The time that would be required to validate the desired MTBF of 50,000 hours is dependent upon a number of factors. Ignoring accelerated testing, the factors that would determine test time would be the risk level, the ratio of the Design MTBF to Minimum Acceptable MTBF of 50,000 hours (known as the Discrimination Ratio) 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 2,477,839 hours with less than 40 failures to demonstrate an MTBF of 50,000 hours. A sequential test could arrive at a reject decision in as little as 1,863 hours and an accept decision in as little as 329,584 hours with the actual test time being driven by the number of failures observed. The test would be truncated at 2,477,839 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 220,000 hours. A sequential test could arrive at a reject decision in as little as 8,834 hours and an accept decision in as little as 103,972 hours. The test would be truncated at 230,256 hours. Since the reliability is assumed to follow an exponential distribution (constant failure rate), it would not matter if the time was accumulated on 1 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 by increasing the stress on the equipment and applying an acceleration factor. The type of stress to be used 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.
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.
Senior Reliability Engineer
Reliability Information Analysis Center