Comparing Two Products Using a
Single Metric
A common task for a reliability
engineer is to determine if one product is better than another.
Often, comparison of a single metric, such as the time by which
X% of the population is expected to fail (also known as the BX
life), is used to answer the question of which product is
superior. This article will illustrate two graphical methods to
compare the B10 lives of two different designs using ReliaSoft's
Weibull++
software.
To download the *.rso7 file
for this example, rightclick here to
save the file to your computer. You must have Weibull++
installed in order to be able to view this file. Free
demonstration copies of the software are available for download
from
http://Download.ReliaSoft.com.
Example
Joe has been assigned the task of determining whether a product
that he buys from Vendor A can be replaced with a product from
Vendor B. He knows that his budget will allow up to 10% returns
during the warranty period, so Joe wants to compare the B10
lives of the products. He has the results of the original life
test done previously on product A, and he has 5 samples of the
new product, which he tests to failure. The results of these
tests are shown in Table 1.
Table 1 
TimestoFailure of Products A and B in Hours
Product A 
Product B 
300 
402 
449 
1116 
587 
1166 
619 
1233 
700 
1460 
958 

2129 

2208 

2279 

2793 

He enters the data into two
Data Sheets in a Standard Folio and renames these sheets Product
A and Product B. He knows from previous experience with this
product that it will fail due to wearout, so he computes the
Weibull distribution parameters for each data set. The computed
parameters are shown in Figures 1 and 2.
Figure 1: The Product A Data
Set
Figure 2: The Product B Data Set
Joe decides to compare the B10
lives of his two products by looking at the probability plots
for each data set on the same graph. He rightclicks the
Additional Plots
folder in the Project Explorer and chooses Add Multiplot.
In the Select Warranty Subsets/Folio Data Sheets window, Joe
chooses the data sets for both products, as shown in Figure 3,
and then clicks OK.
Figure 3: Selecting Data Sets
for the Multiplot
He knows that for a given
unreliability (10%), he wants to see the variability in time
(B10 life), so Joe chooses to add confidence bounds on time
(also called "Type I" confidence bounds) to the plot. He shows
these bounds on the plot by rightclicking within the plot and
choosing Confidence Bounds from the shortcut menu that
appears. He makes the selections shown in Figure 4 to put 90%
twosided bounds on the plot.
Figure 4: Setting Up Confidence
Bounds to Determine Variability in B10 Life
After Joe changes the line
colors and styles for the confidence bounds using the Plot
Setup, Joes plot looks like the one shown in Figure 5.
Figure 5: The Probability Plots
for Products A and B with Confidence Bounds.
Note that the blue
curve and dotted lines represent product A, while the black
curve and dashed lines represent Product B. Since the confidence
bounds for Product A surround the Product B probability line and
the confidence bounds for Product B surround the Product A
probability line at a 10% unreliability, Joe concludes that
there is no statistical difference between the B10 lives of the
products from Vendors A and B. It is worth noting that this may
not mean that the products from the two vendors actually have
the same reliability/B10 life this is a small data set, and
the wide confidence bounds indicate that there is simply not
enough data to draw a firm conclusion.
Joe decides to prepare a report
for his manager. He rightclicks the Reports folder in
the Project Explorer and chooses Add Report. In the
Report Wizard, Joe leaves the Default Data Source field empty
and verifies that the Based on an existing Template check
box is cleared, as shown in Figure 6.
Figure 6: Setting up a Blank
Report
He then clicks OK. A
warning appears, alerting him that he has not defined a data
source for the report and asking if he wants to continue. Joe
clicks Yes to bring up the blank report. He types column
headings and labels into the report as shown in Figure 7.
Figure 7: Creating Headings and
Labels for the Report
With cell B2 selected, Joe
clicks the Function Wizard icon.
He chooses the TIMEATPF
function and enters the information as shown in Figure 8 to
calculate the upper bound on the B10 life at the 95% onesided
confidence level. (Note that this is equivalent to the 90%
twosided bound plotted in Figure 5.)
Figure 8: Using the Function
Wizard to Compute the Upper Bound on B10 Life for Product A
Joe clicks Insert to put
the value of 719 hours into cell B2 in the report. In a similar
manner, he uses the Function Wizard to obtain the complete table
shown in Figure 9. (Note that the confidence level in the
Function Wizard is 0.05 to calculate the values in the Lower B10
column and is left blank to calculate the values in the
Estimated B10 column.)
Figure 9: The Completed Table
of B10 Lives for Products A and B
Joe adds a graph
to the report as follows. He highlights cells A1 through D3, and
then clicks the Chart Wizard icon.
The cursor becomes a bold
cross. He places the cursor at the top left of where he wants
the chart to be located in the report, then clicks and drags the
cursor to the bottom right of the desired location. When he
releases the mouse button, the Chart Wizard appears. Joe does
the following in the Chart Wizard:
 Gallery Page: chooses
Hi Lo chart type
 Style Page: chooses chart
style
3
 Layout Page: enters B10
Comparison as the chart title
 Axes Page: enters B10
Life (hours) as the Value (Y) axis title
Joe then clicks Finish
to create the chart. Figure 10 shows the report.
Figure 10: Graphical Display of
the Results in the Report
Since he can draw a horizontal
line that intersects both data sets, he again concludes that he
cannot tell a difference in the B10 lives of the products from
Vendors A and B.
Conclusion
This article discussed two graphical methods to compare two data
sets using the B10 life metric. Weibull++ also allows you
to calculate the BX life for an individual data set using the
Quick Calculation Pad (QCP). You may find this to be a quick and
easy way to determine the B10 life in cases where you only need
the metric. However, for times when you need to present the
information graphically for maximum impact or rapid
understanding, the methods presented in this article will be
appropriate.
