This response assumes that you are trying to demonstrate a certain MTBF (reliability) and are trying to determine the test duration, applied stress levels and test sample size.
The time that would be required to validate a desired MTBF is dependent upon a number of factors. Ignoring accelerated testing for the moment, the factors that would determine test time would be the risk level, the ratio of the Design MTBF to Minimum Acceptable MTBF of (known as the Discrimination Ratio), observed number of failures and whether the test will be fixed length or sequential. Generally, the required test time decreases with increasing risk levels and higher discrimination ratios. Additionally, a sequential test, in which a decision to accept, reject or continue testing is made continually throughout the test, may allow you to arrive at a decision quicker than using a fixed length test. For example, assuming a producer and consumer risk of 0.1 and a discrimination ratio of 1.5, a fixed length test would require 482,000 hours with less than 40 failures to demonstrate an MTBF of 10,000 hours. A sequential test could arrive at a reject decision in as little as 373 hours and an accept decision in as little as 65,917 hours with the actual test time being driven by the number of failures observed. The test would be truncated at 495,568 hours. Likewise, if we assume a producer and consumer risk of 0.2 and a discrimination ratio of 3.0, a fixed length test would require 44,000 hours and 2 failures or less. A sequential test could arrive at a reject decision in as little as 1,767 hours and an accept decision in as little as 20,794 hours. The test would be truncated at 46,051 hours. Since the reliability is assumed to follow an exponential distribution (constant failure rate), it would not matter if the time was accumulated on one unit or spread over many units. The number of test units would be driven by cost of the units, test facilities and calendar time available. Sources such as MIL-STD-781 and the RIAC System Reliability Toolkit provide further discussion on this topic.
It is possible to reduce test time calculated above by increasing the stress on the equipment and applying an acceleration factor. Overall there are four basic forms of accelerated life models: linear, exponential, power and logarithmic. The type of model chosen is driven by the type of stress applied during the test, which in turn should be determined by the expected predominant failure mechanisms. For example, the Arrhenius model is typically used to accelerate time with respect to temperature. The key to using this model is choosing an appropriate activation energy. In the absence of an activation energy, an approximation is that the failure rate doubles for every 10C rise in temperature. Another example involves the use of the power law model to determine an acceleration factor for vibration and voltage stress. Still another example is a fatigue life model such as Coffin-Manson to model the lifetime of solder joints subjected to cyclic fatigue. In the event that a combined stress environment is desired, compound acceleration models which are additive or multiplicative combinations of the basic forms are used. Sources including the RIAC System Reliability Toolkit can provide further discussion on this topic.
The use of accelerated testing can result in considerable savings of test time and money and help to identify design and manufacturing deficiencies. However, some things to beware of include multiple unrecognized failure modes, multiple time scales due to more than one accelerating variable, masked failure modes and the use of inappropriate acceleration models. Furthermore, as the system complexity increases so does the difficulty in formulating stress conditions that do not change the inherent failure mechanisms occurring within the equipment.
Richard Wisniewski
Senior Reliability Engineer
Reliability Information Analysis Center
(315) 351-4221
