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What is MTBF (mean time between failures)?

The average interval between failures. For a synchronizer it is the average time between metastable events that fail to resolve and propagate onward, given by MTBF = e^(t_r/τ) ÷ (T_0 × f_clk × f_data). Adding stages lengthens the resolution time t_r and increases it exponentially.

Japanese name: MTBF(平均故障間隔)

MTBF (mean time between failures) appears in 8 practice questions across 5 topics, including Timing analysis and CDC, Yield and quality control, Reliability.

Two-flip-flop synchronizer Source clock domain Destination clock domain Source FF FF1 FF2 Async Direct Synced output Source clock Dest. clock Metastable risk Dest. clock FF1 output Unsettled FF2 output ~1 cycle If FF1 settles before the next edge, FF2 gets the correct value
Two-flip-flop synchronizer · View in diagrams

Field: Timing analysis and CDC

Try it: questions about MTBF (mean time between failures)

Which correctly describes MTBF (mean time between failures)?

  1. AThe average time from a failure until repair is completed
  2. BThe shortest time until the first failure occurs
  3. CFor a repairable system, the average operating time from one failure to the next
Show answer and explanation

Answer: C. For a repairable system, the average operating time from one failure to the next

MTBF (mean time between failures) is the average operating time between failures of a system that is repaired and kept in service; higher means more reliable. Mean time from failure to completed repair is MTTR, and mean time to failure for non-repaired parts is MTTF. Because MTBF is an average, it does not mean nothing fails before then, nor is it the shortest time to first failure.

How does the mean time between failures (MTBF) due to metastability change when a two-flip-flop synchronizer is extended to three stages?

  1. AThe time available for metastability to resolve increases by about one period, and MTBF grows exponentially
  2. BMTBF increases 1.5 times, in proportion to the number of stages
  3. CHow likely metastability is depends on the input side, so MTBF does not change
Show answer and explanation

Answer: A. The time available for metastability to resolve increases by about one period, and MTBF grows exponentially

Synchronizer MTBF is approximately MTBF = e^(t_r/τ) ÷ (T_0 × f_clk × f_data), where t_r is the time available for metastability to resolve and τ and T_0 are constants determined by the flip-flop's characteristics. Adding a stage extends t_r by about one period. For example, with τ = 20 ps, increasing t_r by 1 ns multiplies MTBF by e^50, more than 10^21 times. The probability of the first stage going metastable is unchanged, but the probability that it resolves before propagating further rises sharply.

MTBF (mean time between failures) in the explanations

Questions that mention MTBF (mean time between failures) (8)

  1. Which correctly describes MTBF (mean time between failures)?
  2. How does the mean time between failures (MTBF) due to metastability change when a two-flip-flop synchronizer is extended to three stages?
  3. Raising the clock frequency on the receiving side of a synchronizer shortens MTBF. Why?
  4. What is the state called when a flip-flop receiving an asynchronous signal violates setup or hold time and its output is temporarily neither 0 nor 1?
  5. Which is the general explanation of the difference between a product's "quality" and its "reliability"?
  6. In sampling inspection, which judges an entire lot as accepted or rejected by inspecting a sample, which metric expresses the quality level considered acceptable?
  7. Which is a correct precaution about the connection between the first and second stages of a two-flip-flop synchronizer?
  8. Which correctly describes the book-to-bill (BB) ratio, used as an indicator of the semiconductor equipment market?

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Related terms

Synchronizer Flip-flop MTTF (mean time to failure) Metastability Hold time Yield Asynchronous FIFO Clock domain Clock uncertainty Critical path

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