To Burn-In, or Not to Burn-In: That’s the Question
Abstract
:1. Introduction
2. Analysis
2.1. Prediction Based on the Analytical Approximation of the Bathtub-Curve (BTC)
2.2. Prediction Based on the Analysis of the SFR Process
3. Conclusions
- Two mutually complementing modeling studies have been carried out: (1) the analysis of the configuration of the IMP of the BTC, the reliability “passport” of an established semiconductor technology; and (2) the analysis of the role of the random SFR of the mass-produced components that the product of interest is comprised of.
- The first analysis has shown that the BTC-based time-derivative of the failure rate at the initial moment of time can be considered as a suitable criterion of whether BIT should or does not have to be conducted. If this derivative is small, no BIT might be needed, because the initial part of the IMP is more-or-less parallel to the time axis, and this is an indication that there are no highly unreliable items (“freaks”) in the lot and that the initial moment of time is, in effect, the start of the steady-state BTC condition. In the opposite extreme case, when this derivative is significant, BIT is needed, but could be made very short, because the “freaks” are so unreliable that even a very short and weak BIT could successfully remove them.
- The second analysis has indicated that the above criterion is, in effect, the variance of the random SFR of the mass-produced components that the product manufacturer received from numerous vendors, whose commitments to reliability were unknown, and their random SFR might vary therefore in a very wide range, from zero to infinity.
- A solution for the case of the normally distributed random SFR was obtained. Using this solution, probabilities of non-failure as functions of time and the ratio of the mean value of the random SFR of the mass-produced components to its standard deviation (in analysis of structures this ratio is known as safety factor) were calculated. This adds useful information to the next-step investigations and a more effective answer to our fundamental “question in question”.
- Although this paper does not offer a straightforward and an ultimate answer to this question, the suggested physics-of-failure and statistics-of-failure based criterion, and the calculated probabilities of non-failure for the given loading conditions and time of testing, provide a useful step forward in advancing today’s BIT practice, which is based on the HALT, a “black box” that has many merits, but does not quantify reliability, even on a deterministic basis.
- Future work should include experimental verification of the suggested “to burn-in or not to burn in” criterion, as well as its acceptable values, which would enable to answer the “to burn-in or not to burn-in” question. It should include also investigation of the effects of other possible distributions of the random SFR, such as, for example, Rayleigh distribution.
Conflicts of Interest
Acronyms
BAZ | Boltzmann-Arrhenius-Zhurkov’s (equation) |
BIT | Burn-in Testing |
BTC | Bathtub Curve |
DfR | Design for Reliability |
FOAT | Failure Oriented Accelerated Testing |
HALT | Highly Accelerated Life Testing |
IMP | Infant Mortality Portion (of the BTC) |
PDfR | Probabilistic Design for Reliability |
SFR | Statistical Failure Rate |
Appendix A
SFR of a Product Comprised of Mass-Produced Components
Appendix B
Prediction Based on the Application of the BAZ Equation
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−3.0 | −2.5 | −2.0 | −1.5 | −1.0 | −0.5 | −0.25 | 0 | 0.25 | |
3.0000 | 2.5005 | 2.0052 | 1.5302 | 1.1126 | 0.7890 | 0.6652 | 0.5642 | 0.4824 | |
−0.9990 | −0.9906 | −0.9500 | −0.8352 | −0.6472 | −0.4952 | −0.4040 | −0.3272 | −0.2644 | |
0.5 | 1.0 | 1.5 | 2.0 | 2.5 | 3.0 | 3.5 | 4.0 | 4.5 | |
0.4163 | 0.3194 | 0.2541 | 0.2080 | 0.1618 | 0.1456 | 0.1300 | 0.1166 | 0.1053 | |
−0.1938 | −0.1306 | −0.0922 | −0.0924 | −0.0324 | −0.0312 | −0.0268 | −0.0226 | −0.0190 | |
5.0 | 6.0 | 7.0 | 8.0 | 9.0 | 10.0 | 11.0 | 12.0 | 13.0 | |
0.0958 | 0.0809 | 0.0699 | 0.0615 | 0.0549 | 0.0495 | 0.0451 | 0.0414 | 0.0391 | |
−0.0149 | −0.0110 | −0.0084 | −0.0066 | −0.0054 | −0.0044 | −0.0037 | −0.0023 | −0.0030 | |
15.0 | 20.0 | 30.0 | 50.0 | 100.0 | 200.0 | 500.0 | 1000.0 | 1500.0 | |
0.0332 | 0.0249 | 0.0166 | 0.0100 | 0.0050 | 0.0025 | 0.0010 | 0 | 0 | |
−0.0017 | −0.0008 | −0.0003 | −0.0001 | −2.5 × 10−5 | −5.0 × 10−6 | −2.0 × 10−6 | 0 | 0 |
s | 0 | 0.1 | 0.2 | 0.3 | 0.4 | 0.5 | 0.6 | 0.7 | 0.8 |
0.5642 | 0.6021 | 0.6433 | 0.6881 | 0.7366 | 0.7890 | 0.8451 | 0.9033 | 0.9708 | |
s | 0.9 | 1.0 | 1.5 | 2.0 | 2.5 | 3.0 | 3.5 | 4.0 | |
1.0397 | 1.1126 | 1.5302 | 2.0052 | 2.5005 | 3.0000 | 3.5000 | 4.0000 |
−3.0 | −2.5 | −2.0 | −1.5 | −1.0 | −0.5 | −0.25 | 0 | 0.25 | |
3.0000 | 2.5005 | 2.0052 | 1.5302 | 1.1126 | 0.7890 | 0.6652 | 0.5642 | 0.4824 | |
x | x | x | x | x | x | x | x | x | |
0 | x | x | x | x | x | x | x | 1.0000 | 0.7857 |
1 | x | x | x | x | 1.0000 | 0.4543 | 0.3687 | 0.3236 | 0.2393 |
2 | x | x | 1.0000 | 0.2165 | 0.1081 | 0.0938 | 0.0975 | 0.1047 | 0.1141 |
3 | 1.0000 | 0.0820 | 0.0181 | 0.0101 | 0.0117 | 0.0194 | 0.0258 | 0.0339 | 0.0435 |
4 | 2.4788 × 10−3 | 5.5226 × 10−4 | 3.2856 × 10−4 | 4.7557 × 10−4 | 1.2613 × 10−3 | 3.9938 × 10−3 | 6.8125 × 10−3 | 1.0959 × 10−2 | 0.0166 |
5 | 6.1442 × 10−6 | 3.7173 × 10−6 | 5.9555 × 10−6 | 2.2289 × 10−5 | 1.3638 × 10−4 | 8.2428 × 10−4 | 1.8010 × 10−3 | 3.5458 × 10−3 | 0.6313 × 10−2 |
6 | 1.5230 × 10−8 | 2.5022 × 10−8 | 1.0795 × 10−11 | 1.0447 × 10−6 | 1.4724 × 10−5 | 1.7012 × 10−4 | 4.7614 × 10−4 | 1.1472 × 10−3 | 2.4055 × 10−3 |
7 | 3.7751 × 10−11 | 1.6843 × 10−10 | 1.9567 × 10−9 | 4.8963 × 10−8 | 1.5909 × 10−6 | 3.5111 × 10−5 | 1.2588 × 10−4 | 3.7119 × 10−4 | 9.1664 × 10−4 |
8 | 9.3576 × 10−14 | 1.1337 × 10−12 | 3.5468 × 10−2 | 2.2948 × 10−9 | 1.7189 × 10−7 | 7.2464 × 10−6 | 3.3278 × 10−5 | 1.2010 × 10−4 | 5.6584 × 10−4 |
9 | 2.3195 × 10−16 | 7.6314 × 10−15 | 6.4289 × 10−13 | 1.0756 × 10−10 | 1.8572 × 10−8 | 1.4956 × 10−6 | 8.7979 × 10−6 | 3.8858 × 10−5 | 1.3310 × 10−4 |
10 | 5.7495 × 10−19 | 5.1369 × 10−17 | 1.165 × 10−14 | 5.041 × 10−12 | 2.0066 × 10−9 | 3.0867 × 10−7 | 1.2572 × 10−6 | 5.7495 × 10−5 | 5.3226 × 10−5 |
0.5 | 1.0 | 1.5 | 2.0 | 2.5 | 3.0 | 3.5 | 4.0 | 4.5 | |
0.4163 | 0.3194 | 0.2541 | 0.2080 | 0.1618 | 0.1456 | 0.1300 | 0.1166 | 0.1053 | |
x | x | x | x | x | x | x | x | x | |
0 | 0.6595 | 0.5279 | 0.4666 | 0.4352 | 0.4453 | 0.4174 | 0.4025 | 0.3935 | 0.3876 |
1 | 0.2868 | 0.2787 | 0.2807 | 0.2871 | 0.3222 | 0.3120 | 0.3104 | 0.3116 | 0.3140 |
2 | 0.1247 | 0.1471 | 0.1689 | 0.1894 | 0.2331 | 0.2332 | 0.2393 | 0.2468 | 0.2544 |
3 | 5.4253 × 10−2 | 7.7677 × 10−2 | 0.1016 | 0.1249 | 0.1687 | 0.1743 | 0.1845 | 0.1955 | 0.2061 |
4 | 2.3595 × 10−2 | 4.1008 × 10−2 | 6.1109 × 10−2 | 8.2414 × 10−2 | 0.1220 | 0.1302 | 0.1423 | 0.1548 | 0.1669 |
5 | 1.0262 × 10−2 | 2.1649 × 10−2 | 3.6762 × 10−2 | 5.4367 × 10−2 | 8.8301 × 10−2 | 9.7335 × 10−2 | 0.1097 | 0.1226 | 0.1352 |
6 | 4.4632 × 10−3 | 1.1429 × 10−2 | 2.2115 × 10−2 | 3.5865 × 10−2 | 6.3890 × 10−2 | 7.2745 × 10−2 | 8.4585 × 10−2 | 9.7101 × 10−2 | 0.1096 |
7 | 1.9411 × 10−3 | 6.0337 × 10−3 | 1.3304 × 10−2 | 2.3659 × 10−2 | 4.6227 × 10−2 | 5.4367 × 10−2 | 6.5219 × 10−2 | 7.6904 × 10−2 | 8.8753 × 10−2 |
8 | 8.4422 × 10−4 | 3.1853 × 10−3 | 8.0033 × 10−3 | 1.5608 × 10−2 | 3.3447 × 10−2 | 4.0632 × 10−2 | 5.0287 × 10−2 | 6.0907 × 10−2 | 7.1898 × 10−2 |
9 | 3.6716 × 10−4 | 1.6816 × 10−3 | 4.8146 × 10−3 | 1.0296 × 10−2 | 2.4200 × 10−3 | 3.0367 × 10−2 | 3.8774 × 10−2 | 4.8238 × 10−2 | 5.8245 × 10−2 |
10 | 1.5969 × 10−4 | 8.8777 × 10−4 | 2.8964 × 10−3 | 6.7921 × 10−3 | 1.7510 × 10−2 | 2.2695 × 10−2 | 2.9897 × 10−2 | 3.8205 × 10−2 | 4.7184 × 10−2 |
5.0 | 6.0 | 7.0 | 8.0 | 9.0 | 10.0 | 11.0 | 12.0 | 13.0 | |
0.0958 | 0.0809 | 0.0699 | 0.0615 | 0.0549 | 0.0495 | 0.0451 | 0.0414 | 0.0391 | |
x | x | x | x | x | x | x | x | x | |
0 | 0.3837 | 0.3788 | 0.3758 | 0.3738 | 0.3722 | 0.3716 | 0.3708 | 0.3702 | 0.3618 |
1 | 0.3168 | 0.3222 | 0.3268 | 0.3305 | 0.3335 | 0.3366 | 0.3388 | 0.3408 | 0.3346 |
2 | 0.2615 | 0.2741 | 0.2842 | 0.2923 | 0.2989 | 0.3048 | 0.3096 | 0.3137 | 0.3094 |
3 | 0.2159 | 0.2331 | 0.2471 | 0.2585 | 0.2678 | 0.2761 | 0.2829 | 0.2888 | 0.2862 |
4 | 0.1783 | 0.1983 | 0.2149 | 0.2286 | 0.2399 | 0.2501 | 0.2585 | 0.2659 | 0.2646 |
5 | 0.1472 | 0.1687 | 0.1868 | 0.2021 | 0.2150 | 0.2265 | 0.2362 | 0.2447 | 0.2447 |
6 | 0.1215 | 0.1435 | 0.1624 | 0.1787 | 0.1926 | 0.2052 | 0.2158 | 0.2253 | 0.2263 |
7 | 0.1003 | 0.1220 | 0.1413 | 0.1580 | 0.1726 | 0.1858 | 0.1972 | 0.2074 | 0.2093 |
8 | 8.2844 × 10−2 | 0.1038 | 0.1228 | 0.1397 | 0.1546 | 0.1683 | 0.1802 | 0.1909 | 0.1936 |
9 | 6.8399 × 10−2 | 8.8301 × 10−2 | 0.1424 | 0.1236 | 0.1386 | 0.1524 | 0.1646 | 0.1757 | 0.1790 |
10 | 5.6473 × 10−2 | 7.5110 × 10−2 | 9.2866 × 10−2 | 0.1093 | 0.1242 | 0.1646 | 0.1504 | 0.1618 | 0.1655 |
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Suhir, E. To Burn-In, or Not to Burn-In: That’s the Question. Aerospace 2019, 6, 29. https://doi.org/10.3390/aerospace6030029
Suhir E. To Burn-In, or Not to Burn-In: That’s the Question. Aerospace. 2019; 6(3):29. https://doi.org/10.3390/aerospace6030029
Chicago/Turabian StyleSuhir, Ephraim. 2019. "To Burn-In, or Not to Burn-In: That’s the Question" Aerospace 6, no. 3: 29. https://doi.org/10.3390/aerospace6030029