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Reliability Statistical Analysis

Reliability Statistical Analysis. Larry Harzstark The Aerospace Corporation January 18, 2006. Outline. Data Model Assumptions Model Estimation Perceptivity FIT Rate Calculator Results. Data. Data Sets contain many variables: Number of FPGAs Tested Voltage and temperature of the test

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Reliability Statistical Analysis

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  1. Reliability Statistical Analysis Larry Harzstark The Aerospace Corporation January 18, 2006

  2. Outline • Data • Model Assumptions • Model Estimation • Perceptivity • FIT Rate Calculator • Results

  3. Data • Data Sets contain many variables: • Number of FPGAs Tested • Voltage and temperature of the test • Number of each type of antifuse in particular FPGA design tested • Amount of time on test • Interval of time when and if an antifuse failure* occurred • Type of antifuse that failed • Timing delay of antifuse failure * Failure defined as an antifuse with a delta timing delay increase greater than a pre-specified value

  4. Model Assumptions • Antifuse types can be divided into two categories • Sensitive antifuse types (more susceptible to failure) • The usage class of antifuse in a circuit or net segment path where testing has shown observable timing faults • Non-sensitive antifuse types • The type or usage class of antifuses in a circuit or net segment path for which no failures or timing faults have been observed • Lifetime data for sensitive antifuse types can be described by a one-population Weibull distribution • Commercial parts and RT parts are assumed to have the same shape factor, but different scale factors • Lifetime data for non-sensitive antifuse types can be described by a one-population Weibull distribution with the same shape factor as the sensitive antifuse types • Commercial and RT data for non-sensitive antifuse types can be grouped together under the assumption that RT parts are more robust than commercial parts and no non-sensitive antifuse failures have occurred • It is assumed that there is no voltage or temperature acceleration

  5. Model Estimation • Distributions are estimated at the antifuse level • Weibull distribution for sensitive antifuse types is estimated using Maximum Likelihood Estimation (MLE) • Aerospace uses S-Plus software with SPLIDA package to estimate MLE parameters • Failure times are not assumed, interval data is used • Confidence intervals for sensitive antifuse types are computed by determining the corresponding likelihood region for the estimated parameters • Scale factor for Weibull distribution for non-sensitive antifuse types cannot be calculated since no failures have occurred – scale factor is bounded using a 50% bound • Confidence intervals for non-sensitive antifuse types are determined using appropriate bounds on the scale factor

  6. Perceptivity • Different levels of perceptivity were considered and model estimations were computed for each level of perceptivity • High Perceptivity • Assumes any antifuse that has a timing delay that is greater than 2 ns is a failure • Medium Perceptivity • Assumes any antifuse that has a timing delay that is greater than or equal to 10 ns is a failure • Low Perceptivity • Assumes any antifuse that has a timing delay that is greater than or equal to 70 ns is a failure

  7. FIT Rate Calculator • User inputs • Antifuse count breakdown for design of interest • Length of mission in years • Screen time prior to launch of FPGA (restricted to 0, 250, or 500 hours to obtain information on confidence intervals) • Desired level of perceptivity • Calculator assumptions • If a single antifuse fails in an FPGA, then the FPGA fails • Desired level of perceptivity is the same for all antifuses in the design • Calculator outputs • Maximum likelihood estimates for mission reliability and average FIT rate • 60% and 90% upper confidence bounds for the average FIT rate

  8. Results • Assumptions: • 10 year mission • 866 sensitive antifuse types in design* • 14,837 non-sensitive antifuse types in design* • High perceptivity required • Results are regularly updated to incorporate new data * Number of antifuses in an “average” customer design

  9. Summary • Reliability statistical analysis and calculator affords the user community a vehicle for calculation of failure rates

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