This is a rough collection of Weibull analysis routines. I make no claim to the accuracy.
Routines are for low sample sizes. I believe at large sample sizes, maximum likelihood methods are more accurate. The Weibull fits here are done as Y on X and X on Y regressions - the equivalent to graphing on Weibull paper. The class can handle suspensions.
A class for Weibayes analysis is also included.
Also included is are a few methods to determine test time or number of samples.
I wrote this while working at a manufacturing company. Before I could polish it up, I left for a completely different job. I doubt I will use this again, but I wanted to pull the work in progress out of the iPython notebook where it was and stick it in a file. As a result, there are some duplicate functions in the file. I couldn't be bothered to clean those up...
Suspended data can be fit as well as unsuspended data. Four fits are performed:
- xy - X on Y, no suspensions
- yx - Y on X, no suspensions
- sxy - X on Y with suspensions
- syx - Y on X with suspensions
Beta and eta are reported for each fit. I guess I never got around to putting the fit parameters on the plot like I did for the Weibayes analysis below.
| end time | suspended |
|---|---|
| 90 | False |
| 96 | False |
| 100 | True |
| 30 | False |
| 49 | False |
| 45 | True |
| 10 | True |
| 82 | False |
import weibull
data = [90, 96, 100, 30, 49, 45, 10, 82]
suspensions = [False, False, True, False, False, True, True, False]
x = weibull.weibull(data, suspensions=suspensions)
# fit() is similar and probably an earlier iteration. use fit2()
x.fit2()
# plot the data and fit with suspensions. set susp = 0 to ignore
# suspensions.
x.plot(susp=1)
# plot the y on x fit, ignoring suspensions
x.plot_fits('yx', linestyle = '--')
# out
# beta: 2.02, eta: 95.00
# beta: 2.16, eta: 79.80
Target lifetime is t = 100, reliability is 90% (r = 0.9), and 95% confidence limit (cl = 0.95). Beta is 1.5. The first scenario is you have 48 time units to test; how many test units do you need? The answer is 86 units
weibull.weib_n(48, t = 100, r = .9, cl = .95, beta = 1.5)
# 85.49..
The second scenario is that you have 20 units to test; how long should you test? 126.4 time units.
weibull.weib_t(20, t = 100, r = .9, cl = .95, beta = 1.5)
# 126.4...
The company I worked for didn't like any failures in our testing. They used canned software for Weibayes. The software used a confidence limit of 50% as a default, so that's what a lot of our testing analysis ended up using. The class here has 50% hardcoded in. You can changed it, but the default is always there.
Confidence limits are expressed in the equation as r, where r = -ln(cl). A few values are shown in the table below.
| Confidence | r |
|---|---|
| 50% | 0.693 |
| 63% | 1.0 |
| 80% | 1.61 |
| 90% | 2.3 |
| 95% | 3.0 |
| 99% | 4.6 |
We had a product that needed to be tested to B2 life of 40 million time units with a confidence limit of 95%. The product had an expected beta of 2 (lots of historical data there). B2 life is the same as 98% survival. The test design said we needed to run 62 units (the limit of our test rig) for 62 million time units with no failures:
weibull.weib_t(62, 40e7, r=.98, cl=.95, beta=2)
# 618601344.51919436
Weibayes analysis on the data would arrive at the same result.
# 62 units run to 62 million time units
t = [6.2e7]*62
ww = weibull.weibayes(t, cl = 95, beta = 2)
# display plot and lifetime block
ww.display()
# annotate with B2 (98% survival) values
ww.plot_annotate(2)
# output
# B 50.0 95.0
# 1.0 5.878481e+07 2.827654e+07
# 2.0 8.334501e+07 4.009044e+07
# 5.0 1.328021e+08 6.388021e+07
# 10.0 1.903328e+08 9.155351e+07
