|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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 |
|
|
|
|
|
|
|
|
|
|
|
|
|
Copyright © 2010 by Macroknow Inc. All Rights
Reserved. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|