Document Number: 40018
Revision 08-Jul-03
www.vishay.com
42
M39003/01/03/06/09
Vishay Sprague
For technical questions, contact tantalum@vishay.com
FOR EXAMPLE: 20000.00
If a 15µF, 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:
F(x) = 1 - e ( )
F(x) = Cumulative fraction failed (P) at time (t)
t = Actual test time
ß = Weibull shape parameter (beta)
a = Weibull scale parameter (alpha)
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 which-
ever 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 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 burn-
in 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
Vs/Vr
1.0
1.1
1.2
1.3
1.4
1.5
1.527
A.F.
1.0
6.53
42.7
279.0
1824.0
—
11923.0
tß
a
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.
WEIBULL DISTRIBUTION METHOD FOR
DETERMINING FAILURE RATE, MIL-C-39003
RELIABILITY LIFE CYCLE -
TYPICAL "BATHTUB" CURVE
USEFUL LIFE PERIOD
WEAROUT
PERIOD
FAILURE RATE
INFANT
FAILURE
PERIOD
TIME
Solid-Electrolyte TANTALEX® Capacitors,
Military MIL-C-39003 Qualified, Syles CSR13, 21, 23, 33
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 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:
A.F. = 7.034 x 10-9 e (18.7724 Vs/Vr)
Vs = Voltage Stress
Vr = Rated voltage of unit under test
The acceleration factors used in MIL-C-39003 are as shown: