Sometimes you need a quick Weibull plot when you don’t have a computer nearby. Download the attached PowerPoint file for both worked out problems and for Weibull probability plot paper.
The most difficult portion of making a Weibull probability plot is acquiring the data. You need agetofailure data, easy to say but difficult to obtain, which is the same type of information which will appear on your tombstone: (death date) – (birth data) = (agetofailure). Some times this agetofailure is years, months, days, etc. Sometimes the agetofailure data is cycle, number of hot cycles, number of cold cycles, etc. Sometimes the agetofailure data is storage time, etc. Use the measure that motivates failure and the data must be consistent.
Here is the agetofailure data (weeks) on the PowerPoint file:
140
37
69
73
108
63
Yes, it is another “massive” data set of 6 data points.
Most people think this data is too small to be meaningful. My next question is: “How many more data points would you like to purchase using money from your pocket to cover the expenses?” The usual answer is none!
Small data sets mean we need to use the data we have to get our nose pointed in the general direction. We cannot wait for the dead bodies to pile up alongside the road while we delay corrective action waiting more data. It’s important to take action to prevent the failures!!! Usually you’ll get a reasonable indication of corrective action from a small set of data. By the way, in most cases you’ll never live long enough to get a precise data set. By the time you’ve got all the data you need for a risk free decision it doesn’t matter because you are dead and gone!
Step 1 for Weibull analysis
Rank the data in ascending (rank) order:
37
63
69
73
108
140
This is Xaxis data you will need for the Weibull plot
Step 2 for Weibull analysis
Compute a Yaxis plotting position to be used with Step 1’s Xaxis data. Use Benard’s median
rank plotting position. (You can read Benard’s 1953 paper as translated by Ron Schop or many
other plotting positions are summarized by Mische’s unpublished 1979 ASME paper.)
Benard’s median rank plot position equation is (i0.3)/(N+0.4) where i is the rank number and N
is number of data points. We have N = 6
for the dataset in Step 1 and the Yaxis plot position for i = 1 though 6 is:
i = 1 10.9%
i = 2 26.6%
i = 3 42.2%
i = 4 57.8%
i = 5 73.4%
i = 6 89.1%
This is the Yaxis data you will need for the Weibull plot.
Step 3 for Weibull analysis
Plot the data on 1:1 Weibull probability paper.
The 1:1 scale is important because of measuring X and Y dimensions on
the graph to calculate the slope of the line, b.
Figure 1: Raw Data Plot On 1:1 Weibull Probability Paper 

Step 4 for Weibull analysis
Draw a
trend line by estimating the best fit with the data.
Figure 2: Draw Best Fit Trendline 

Step 5 for Weibull analysis
Where the
trend line crosses the 63.2% horizontal line, drop a vertical line to define
the characteristic value, h. The h value is a mathematical property
of the Weibull plot based on this premise: if you know the value of h, all trendline will pass
through this point without regard to the line slope, b.
Figure 3: Find The Characteristic Value, h
at CDF=63.2% 

Step 6 for Weibull analysis
Measure the
rise over the run for the line slope, b.
Figure 4: Calculate the line slope b 
Please note,
not all printers will maintain the aspect ratios for 1:1 plots. This means the b values may be in error
by ±10% so don’t expect high accuracy unless you have precision graph paper.
Can you do the Weibull trendline regression in Excel? The answer is yes, but.
Problem #1:
At the university you learned to do YontoX regressions based on the pattern
of error (your largest errors were in the Yaxis): For your experiments, you carefully
controlled error in the Xaxis and took your variability in the Yaxis. For reliability issues, you’ll find your
smallest errors are in the Yaxis for the plot positions and larger errors are
in the Xaxis concerning agetofailure.
Properly handle data errors for a Weibull plot requires regressing the Xaxis onto the Yaxis. Else you have not handled your data
collection errors properly.
Problem #2:
The Excel regression details are shown in the sample
Excel spreadsheet which you can download and examine.
Problem #3:
By the time you’ve constructed your Excel spreadsheet you could have for less
cost purchased SuperSMITH software consisting of SuperSMITH
Weibull (for probability plots) and SuperSMITH
Visual (for reliability growth plots) software. Furthermore, it’s unlikely you will know and
remember how to handle all of the Weibull rules learned during the past 80
years on how to analyze the different constraints such as when you have suspensions
(censored data), etc.
You can download a PDF copy of this Problem Of The Month by clicking here.
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