R4=R2*R2; 10 label TIME= RESIST= Resistance RESIST2= Squared Resistance 11 12 cards; R= Centered Resistance ; 13 10.54 4.62 10.18 4.99 10.59 4.48 14 10.16 5.03 9.50 4.81 10.10 4.98 15 16 9.62 9.92 4.86 5.04 10.08 10.02 4.94 5.05 9.92 10.19 4.79 5.01 17 18 9.57 9.15 4.97 4.14 9.74 9.59 4.96 4.73 9.80 9.81 4.90 4.90 19 9.55 4.74 9.66 4.99 10.05 5.15 20 21 9.68 9.93 4.87 4.97 10.61 9.89 4.71 4.95 10.31 9.81 4.88 5.17 22 9.20 4.35 10.10 4.94 9.40 4.61 23 24 10. proc print; var TIME RESIST r1; 25 proc plot; plot TIME*RESIST; 26 proc reg; model TIME=RESIST RESIST2/r cli clm; 27 output out=out1 r=resid p=pred; 28 label RESID= Residuals PRED= Predicted Values ; 29 30 proc plot; plot RESID*RESIST/vref=0; 31 proc rank normal=blom; var RESID; ranks QNORM; 32 proc plot; plot RESID*QNORM; 33 label QNORM= Normal Quantiles ; 34 35 proc reg; model TIME=RESIST; 36 proc reg; model TIME=RESIST RESIST2 RESIST3; 37 proc reg; model time=resist resist2-resist4; 38 39 proc corr; var resist resist2-resist4; 40 proc corr; var r1-r4; 41 42 proc reg; model time=r1-r3; 43 proc reg; model time=r1-r4;
of System due to the Hot Electron Effect OBS TIME RESIST R1 1 4.62 10.54 0.651 2 4.99 10.18 0.291 3 4.48 10.59 0.701 4 5.03 10.16 0.271 5 4.81 9.50-0.389 6 4.98 10.10 0.211 7 4.86 9.62-0.269 8 4.94 10.08 0.191 9 4.79 9.92 0.031 10 5.04 9.92 0.031 11 5.05 10.02 0.131 12 5.01 10.19 0.301 13 4.97 9.57-0.319 14 4.96 9.74-0.149 15 4.90 9.80-0.089 16 4.14 9.15-0.739 17 4.73 9.59-0.299 18 19 4.90 4.74 9.81 9.55-0.079-0.339 20 21 4.99 5.15 9.66 10.05-0.229 0.161 22 4.87 9.68-0.209 23 24 4.71 4.88 10.61 10.31 0.721 0.421 25 4.97 9.93 0.041 26 4.95 9.89 0.001 27 5.17 9.81-0.079 28 29 4.35 4.94 9.20 10.10-0.689 0.211 30 4.61 9.40-0.489 2
of System due to the Hot Electron Effect 2 Plot of TIME*RESIST. Legend: A = 1 obs, B = 2 obs, etc. 5.2 + A A 5.1 + A A A A 5.0 + A A A A A A A A A 4.9 + B A A A A 4.8 + A F a i A A l A u 4.7 + r e T A A i 4.6 + m e 4.5 + A 4.4 + A 4.3 + 4.2 + A 4.1 + ---+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+-- 9.15 9.25 9.35 9.45 9.55 9.65 9.75 9.85 9.95 10.05 10.15 10.25 10.35 10.45 10.55 10.65 NOTE: 1 obs had missing values. Resistance 3
of System due to the Hot Electron Effect 3 Model: MODEL1 Model 2 1.27669 0.63834 74.232 0.0001 Error 27 0.23218 0.00860 Root MSE 0.09273 R-square 0.8461 Dep Mean 4.85100 Adj R-sq 0.8347 C.V. 1.91161 Variable DF Estimate Error Parameter=0 Prob > T Label INTERCEP 1-109.234255 9.75925927-11.193 0.0001 Intercept RESIST 1 22.882352 1.97165807 11.606 0.0001 Resistance RESIST2 1-1.145765 0.09950453-11.515 0.0001 Squared Resistance of System due to the Hot Electron Effect 4 Dep Var Predict Std Err Lower95% Upper95% Lower95% Upper95% Std Err Student Obs TIME Value Predict Mean Mean Predict Predict Residual Residual Residual 1 4.6200 4.6609 0.044 4.5706 4.7511 4.4503 4.8715-0.0409 0.082-0.501 2 4.9900 4.9697 0.022 4.9237 5.0157 4.7740 5.1655 0.0203 0.090 0.225 3 4.4800 4.5945 0.050 4.4923 4.6967 4.3785 4.8105-0.1145 0.078-1.464 4 5.0300 4.9782 0.022 4.9327 5.0236 4.7825 5.1738 0.0518 0.090 0.576 5 4.8100 4.7428 0.025 4.6915 4.7941 4.5457 4.9399 0.0672 0.089 0.753 6 4.9800 4.9980 0.022 4.9535 5.0425 4.8026 5.1934-0.0180 0.090-0.200 7 4.8600 4.8598 0.022 4.8154 4.9043 4.6644 5.0552 0.000164 0.090 0.002 8 4.9400 5.0028 0.022 4.9584 5.0472 4.8074 5.1982-0.0628 0.090-0.696 9 4.7900 5.0081 0.021 4.9640 5.0521 4.8128 5.2034-0.2181 0.090-2.417 10 5.0400 5.0081 0.021 4.9640 5.0521 4.8128 5.2034 0.0319 0.090 0.354 11 5.0500 5.0116 0.022 4.9674 5.0558 4.8163 5.2070 0.0384 0.090 0.425 12 5.0100 4.9651 0.023 4.9189 5.0114 4.7693 5.1610 0.0449 0.090 0.499 13 4.9700 4.8151 0.023 4.7687 4.8615 4.6192 5.0109 0.1549 0.090 1.723 14 4.9600 4.9439 0.021 4.9006 4.9871 4.7488 5.1390 0.0161 0.090 0.179 15 4.9000 4.9735 0.021 4.9300 5.0170 4.7783 5.1687-0.0735 0.090-0.814 16 4.1400 4.2130 0.058 4.0939 4.3320 3.9885 4.4374-0.0730 0.072-1.008 17 4.7300 4.8337 0.022 4.7882 4.8792 4.6380 5.0293-0.1037 0.090-1.151 18 4.9000 4.9777 0.021 4.9341 5.0212 4.7825 5.1729-0.0777 0.090-0.860 19 4.7400 4.7956 0.023 4.7480 4.8431 4.5995 4.9917-0.0556 0.090-0.619 20 4.9900 4.8915 0.021 4.8479 4.9352 4.6963 5.0867 0.0985 0.090 1.091 21 5.1500 5.0083 0.022 4.9640 5.0525 4.8129 5.2036 0.1417 0.090 1.572 22 4.8700 4.9060 0.021 4.8626 4.9494 4.7108 5.1011-0.0360 0.090-0.399 23 4.7100 4.5663 0.052 4.4590 4.6737 4.3479 4.7848 0.1437 0.077 1.876 24 4.8800 4.8924 0.026 4.8389 4.9460 4.6948 5.0901-0.0124 0.089-0.140 25 4.9700 5.0095 0.021 4.9654 5.0536 4.8141 5.2048-0.0395 0.090-0.437 26 4.9500 5.0025 0.021 4.9585 5.0465 4.8072 5.1978-0.0525 0.090-0.582 27 5.1700 4.9777 0.021 4.9341 5.0212 4.7825 5.1729 0.1923 0.090 2.131 28 4.3500 4.3058 0.051 4.2006 4.4111 4.0884 4.5233 0.0442 0.077 0.572 29 4.9400 4.9980 0.022 4.9535 5.0425 4.8026 5.1934-0.0580 0.090-0.643 30 4.6100 4.6201 0.031 4.5567 4.6834 4.4195 4.8206-0.0101 0.087-0.115 31. 5.0128 0.022 4.9686 5.0569 4.8174 5.2081... Sum of Residuals 4.38E-13 Sum of Squared Residuals 0.2322 Predicted Resid SS (Press) 0.3037 4
of System due to the Hot Electron Effect 5 Plot of RESID*RESIST. Legend: A = 1 obs, B = 2 obs, etc. 0.20 + A A 0.15 + A A 0.10 + A A 0.05 + A A A A A A A R e 0.00 +-----------------------------------A-------------------------------------------------------------------------- s A i A d A u a A l A A s -0.05 + A A A A A A A -0.10 + A A -0.15 + -0.20 + A -0.25 + ---+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+-- 9.15 9.25 9.35 9.45 9.55 9.65 9.75 9.85 9.95 10.05 10.15 10.25 10.35 10.45 10.55 10.65 NOTE: 1 obs had missing values. Resistance 5
of System due to the Hot Electron Effect 6 Plot of RESID*QNORM. Legend: A = 1 obs, B = 2 obs, etc. 0.20 + A A 0.15 + A A 0.10 + A A 0.05 + A A A A A A A R e 0.00 + A s A i A d A u a A l A A s -0.05 + A A A A A A -0.10 + A A -0.15 + A -0.20 + A -0.25 + -+----------+----------+----------+----------+----------+----------+----------+----------+----------+----------+ -2.5-2.0-1.5-1.0-0.5 0.0 0.5 1.0 1.5 2.0 2.5 NOTE: 1 obs had missing values. Normal Quantiles 6
of System due to the Hot Electron Effect 7 Model 1 0.13652 0.13652 2.785 0.1063 Error 28 1.37235 0.04901 Root MSE 0.22139 R-square 0.0905 Dep Mean 4.85100 Adj R-sq 0.0580 Variable DF Estimate Error Parameter=0 Prob > T Label INTERCEP 1 3.015242 1.10067546 2.739 0.0106 Intercept RESIST 1 0.185636 0.11122794 1.669 0.1063 Resistance Model 3 1.27843 0.42614 48.081 0.0001 Error 26 0.23044 0.00886 Root MSE 0.09414 R-square 0.8473 Dep Mean 4.85100 Adj R-sq 0.8297 Variable DF Estimate Error Parameter=0 Prob > T Label INTERCEP 1-216.439192 241.98353889-0.894 0.3793 Intercept RESIST 1 55.462179 73.50494647 0.755 0.4573 Resistance RESIST2 1-4.442173 7.43511582-0.597 0.5554 Squared Resistance RESIST3 1 0.111043 0.25043680 0.443 0.6611 Model 3 1.27843 0.42614 48.081 0.0001 Error 26 0.23044 0.00886 Root MSE 0.09414 R-square 0.8473 Dep Mean 4.85100 Adj R-sq 0.8297 NOTE: Model is not full rank. Least-squares solutions for the parameters are not unique. Some statistics will be misleading. A reported DF of 0 or B means that the estimate is biased. The following parameters have been set to 0, since the variables are a linear combination of other variables as shown. RESIST4 = -9462 * INTERCEP +3843 * RESIST -584.6723 * RESIST2 +39.5032 * RESIST3 Variable DF Estimate Error Parameter=0 Prob > T Label INTERCEP B -216.439192 241.98353889-0.894 0.3793 Intercept RESIST B 55.462179 73.50494647 0.755 0.4573 Resistance RESIST2 B -4.442173 7.43511582-0.597 0.5554 Squared Resistance RESIST3 B 0.111043 0.25043680 0.443 0.6611 RESIST4 0 0... 7
of System due to the Hot Electron Effect 10 Correlation Analysis 4 VAR Variables: RESIST RESIST2 RESIST3 RESIST4 Simple Statistics Variable N Mean Std Dev Sum Minimum Maximum Label RESIST 31 9.892581 0.363941 306.670000 9.150000 10.610000 Resistance RESIST2 31 97.991332 7.210220 3037.731300 83.722500 112.572100 Squared Resistance RESIST3 31 971.925885 107.321884 30130 766.060875 1194.389981 RESIST4 31 9652.611463 1422.428945 299231 7009.457006 12672 Pearson Correlation Coefficients / Prob > R under Ho: Rho=0 / N = 31 RESIST RESIST2 RESIST3 RESIST4 RESIST 1.00000 0.99972 0.99887 0.99748 Resistance 0.0 0.0001 0.0001 0.0001 RESIST2 0.99972 1.00000 0.99972 0.99888 Squared Resistance 0.0001 0.0 0.0001 0.0001 RESIST3 0.99887 0.99972 1.00000 0.99972 0.0001 0.0001 0.0 0.0001 RESIST4 0.99748 0.99888 0.99972 1.00000 0.0001 0.0001 0.0001 0.0 of System due to the Hot Electron Effect 11 Correlation Analysis 4 VAR Variables: R1 R2 R3 R4 Simple Statistics Variable N Mean Std Dev Sum Minimum Maximum R1 31 0.003581 0.363941 0.111000-0.739000 0.721000 R2 31 0.128193 0.171877 3.973991 0.000001000 0.546121 R3 31 0.004034 0.145284 0.125066-0.403583 0.374805 R4 31 0.045022 0.090521 1.395690 1.000006E-12 0.298248 Pearson Correlation Coefficients / Prob > R under Ho: Rho=0 / N = 31 R1 R2 R3 R4 R1 1.00000 0.05906 0.87959 0.07214 0.0 0.7523 0.0001 0.6997 R2 0.05906 1.00000 0.08045 0.97441 0.7523 0.0 0.6670 0.0001 R3 0.87959 0.08045 1.00000 0.07087 0.0001 0.6670 0.0 0.7048 R4 0.07214 0.97441 0.07087 1.00000 0.6997 0.0001 0.7048 0.0 8
of System due to the Hot Electron Effect 12 Model: MODEL1 Model 3 1.27843 0.42614 48.081 0.0001 Error 26 0.23044 0.00886 Root MSE 0.09414 R-square 0.8473 Dep Mean 4.85100 Adj R-sq 0.8297 C.V. 1.94071 Variable DF Estimate Error Parameter=0 Prob > T Label INTERCEP 1 5.002123 0.02176143 229.862 0.0001 Intercept R1 1 0.182361 0.10001858 1.823 0.0798 R2 1-1.147858 0.10112907-11.350 0.0001 R3 1 0.111043 0.25043667 0.443 0.6611 of System due to the Hot Electron Effect 13 Model: MODEL1 Model 4 1.28114 0.32029 35.161 0.0001 Error 25 0.22773 0.00911 Root MSE 0.09544 R-square 0.8491 Dep Mean 4.85100 Adj R-sq 0.8249 C.V. 1.96747 Variable DF Estimate Error Parameter=0 Prob > T Label INTERCEP 1 4.991867 0.02898859 172.201 0.0001 Intercept R1 1 0.192802 0.10318903 1.868 0.0735 R2 1-0.900328 0.46527614-1.935 0.0644 R3 1 0.085698 0.25810789 0.332 0.7426 R4 1-0.479960 0.87999520-0.545 0.5903 9