Reliability HotWire

Issue 98, April 2009

Hot Topics
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.