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2.5.2 Reliability Statistics in Electronics

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First, identify what type of characterization is needed for the application. Questions to consider include:

 Is a rate being modeled?

 Is there a specific number of trials?

 Is the probability of success the same for all trials?

 Are there discrete functions requiring analysis: pass/fail, working/non‐working, on/off?

 Are there continuous functions requiring analysis: controlled by a continuous variable like time?

 Are there point functions requiring analysis: repairable systems where more than one failure or type may occur over time?

Frequently used reliability statistics for electronics include:

 Failure rate = failure per unit of time for a population. Examples:– 4 failures (population) per million operating hours = 4 hours.– 1000 items operating for a year before failure = 1000 hours 365 days operating hours.– Note: In some texts, the term failure rate is reserved for repairable systems (more than one failure per device is possible) and the term hazard rate (H) is used for non‐repair able systems (only one failure per device is possible). In practice, the terms are used interchangeably, with the term failure rate commonly used in the US.

 Mean time between failure (MTBF). Example:– MTBF = 1 / failure rate– Using the failure rate, the MTBF is 1 4 hours = 250,000 hours.

 Percent or probability of survival or failure at a point along a timeline. Examples:– Reliability = 99.7% (0.9970) at 1 year, 98.9% at 3 years (warranty), 96.5% at 10 years (design life).– Failure = 1 − reliability or . So, failure is equal to 100 99.7 = 0.3% (.0030) at 1 year. 100 98.9 = 1.1% at 3 years (warranty). 100 96.5 = 3.5% at 10 years (design life).– 3 failed out of 1000, 11 failed out of 1000, 36 failed out of 1000.

 The FIT (failure in time) rate is defined as the expected number of component failures per billion (10) hours:– The FIT rate can be easily converted to the MTBF in hours where: MTBF = 10 hours/FIT.– The annualized failure rate (AFR) is calculated as AFR = (FIT 8760)/10 hours.– The advantage of using FIT rates rather than MTBF is that FIT rates are additive. For example, if the FIT rate of Part A is 125, and the FIT rate of all other component failures is 75, the FIT rate of the system is 125 + 75 = 200.– A FIT rate of 200 corresponds to an MTBF of (10 hours / 200) = 5 hours. (5 hours is a very low failure rate.)– A FIT rate of 200 also corresponds to an AFR of (200 hours 8760)/10 hours = 0.00175 = 0.175%.

 DPPM = Defective parts per million– Example:– 20 pieces are defective in a lot of 1000 pieces. The DPPM is equal to (20 / 1000) =.02 or 2.0% defect ive. 0.020 1,000,000 = 20,000 DPPM.

Design for Excellence in Electronics Manufacturing

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