Transcript Student Tutorial.ppt

SuperSMITH Software
WinSMITH Weibull Student Version
Step-by-Step Tutorial using
Case Studies
By Dr. Robert B. Abernethy
Copyrighted 2006
Problem#1:Plotting a Weibull with suspensions
Produce a Weibull plot based on the following data:
Note the differences between the two plots.
1. Use Median Ranked Regression (MRR),
2. then Maximum Likelihood Estimates (MLE).
Failure Time
(cycles)
1500
1750
2250
4000
4300
5000
7000
Status
Failure
Suspension
Failure
Failure
Failure
Suspension
Failure
Step by Step
• Open WinSMITH Weibull Student
Version (WSWS): double click the icon
on the desktop or go to “Start-->
Programs-->Supersmith Weibull
• Input the data, using a negative sign for
suspensions. Or you can cut and paste
from EXCEL.
Inputting data to SuperSMITH
Then click on the “paste”
bottle graphic.
After a few seconds, SuperSMITH automatically produces
your Weibull plot
Now, click on “Labels”
to put your titles on the plot
Notice that the suspensions that were put in as a negative
numbers show up as a >1750 and >5000
Customize your plot with titles
Finally, click
“Exit”
Click here to put a
label on the plot
Type in your title and click the green check
Do the same for the y-axis title,
and put your initials in
Getting your plot into PowerPoint
In order to save this plot to a PowerPoint slide click on the
“printer” graphic.
Getting your plot into Powerpoint(continued)
Now click on the “clipboard” graphic;
Then go to a blank page in Powerpoint and “paste.”
Final Median Ranked Regression Weibull
To do an Maximum Likelihood (MLE) Weibull
Click on this symbol
To do an MLE Weibull(continued)
Click on this symbol
To do an MLE Weibull(continued)
This is an MLE Weibull, and note the poor fit
Problem #2
•
The following data represents the life of precision grinder wheels measured in
number of pieces produced.
•
Fit a Weibull to this data.. Is a t0 needed?
Do a Ranked Regression as in Problem 1:
Note the curvature in the Weibull plot
To do a t0 correction in WSWS
Click on t0 – 3 parameter Weibull button
To do a t0 correction in WSWS (continued)
Click on this button, then click
On the green “check”
To do a t0 correction in WSWS (continued)
.
Note the
improvement
in r2.. from 0.764
before to 0.98 now
Problem #3
•
The following data represents the shear strength of brass and steel brake rivets.
•
Do a Weibull of each… is there a significant difference between the two?
First, the brass rivet Weibull
Cut and paste the data from EXCEL™,
or punch in directly, then …
Click here to put confidence bounds on the plot
Put confidence bounds on this Weibull
Click on this button for 2-sided
Confidence bounds……………...
Continuing to put Confidence bounds on a Weibull line
Accept 90% confidence…….
You now have a Weibull Plot for Shear strength
of Brass rivets , with 90% confidence bounds
18
110
Note that the confidence bound at 10% failure or 90% reliability is
(8.7-104.7) This may be read from the plot or the “report.”
How to bring up the “Report”
To see the “Report” Click on the right Tab
The Report Shows Exact Readings From The Plot
Here are the exact 90% Confidence B10 Bounds which are also
90% Reliability Bounds. Other B lives may be added using the
report icon. Also shown are confidence bounds for eta and beta.
Now repeat this procedure for the steel rivets
90% confidence bounds at 10% reliability are (152.9-513.1)
Declare a Significant Difference
•Confidence bounds for Brass rivets at 90% reliability
are (8.7-104.7).
•Confidence bounds for steel rivets at 90% reliability
are (152.9-513.1).
Conclusion: Since these bounds do not overlap at the B10 level,
there is a significant difference in the strength of the brass and steel
rivets with 90% confidence.
Problem #4
•
The following data represents the pull strength of spot welds from the lab:
Pull Strength(Newtons)
142
146
150
154
158
162
166
•
Fit a Weibull to this data.. Anything surprising … do you believe the value of
the calculated b?
Doing a Ranked Regression Weibull as before
b seems high, try Lognormal and
Normal.
Now try a Lognormal
Click on this button
Now try a Lognormal, continued
Click on this button (if you wait a second or two
The name of the option will appear below it in a yellow box).
Now let’s try a Normal
Click on this button
Now let’s try a Normal (continued)
Click on this button
Now let’s try a Normal (continued)
Click on this button, then
Then “NO” on “Lower bias?”
So far, where are we?
Distribution
Weibull
Lognormal
Normal
r^2
0.975
0.992
0.992
Hmmm, looks like log-normal or Normal..
But wait , look at the original Weibull…
It’s a little hard to tell, but it seems like
There may be curvature .. Let’s try a
T0 correction.
Doing a t0 correction
Click on this button
Doing a t0 correction (continued)
Click on this button, and the
“No” will change to “Yes”,then click the Green check
Doing a t0:
The fit is better,
R2=.995,
so, 3-parameter Weibull
is your best choice????
To Find the Best Distribution
r2 is a good measure of fit but (r2 – CCC2) is more accurate
as explained in Chapter 3. Remember the “Report” we used
in Problem 3? It contains (r2 – CCC2) and this allows us to
do an accurate distribution analysis. If we click on the tab
above the plot for each distribution, the results are:
Weibull 2-parameter (r2 – CCC2) = 0.1487
Weibull 3-parameter
= 0.0739
Log Normal
= 0.1511
Therefore from a statistical view the Log Normal best fits
our data set. However, the physics of failure and prior
experience may provide more information, at least equally
important, as discussed in Chapter 3.
Remember the Pump Problem in Chapter 4?
Let’s see if we can
do the Abernethy
Risk failure forecast
to predict the
number of failures
on the 18 remaining
pumps in the next
year. To make the
Weibull plot, Figure
4.1, enter the data
shown in Table 4-1
and repeated here.
-1000
-1000
2000
-2000
-2000
-2000
-2000
3000
-3000
-3000
-3000
-3000
-4000
-4000
-4000
-4000
-4000
Here is the plot. R squared is 1.0 because we only have two
failures. The expected usage for 1 year is 1000 hours for each
pump or 83.3 hours per month. Select the Abernethy Risk icon.
To make a failure forecast click on the Abernethy
Risk Icon which is here.
Enter Usage = 83.3 hours per month and click on
the Green Check
What does this tell us? Expect 2.3 failures in the next year.
Expect the next failure in four months. The Now Risk is
2.5, close to the observed number 2, so a batch problem is
not indicated. In five years expect 14 failures.
Summary
• We have illustrated how to input data, failures and
suspensions, obtain MRR and MLE plots, add confidence
bounds, do a distribution analysis and a failure forecast.
• We hope we have helped introduce you to Weibull
Analysis and we would be pleased if you would send us
your questions and/or comments.
• Bob Abernethy …[email protected]