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Table of Contents

Application Note

High Reliable BAW Oscillator MTBF and FIT Rate
Calculations

Purnachandar Poshala
ABSTRACT
Bulk acoustic wave (BAW) resonator technology provides high reliability for BAW-based oscillators in mean time
between failures (MTBF) and failure in time (FIT) values. Oscillators are typically integral to the system and often
have to perform reliably over the lifetime of the product.
Product developers need to develop products that can run reliably over the product lifetime and having the best
MTBF for BAW oscillators helps product developers easily select the oscillator component.
This application note provides calculation and results for MTBF and FIT values for BAW oscillators and provides
the procedure for these calculations.

Table of Contents
1 Introduction.............................................................................................................................................................................22 MTBF and FIT Calculations for BAW Oscillators.................................................................................................................23 Using the Online Estimator to Calculate MTBF and FIT......................................................................................................44 Importance of Mission Profiles for FIT Rate Calculations.................................................................................................. 6
5 Summary................................................................................................................................................................................. 7
6 References.............................................................................................................................................................................. 7

List of Figures
Figure 2-1. Snapshot of Online MTBF and FIT Estimates for the LMK6x................................................................................... 3
Figure 3-1. Snapshot of the Online MTBF and FIT Estimator Tool..............................................................................................4
Figure 3-2. Generated MTBF and FIT Information for the LMK6C ............................................................................................. 5
Figure 3-3. Snapshot of De-rating Tool Using 55 °C Use Case...................................................................................................6

List of Tables
Table 2-1. Data for Acceleration Factor Calculation.................................................................................................................... 2
Table 2-2. Data for Failure Rate Calculation ...............................................................................................................................3
Table 2-3. Chi-squared Values for Failure Number and Confidence level................................................................................... 3
Table 4-1. De-rated FIT Calculation.............................................................................................................................................6Trademarks
All trademarks are the property of their respective owners.

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Introduction

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1 Introduction
The calculation of failure rates is an important metric in assessing the reliability performance of a product.
JEDEC describes a method for calculating FIT rates in JEDEC JESD85 METHODS FOR CALCULATINGFAILURE RATES IN UNITS OF FITS . In this method, a known sample size of the component is placed underenvironmental stressess such as High Temperature Operating Life (HTOL) test. HTOL tests operate at hightemperatures, such as 125 °C, for a certain duration and the number of components that fail during the test are
noted and used in the calculation of FIT rates.
Reliability data is expressed either in failure in time (FIT) or mean time between failure (MTBF), or other similarparameters. FIT is equal to one failure occurring in 10×108 device hours (or 1 billion hours). FIT is typically theunit used to express the failure rate and can be defined as 1 parts per million (PPM) per 1000 hours of operationor one failure per 1000 devices run for 1 million hours of operation.
MTBF is the inverse of the FIT value (10×108/FIT). Most of these methods only apply to constant failure
rates. These methods assume that a χ2 (chi-square) distribution is a reasonable approximation of the failure
distribution over time. The examples provided in this application note use failures that exhibit an Arrhenius
behavior. A higher MTBF value (or lower FIT value) corresponds to a more reliable product that experiences
fewer problems or failures over the lifetime, resulting in lower repair costs and unplanned downtime.

2 MTBF and FIT Calculations for BAW Oscillators
Having a FIT rate of 1 indicates one failure over 1 billion hours of operation. A preferable method for calculating
FIT is to use HTOL reliability data and use the Arrhenius equation for acceleration, assuming a χ2 distribution asa reasonable approximation of the failure distribution over time. The JESD85 standard document, referenced inSection 1 is used for the calculations. While JESD85 shows methodologies for assessing FIT due to different failmechanisms, for most modern-day semiconductor technologies, the qualification acceptance is 0 failures.
Sample sizes for running HTOL vary from different qualification standards. For the LMK6x BAW oscillatorsfrom Texas Instruments, see www.ti.com for the HTOL test data under the quality, reliability, and packaging
information for the LMK6x device. Select the part number in the web site for view or download the reliability datafor that particular device. Based on the LMK6C, LMK6D, LMK6P, LMK6H data, sample size for HTOL is 7859,
test duration is 1000 hours, the number of failures is zero, and the test temperature is 125 °C. This data is valid
at the time this application note is written. For latest data, refer to the above product page links.
The step-by-step procedure for FIT calculation for LMK6x BAW oscillators is as follows:
Step 1: Calculate Acceleration Factor (AF)Calculate the Acceleration Factor (AF) using the data in Table 2-1. A common practice to gauge FIT is to de-rate
to 55 °C (operating or use temperature) based on the activation energy of 0.7 eV. The equation for calculating
AF is shown in Equation 1.
Acceleration Factor = exp

Ea ×1
1
Tuse − Tstressk(1)Substituting the values from Table 2-1 into the AF equation results in an factor of 78.6.
exp

20.7 eV1 − 1×55 °C 125 °C
8.6 × 10−5 eV/K

= 78.6(2)

Table 2-1. Data for Acceleration Factor Calculation
VariableValue

Accelerated Test Temperature (Tstress)

125 °COperating or Use Temperature (Tuse)55 °C

Activation Energy (Ea)

0.7 eV

Boltzmann's Constant (k)8.6×10-5 eV/K

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MTBF and FIT Calculations for BAW Oscillators

Step 2: Calculate the Failure Rate
After calculating the acceleration factor, the next step is to calculate the failure rate (FIT). For this calculation, theconfidence level is 60% (which is typical for industrial calculations) and the data in Table 2-2 is used.
Table 2-2. Data for Failure Rate Calculation
Variable

Value

Number of Samples (ss)7859

Test Duration (t)1000 hours

Confidence Level (CL)60%

The equation for calculating FIT rate is shown in the following equation. Where χ2 is the chi-square value and f is
the number of failures.
Failure Rate FIT =Χ2 %CL, 2 × f + 2 × 109
2 × t × ss × AF

(3)

Table 2-3 provides a quick reference for χ2 (chi-squared) values for different failures and different confidencelevels (60% and 90%).
Table 2-3. Chi-squared Values for Failure Number and Confidence level
Number of Failures (f)Confidence Level (60%)

Confidence Level (90%)

01.8334.605

14.0457.779

26.21110.6453

8.351

13.362

With a confidence level of 60% and the number of failures equal to zero, (f) = 0, a χ2 value of 1.833 is obtained
from Table 2-3. HTOL data for BAW oscillators is 0 failures in 7859 samples for 1000 hours of HTOL operation at125 °C, which when substituted into Equation 3, the FIT value is calculated to be 1.5 for 55 °C operation.
91.833 × 10Failure Rate FIT = 2 × 1000× 7859 × 78.6 ≅ 1.5(4)1MTBF = FIT= 6.66666667 × 108 = 6.7 × 108(5)As described in Section 1, the MTBF value is the inverse of the FIT value, as demonstrated in Equation 5.

This result indicates that the BAW oscillator mean time between failure is approximately 0.67 billion hours under
the conditions used in this section. Figure 2-1 shows a snapshot from TI online data for LMK6x BAW oscillators,
which supports these results.

Figure 2-1. Snapshot of Online MTBF and FIT Estimates for the LMK6x
To find the MTBF or FIT data information shown in Figure 2-1, refer to the LMK6x data sheet folder Ordering &quality tab and click on the View or Download link under Quality reliability & packaging information column.
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Using the Online Estimator to Calculate MTBF and FIT

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As a final example of how to use the information available on www.ti.com, for 35 °C operation, the FIT rateis calculated to be 0.3 with the exact same conditions used throughout this section. The MTBF is 3.32×109.
This result indicates that the BAW oscillator can operate for 3.32 billion hours without a fail at 35 °C usagetemperature.

3 Using the Online Estimator to Calculate MTBF and FIT
TI provides an online calculator, the MTBF/FIT estimator tool, for calculating MTBF and FIT. Figure 3-1 shows asnapshot of the online calculator. This section describes how to use the estimator tool using the LMK6C as anexample.
Enter the TI part number in the input provided under the MTBF and FIT estimator, shown Figure 3-1. Then clickon Search button.

Figure 3-1. Snapshot of the Online MTBF and FIT Estimator Tool

4

High Reliable BAW Oscillator MTBF and FIT Rate Calculations
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Using the Online Estimator to Calculate MTBF and FIT

Select the specific part number under the LMK6x list provided. Clicking on the individual part generates MTBFand FIT information, as shown Figure 3-2.

Figure 3-2. Generated MTBF and FIT Information for the LMK6C

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Importance of Mission Profiles for FIT Rate Calculations

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Above the information shown in Figure 3-2 is a button for the de-rating tool. Use this de-rating tool to find theFIT calculation for different usages and operating temperatures other than the calculations for 55 °C calculated
in the previous section. Enter the BAW oscillator FIT rate of 1.5 at 55 °C operation and use the scrolling
option to increase/decrease the application temperature to determine the MTBF numbers at different operating
temperatures.

Figure 3-3. Snapshot of De-rating Tool Using 55 °C Use CaseAs Figure 3-3 shows, for 35 °C operating temperature use case, the FIT value is 0.3.

4 Importance of Mission Profiles for FIT Rate Calculations
Mission profile is an important method for evaluating FIT rates in more practical use cases. The Calculating FITfor a Mission Profile application note explains how to use de-rating tools provided by TI in more detail.
The FIT rate calculations are worst-cast FIT values assuming one single operating temperature throughout thelifetime of the device. But in reality, the end system or end product where the oscillator is mounted is notexperiencing the same higher temperature throughout the full device lifetime. The oscillator typically experiencesa variety of temperatures over a period of time. The FIT value can be better than the worst-case value if theexact operating (use) temperatures are known and also the approximate percentage of time the oscillator isexperiencing this temperature over the lifetime of the device.
Table 4-1 provides an example mission profile along with the FIT calculations. For speicific applications, creatinga similar table to Table 4-1, can help in calculating the FIT rate for a real system. This table values are different
for different application use cases.
Table 4-1. De-rated FIT Calculation
Operating or Use Temperature(°C)% TimeDe-Rated FIT

FIT x(% Time)

2025

0.1

0.025

30

350.2

0.07

60

30

2.2

0.66

85

1011.9

1.19Mission Profile FIT rate6High Reliable BAW Oscillator MTBF and FIT Rate Calculations
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1.945

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Summary

The FIT number is 1.945 for this example use-case. If this example is calculated just at 85 °C operation
temperature with 100% time, the FIT number is 11.9, which is much higher than the practical use-case. Hence,understanding the use case of the system and using the MTBF or FIT calculator to find out the FIT number forthe actual use-case is crucial.

5 SummaryThis application note demonstrates how to calculate FIT rates for BAW oscillators using actual HTOL test data.
As shown in these calculations, at 35 °C usage temperature, the BAW oscillator FIT rate is 0.3, which is theindustry best for the oscillators across all the technologies of crystals and MEMS-based devices. A FIT rate of0.3 is equivalent to 3.3 billion hours of MTBF. Typical crystal oscillator FIT rates are 15 to 30, indicating improved
reliability in BAW oscillators in comparison to crystal oscillators with similar specifications.

6 References•••JEDEC, JESD85 METHODS FOR CALCULATING FAILURE RATES IN UNITS OF FITS JESD85 standard
Texas Instruments, Calculating FIT for a Mission Profile application note
Texas Instruments, LMK6x Low Jitter, High-Performance BAW Oscillator data sheet

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