LINEAR REGRESSION ANALYSIS Confidence Level
             
Time-to-Failure Data for Bearings 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.
'Best' Fit for Linearized PDF: Lognormal: InvNorm(Q) vs. Ln(T+t)
PDF   Lognormal
Y-Axis   InvNorm(Q)
X-Axis   Ln(T+t)
Slope   1.382209976
Intercept   -7.899243394
Slope   0.03562985
Intercept   0.205052574
Standard Error of Y Estimate 0.132419008
Regression Sum of Squares 26.38886567
Residual Sum of Squares 0.49097422
Degrees of Freedom 28
R2   0.981734481
F Statistic   1504.943049
Linear Regression Parameters and Statistics
Variables Parameters Standard Error
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
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
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
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
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
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
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
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
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
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
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
Legend
SYMBOL VARIABLE NOTE
T1=T Lower Group Limit        
T2=T+t Upper Group Limit        
Q(T+t) Unreliability   Estimated Using Median Ranks
R(T+t) Reliability   R=1-Q    
Ln Natural Logarithm with Base e      
R2 Coefficient of Determination Square of Sample Correlation Coefficient
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