Reliability Statistical Analysis

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