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Demonstration Test Design Using
the DRT Tool in Weibull++
Demonstration test design is typically used to show that a
certain product has met or exceeded a given reliability at a
given confidence level. While it is desirable to be able to test
a large number of units in order to obtain the reliability
information for a product or design, time and resource
constraints sometimes make this impossible. In such cases, it is
necessary to design a test that will demonstrate the requirement
while meeting the constraints on the number of units available
for use and/or the length of time available for testing. Quite
often, it will be desirable to demonstrate that the goal has
been met with a zero-failure test and, at the same time, to keep
the testing cost as low as possible. [1] In this article, we
show how to use the Design of Reliability Tests (DRT) tool in
Weibull++ 7 to
design such a demonstration test.
Example
A manufacturer has designed a new product and has claimed that
the new design has a mean time to failure (MTTF) of 10,000 hours
with 99% confidence. Now some customers want the manufacturer to
demonstrate this claim. Reliability engineer Barbara is assigned
to this project. She uses the Design of Reliability Tests (DRT)
tool in
Weibull++ 7 to design the demonstration test.
Based on previous engineering
data, Barbara supposes that the life distribution for this
product follows a Weibull distribution. The data from the
previous design analysis using Weibull++ showed that the
Weibull life distribution had a shape parameter
β =
1.3. Barbara decides to use this value in the new product
demonstration test. Barbara has only 30 units available for the
test. She wants to know the test time required if 0 failures are
allowed in the test. She enters all of this information in the
DRT and clicks Calculate. Figure 1 shows the inputs and
results.
Figure 1: The DRT in Weibull++
7
The results show a test time of
2561.35 hrs. This means that if Barbara wants to demonstrate
that this new design has MTTF = 10,000 hrs with 99% confidence,
she must have 30 units tested for at least 2561.35 hrs, with no
failures occurring during the test.
Barbara wants to know how the
test sample size and the number of expected failures affect the
test time, so she clicks the Tables/Plots button. The DRT
Results Page appears. In the Table/Plot Setup area of the
Control Panel she enters 30 for the end test unit and
leaves the default values for the other fields, then clicks the
Generate Table icon.
Figure 2 shows the calculated
test times for the number of units from 1 to 30 and the number
of allowable failures from 0 to 5.
 
Figure 2: Test Time Table
Barbara then clicks the Plot
icon.
Figure 3 shows the resulting
plot of test time vs. test units.
Figure 3: DRT Plot
Examining the plot, Barbara
notices that the curve becomes flat when the sample size is
greater than 20. Knowing that each unit is expensive, she
wonders if it would be possible to use a smaller sample size to
do this demonstration.
To explore the relationship
between cost and number of test units, Barbara does the
following calculation: Based on the fact that one test unit
costs $2600 and one hour of test time costs $30*
, the total cost for the test with the 0 failure test design
would be:
where N is the sample
size and hrs(N) is the minimum required test time, which
is a function of sample size. The minimum required test times
for different sample sizes with 0 failures are shown in the
second column in Figure 2. Table 1 lists the total cost for each
sample size from 1 to 30.
Table 1:
Total Test Costs for Different Sample Sizes
|
Test Units |
Cost ($) |
Test Units |
Cost ($) |
| 1 |
1054168.81 |
16 |
166221.10 |
| 2 |
622187.21 |
17 |
163142.90 |
| 3 |
459470.10 |
18 |
160626.52 |
| 4 |
372405.05 |
19 |
158589.55 |
| 5 |
317907.75 |
20 |
156965.21 |
| 6 |
280608.50 |
21 |
155698.78 |
| 7 |
253576.06 |
22 |
154744.97 |
| 8 |
233199.30 |
23 |
154065.93 |
| 9 |
217401.46 |
24 |
153629.80 |
| 10 |
204898.59 |
25 |
153409.56 |
| 11 |
194851.82 |
26 |
153382.10 |
| 12 |
186688.50 |
27 |
153527.56 |
| 13 |
180003.64 |
28 |
153828.76 |
| 14 |
174502.25 |
29 |
154270.78 |
| 15 |
169964.05 |
30 |
154840.57 |
From Table 1, Barbara finds
that choosing 26 units for test yields the lowest total test
cost, $153,382.10. This is $1,458.50 less than the test cost for
30 units, but the total test time for 26 units is 298.05 hrs,
about 12.4 days longer than the test time for 30 units. Barbara
consults the project manager and finds that the extended testing
time is acceptable, so she decides to use 26 test units.
*To simplify calculations, we assume here
that the cost per unit of test time is not related to the sample
size.
References
1. ReliaSoft Corporation,
Life
Data (Weibull) Analysis Reference, ReliaSoft Publishing,
Tucson, AZ, 2008, pp. 477-486.
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