M39003 VAISH [Vaishali Semiconductor], M39003 Datasheet - Page 16

• Manufacturer Part Number: M39003
• Manufacturer: VAISH [Vaishali Semiconductor]

WEIBULL DISTRIBUTION METHOD FOR
DETERMINING FAILURE RATE, MIL-C-39003
The current issue of Military Specification MIL-C-39003
incorporates Weibull distribution techniques as a means for
calculating failure rates for solid tantalum capacitors. The
exponential failure rates (M, P, R and S) are inactive for new
designs. Weibull graded failure rate level "B" capacitors
supersede exponential failure rates M, P, R and S.
Increasingly, more stringent quality measurement systems
are being used in the electronics industry. AQL sample plans
are being replaced by programs measuring component
quality in PPM (Parts Per Million). Product quality
specifications seemingly approach perfection. Procedures
used to calculate PPM quality levels are based on
manufacturers' in-process controls and final inspection
results and by users' data at incoming inspection and
equipment assembly.
Initial quality requirements are only part of a good product
specification. Reliability and useful life should be considered
as well - to fit the reliability and useful life requirements of end
equipment.
Reliability is a measure of the expected failure rate during the
useful life of the capacitor. When plotted the failure rate
follows a characteristic "bathtub" curve, covering three
periods in the typical capacitor life cycle.
The bathtub curve shows the early time period called infant
failure period, the uniform failure rate period or useful life and
a period of increasing failure rate due to wearout.
The Weibull shape parameter beta (ß) is shown as less than
one (ß < 1) during infant mortality, one (ß = 1) during the
useful life and greater than one (ß > 1) during the wearout
period. Since Weibull distribution works well on units with a
beta less than 1, solid tantalum capacitors can use this
method for determining failure rates. Solid tantalum
capacitors fail early in life (normally during the aging or
burnin cycles) and show a slightly decreasing failure rate
with time - however, there is no known wearout failure mode.
The processing of solid tantalum capacitors is not "perfectly
clean". Impurities in the tantalum powders along with
microscopic dust particles can cause flaws in the dielectric
tantalum oxide. These flaws in the dielectric can cause
failure sites which are normally found during the in-process
aging or burn-in cycles. A very large percentage of failures
Document Number: 40018
Revision: 08-Feb-06
RELIABILITY LIFE CYCLE -
TYPICAL "BATHTUB" CURVE
INFANT
FAILURE
PERIOD
Military MIL-C-39003 Qualified, Syles CSR13, 21, 23, 33
USEFUL LIFE PERIOD
TIME
Solid-Electrolyte TANTALEX® Capacitors,
For technical questions, contact: [e-mail]
WEAROUT
PERIOD
occur during these burn-ins. Since the worst flaws are
presumed to fail first, we eventually arrive at flaw sizes which
are presumably too small to cause further degradation.
Weibull states that the failure rate of a component that shows
a decreasing failure rate with time can be predicted within a
short period of time under accelerated conditions.
Accelerated conditions for solid tantalum capacitors can be
imposed by means of either voltage or temperature stress.
Since temperatures above + 125 °C can cause degradation
of the solid manganese dioxide electrolyte, voltage
acceleration is performed instead.
The Navy's Crane NAD facility completed testing on solid
tantalum capacitors from several manufacturers in late 1981.
During testing, acceleration factors (A.F.) were derived from
life test results and the following formula used:
The acceleration factors used in MIL-C-39003 are as shown:
FOR EXAMPLE:
If a 15 µF, 20 V part is placed on test for 1 hour at + 85 °C
and 26 V (Vs/Vr = 1.3), this is equivalent to 279 hours of
testing at + 85 °C and 20/ V (exponential grading).
To explain the Weibull analysis, several formulas must be
shown. The basic Weibull formula is as shown:
To calculate Weibull failure rates, special burn-in ovens must
be used which will record an actual time to failure for each of
the units on test.
To perform the test, 100 % of the units (or 500 pieces
whichever is less) are placed in the Weibull oven and taken
to test conditions (+ 85 °C and voltage stress per the
acceleration factors chosen). For lots over 500 pieces, the
balance of the lot is placed in a standard burn-in oven at the
same Weibull conditions. Failures that occur during the
start-up are not used in the calculation. After test conditions
are reached (< 5 minutes), the start time is considered to be
t0.
A count of good pieces is taken at no later than 15 minutes
after t0. This will be the sample size. At least two hours after
t0, the number of failures are counted. If no failures occur,
the lot must be put back on test and recounted after 10 hours.
A.F. = 7.034 x 10-9 e (18.7724 Vs/Vr)
Vs = Voltage Stress
Vr = Rated voltage of unit under test
F(x) = Cumulative fraction failed (P) at time (t)
t = Actual test time
ß = Weibull shape parameter (beta)
a = Weibull scale parameter (alpha)
Vs/Vr
1.0
1.1
1.2
1.3
1.4
1.5
1.527
F x ( )
M39003/01/03/06/09
=
A.F.
1.0
6.53
42.7
279.0
1824.0
-
11923.0
20000.00
1 e
–
Vishay Sprague
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⎝ ⎠
tβ
---- -
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www.vishay.com
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