 Reliability Basics

# Accelerated Test Planning in ALTA

[Editor's Note: This article has been updated since its original publication to reflect a more recent version of the software interface.]

In today’s highly competitive environment, companies are pressured to shorten their development cycles, reduce development costs and produce highly reliable products. Accelerated tests are a very powerful tool in achieving these goals, providing the means to observe failures more rapidly under higher-stress operating conditions while accurately predicting reliability under normal operating conditions. However, when performing an accelerated test, it is critical to do enough preparation and planning up front, as poorly planned accelerated tests can result in wasted time, effort and money — and may not even yield the desired information.

In this article, we will present the accelerated test plan methods that are available in ALTA and illustrate the process of generating a test plan through an example. Note that the math behind these plans is beyond the scope of the article. For more details on the theory, please refer to .

## Introduction

ALTA provides a number of different test plans for tests with one or two stresses. The purpose of these plans is to determine the appropriate stress levels that should be used for each stress type and the number of test units that should be allocated to different stress levels.

As with any test plan, some initial assumptions have to be made in order to design the test. For the test plans in ALTA, the required inputs are:

• The life-stress relationship.
• The use stress and the highest possible stress (design limit).
• The test duration.
• The probability of failure at the test duration under use conditions.
• The probability of failure at the test duration under the highest possible stress.

## Plans for Single-Stress Tests

The available test plans for the case of a single stress are:

• The 2 Level Statistically Optimum Plan. The plan will recommend two stress levels. One will be the maximum allowable stress and the second will be computed so that the variance of the B(X) life is minimized.
• The 3 Level Best Standard Plan. The plan will recommend three equally spaced stress levels with equal allocations. One stress will be the maximum allowable stress and the other two stresses will be computed so that the variance of the B(X) life is minimized.
• The 3 Level Best Compromise Plan. The plan will recommend three equally spaced stress levels using the same approach as the 3 Level Standard Plan. The difference is that the proportion of the units to be allocated to the middle stress level is defined by the user.
• The 3 Level Best Equal Expected Number Failing Plan. The plan will recommend three equally spaced stress levels using the same approach as the 3 Level Standard Plan. The difference is that the proportion of units allocated to each stress level is calculated such that the number of units expected to fail at each level is equal.
• The 3 Level 4:2:1 Allocation Plan. The plan will recommend three equally spaced stress levels using the same approach as the 3 Level Standard Plan. The difference is that the allocation of test units from the lowest to the highest stress level is a 4:2:1 ratio. This plan also gives the option to specify a reduction factor in order to keep the low stress level closer to normal stress conditions.

## Plans for Two-Stress Tests

The available test plans for the case of two stresses are:

• The 3 Level Optimum Plan. The plan will recommend three stress level combinations. The proportion of units allocated at each stress level combination is such that the variance on the B(X) life is minimized.
• The 5 Level Best Compromise Plan. The plan will recommend five stress level combinations. The proportion of units allocated at each stress level combination is such that the variance on the B(X) life is minimized.

## Example

Andrew is a reliability engineer for a computer manufacturer. He wants to plan an accelerated life test for a new design of an electronic component. Some initial HALT tests have indicated that temperature is the major stress of concern. The temperature at use conditions is 300 K, while the design limit was found to be 380 K. Looking at historical data of the previous design, he finds that after 2 years of operation (which translates to 6,000 hours of actual usage) approximately 1% of the units had failed and that the beta parameter of the Weibull distribution was 3. Given that the failure mode of the new design is expected to be similar, Andrew feels that this is a good approximation of the beta. Finally, previous accelerated tests have indicated that an acceleration factor of 30 can be achieved at temperature levels close to the design limit.

The available resources that Andrew has at this point are three test chambers, 100 test units and a test time of 2 months or 1,440 hours. He wants to determine the appropriate temperature that should be set at each test chamber and the number of units that should be allocated at each chamber, so he decides to use the test plans utility in ALTA.

In order to generate a test plan, he needs to determine the probabilities of failure at the end of the test at the usage temperature and at the design limit temperature, something that can be accomplished in Weibull++. The first step is to use the Quick Parameter Estimator (QPE) tool in order to determine the eta parameter of the Weibull distribution at the normal use temperature, as shown in Figure 1. Figure 1: Parameter Experimenter

Knowing that the beta parameter of the Weibull distribution is 3 and that at 6,000 hours approximately 1% of the units will fail, he finds that the eta is 27,803 hours. Having that, he adds a standard folio in Weibull++ and clicks the Calculate icon without entering any data in order to define the calculated Weibull parameters, as shown in Figure 2. Figure 2: The parameters of the Weibull distribution at the normal use temperature

He can now calculate the probability of failure at the end of the test using the Quick Calculation Pad (QCP), as shown in Figure 3. Figure 3: Probability of failure at the end of the test at the normal use temperature

Next, he needs to estimate the probability of failure at the end of the test at the design limit temperature of 380 K. Given the fact that the acceleration factor at that condition is expected to be 30, the eta parameter at 380 K will be equal to the eta at usage temperature divided by 30, or equal to 926.8 hours.

Following the same steps as before, he adds another standard folio and enters the following Weibull parameters. Figure 4: The parameters of the Weibull distribution at the design limit temperature

He then calculates the probability of failure at the end of the test at the design limit in the QCP, as shown in Figure 5. Figure  5: Probability of failure at the end of the test at the design limit temperature

Having these two probabilities of failure, Andrew can now generate a test plan. Given that he has three test chambers available, he decides to use a 3-level plan. In this case, he generates a 3 Level Best Standard Plan using the initial assumptions that were made, the available resources and the calculated probabilities of failure. Figure 6 shows the inputs for the test plan utility. Figure 6: Test plan setup window

Note that the Arrhenius life-stress relationship was chosen because the stress is temperature. The BX% Life Estimate Sought is the BX life metric that the selected test plan will attempt to minimize the variance for. In this case, the company’s reliability requirements are in the form of a B10 life, so Andrew has chosen a value of 10. Figure 7 shows the output of the test plan. Figure 7: Output of the test plan

The 3 Level Best Standard Plan has determined that the temperatures for the three chambers should be 349 K, 364 K and 380 K. The test units should be allocated equally across all three chambers.  Andrew wants to compare these results with the other test plan methods, so he follows the same steps to generate test plans using the rest of the available 3-level methods. Table 1 summarizes the results of these test plans. Note that the expected number of failures in the table is the probability of failure at each temperature level multiplied by the number of units allocated at that level.

Table 1: Results of different 3-level test plans

 Best Standard Plan Best Compromise Plan 349 K 364 K 380 K 354 K 367 K 380 K Units on Test 33.3333 33.3333 33.3333 50.7 20 29.3 Probability of Failure 0.1032 0.4723 0.9765 0.1767 0.5743 0.9765 Expected Failures 3.44 15.7433 32.55 8.9587 11.486 28.6115 Equal Expected Number Failing 4:2:1 Allocation 356 K 368 K 380 K 352 K 366 K 380 K Units on Test 62.7992 22.6909 14.5099 57.1429 28.5714 14.2857 Probability of Failure 0.2256 0.6244 0.9765 0.1415 0.5307 0.9765 Expected Failures 14.1675 14.1682 14.1689 8.0857 15.1628 13.95

Andrew sees that the temperature levels recommended by all test plans are fairly similar and with the exception of the Best Standard Plan, where the expected number of failures at 349 K is low, the expected number of failures at each temperature level is reasonable. Knowing that in an accelerated test ideally the number of failures at each level should be similar, he decides to use the Equal Expected Number Failing Plan, where he expects to observe approximately 14 failures in each chamber.

Finally, Andrew wants to evaluate his test plan. Given a confidence level of 80% and his current sample size of 100 units, the bounds ratio (which is the upper confidence bound divided by the lower confidence bound) is 3.3664, as shown in Figure 8. Figure 8: Calculated bounds ratio

If he wanted to reduce the bounds ratio to 2 in order to see tighter confidence bounds at the same confidence level, his sample size should be increased from 100 test units to 307 test units, as shown in Figure 9. Figure 9: Calculated sample size

As with any sort of testing, the larger the sample size, the more certain the results will be. Given the information that Andrew has determined here, he can now address the business decision of whether to accept these bounds or to approach management and request more units for testing.

## References 