WOLFRAM|DEMONSTRATIONS PROJECT

Simultaneous Confidence Interval for the Weibull Parameters

​
scenario
seed
1
suspend
7
simultaneous CI
0.95
display
event matrix
survival plot
contour plot
3D plot
individual plots
1.42603
2.70031
4.44237
shape (α) parameter
520.894
672.683
943.691
scale (β) parameter
time data
90.175
f
161.914
s
250.709
s
277.02
f
305.513
f
337.585
f
414.207
s
415.738
s
438.479
f
516.913
f
535.561
f
613.619
s
652.864
f
658.5
f
668.085
f
687.018
f
690.848
s
712.236
f
785.647
s
900.998
f

This Demonstration shows the construction of the simultaneous confidence interval (CI) for the Weibull parameters
α
(shape) and
β
(scale) maximum likelihood estimators (MLE). In reliability analysis, the Weibull parameters MLE derive from failure and suspension time data of independently operating systems.

Use the "seed" slider to generate a pseudorandom test scenario for 20 independently operating systems. Also, you may use the "suspend" slider to randomly suspend up to seven of these test times (right-censored), implying that the corresponding systems have not failed during their operating period, whereas the rest of the systems did fail at the indicated test times. A table on the right of the graph shows the failure (red "f") and suspension (black "s") times that correspond to the specific test scenario.

You can choose to display:

• the event matrix plot showing the failure (boxes) and suspension (arrows) events across the test period.

• the survival plot showing the selected % pointwise bands (brown dashed lines) about the Kaplan-Meier survival function (blue line), and the Weibull fitted model (red curve).

• the contour plot for the likelihood function, depending on the parameters
α
and
β
. The contours correspond to the simultaneous likelihood CI percentiles. The frame ticks indicate the parameters MLE within the selected CI limits.

• the 3D illustration of the contour plot.

• the CI that corresponds to each parameter (blue area).