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LINEAR REGRESSION ANALYSIS |
Confidence Level |
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Time-to-Failure
Data for Bearings |
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Time-to-Failure
Data for Bearings from Charles Lipson and Narendra J. Sheth, Statistical
Design and Analysis of Engineering Experiments (New York, NY: MacGraw-Hill,
Inc., 1973), pp. 403-406. |
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'Best' Fit for
Linearized PDF: Lognormal: InvNorm(Q) vs. Ln(T+t) |
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PDF |
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Lognormal |
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Y-Axis |
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InvNorm(Q) |
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X-Axis |
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Ln(T+t) |
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Slope |
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1.382209976 |
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Intercept |
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-7.899243394 |
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Slope |
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0.03562985 |
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Intercept |
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0.205052574 |
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Standard
Error of Y Estimate |
0.132419008 |
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Regression
Sum of Squares |
26.38886567 |
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Residual
Sum of Squares |
0.49097422 |
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Degrees
of Freedom |
28 |
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R2 |
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0.981734481 |
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F Statistic |
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1504.943049 |
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Linear Regression Parameters and Statistics |
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Variables |
Parameters |
Standard Error |
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PDF |
Y-Axis |
X-Axis |
Slope |
Intercept |
Slope |
Intercept |
Standard
Error of Y Estimate |
Regression Sum of Squares |
Residual Sum
of Squares |
Degrees of
Freedom |
R2 |
F Statistic |
R2 Rank |
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1 |
Exponential |
Ln(1/(1-Q)) |
T+t |
0.003537146 |
-0.367846121 |
0.000146501 |
0.066228698 |
0.198680222 |
23.0108894 |
1.105267262 |
28 |
95.42% |
582.940367 |
4 |
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2 |
Weibull |
Ln(Ln(1/(1-Q))) |
Ln(T+t) |
1.689131372 |
-10.2073383 |
0.078222396 |
0.450176011 |
0.290715008 |
39.40937366 |
2.36642605 |
28 |
94.34% |
466.2991529 |
5 |
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3 |
Normal |
InvNorm(Q) |
T+t |
0.003633227 |
-1.374207639 |
0.000224776 |
0.101614272 |
0.304833806 |
24.27797772 |
2.601862174 |
28 |
90.32% |
261.2680191 |
8 |
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4 |
Lognormal |
InvNorm(Q) |
Ln(T+t) |
1.382209976 |
-7.899243394 |
0.03562985 |
0.205052574 |
0.132419008 |
26.38886567 |
0.49097422 |
28 |
98.17% |
1504.943049 |
1 |
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5 |
EVD I of
Minima |
Ln(Ln(1/(1-Q))) |
T+t |
0.004172125 |
-2.132095157 |
0.00043538 |
0.19682219 |
0.590449117 |
32.01415525 |
9.761644468 |
28 |
76.63% |
91.82841579 |
10 |
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6 |
EVD I of
Maxima |
Ln(Ln(1/Q)) |
T+t |
-0.004674303 |
1.213919027 |
0.000175772 |
0.079461238 |
0.238376669 |
40.1847435 |
1.591056216 |
28 |
96.19% |
707.1860858 |
2 |
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7 |
Rayleigh |
SQRT(-Ln(R)) |
T+t |
0.001743561 |
0.221309898 |
6.77124E-05 |
0.030610704 |
0.091829399 |
5.59115539 |
0.236113878 |
28 |
95.95% |
663.0374807 |
3 |
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8 |
Pareto |
Ln(1-Q) |
Ln(T+t) |
-1.197480318 |
5.87350451 |
0.105560652 |
0.607509812 |
0.39231815 |
19.8065778 |
4.309578867 |
28 |
82.13% |
128.6863973 |
9 |
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9 |
Frechet |
Ln(Ln(1/Q)) |
Ln(T+t) |
-1.675186598 |
9.019528074 |
0.088285144 |
0.508087914 |
0.328113401 |
38.7613644 |
3.014435313 |
28 |
92.78% |
360.0403029 |
6 |
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10 |
Uniform |
Q |
T+t |
0.00109685 |
0.085134727 |
6.6315E-05 |
0.029978973 |
0.08993426 |
2.212697056 |
0.226468792 |
28 |
90.72% |
273.5719876 |
7 |
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Legend |
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SYMBOL |
VARIABLE |
NOTE |
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T1=T |
Lower Group
Limit |
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T2=T+t |
Upper Group
Limit |
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Q(T+t) |
Unreliability |
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Estimated
Using Median Ranks |
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R(T+t) |
Reliability |
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R=1-Q |
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Ln |
Natural
Logarithm with Base e |
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R2 |
Coefficient
of Determination |
Square
of Sample Correlation Coefficient |
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Copyright © 2010 by Macroknow Inc. All Rights
Reserved. |
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