LINEAR REGRESSION ANALYSIS Confidence Level
             
Time-to-Failure Data for Special Equipment Time-to-Failure Data from Dimitri Kececioglu, Reliability Engineering Handbook, Vol. 1 (Englewood Cliffs, NJ: Prentice Hall, Inc.), pp. 477-480.
'Best' Fit for Linearized PDF: Weibull: Ln(Ln(1/(1-Q))) vs. Ln(T+t)
PDF   Weibull
Y-Axis   Ln(Ln(1/(1-Q)))
X-Axis   Ln(T+t)
Slope   1.998644928
Intercept   -7.149506058
Slope   0.007211203
Intercept   0.024197675
Standard Error of Y Estimate 0.01427953
Regression Sum of Squares 15.66331404
Residual Sum of Squares 0.002242955
Degrees of Freedom 11
R2   0.999856823
F Statistic   76816.73685
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 0.053300269 -0.727660595 0.003859459 0.133970922 0.208180639 8.265832219 0.476730965 11 94.55% 190.7242472 7
2 Weibull Ln(Ln(1/(1-Q))) Ln(T+t) 1.998644928 -7.149506058 0.007211203 0.024197675 0.01427953 15.66331404 0.002242955 11 99.99% 76816.73685 1
3 Normal InvNorm(Q) T+t 0.059422152 -1.861284653 0.002075613 0.072049407 0.111959307 10.27364455 0.137883752 11 98.68% 819.6041129 4
4 Lognormal InvNorm(Q) Ln(T+t) 1.604690917 -5.31203687 0.085385171 0.286515662 0.169078596 10.09706501 0.314463288 11 96.98% 353.1977162 6
5 EVD I of Minima Ln(Ln(1/(1-Q))) T+t 0.070334439 -2.736447259 0.006304602 0.218847587 0.340072531 14.39341441 1.272142586 11 91.88% 124.4573998 8
6 EVD I of Maxima Ln(Ln(1/Q)) T+t -0.073175959 1.758739972 0.001635969 0.056788338 0.088244765 15.57989847 0.085658523 11 99.45% 2000.721893 3
7 Rayleigh SQRT(-Ln(R)) T+t 0.027967123 -0.000355841 0.000109136 0.00378836 0.005886823 2.275743742 0.000381202 11 99.98% 65669.14236 2
8 Pareto Ln(1-Q) Ln(T+t) -1.299153053 3.3587416 0.221933359 0.744712258 0.439469529 6.618095046 2.124468138 11 75.70% 34.26695096 10
9 Frechet Ln(Ln(1/Q)) Ln(T+t) -1.880413827 5.691411096 0.204316467 0.685597595 0.40458479 13.86497962 1.800577371 11 88.51% 84.70326145 9
10 Uniform Q T+t 0.018483531 -0.078961077 0.000869181 0.030171322 0.046883943 0.994025849 0.024179145 11 97.63% 452.2196485 5
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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