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Reliability Physics and Engineering
It would be a great accomplishment if we could simply design and build devices without defects. That should always be our goal—but, obtaining perfection is indeed a difficult/impossible challenge. Given that all devices will likely have a small fraction of the population which is defective, the question that we want to address in this chapter is: can a relatively shortduration stress be used to eliminate the defective/weak devices without causing significant degradation to the good/ strong devices? The use of a shortduration stress to eliminate weak devices is generally referred to as screening. We will find that screening can sometimes be very effective, but not always. Screening effectiveness depends on the exact details of the strength distribution for the devices plus the magnitude and duration of the screening stress.
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1.
A randomly selected sample of capacitors was rampedtofailure using a ramp rate of
R = 1 MV/cm/s at 105 °C. What is the timetofailure
t
_{0} at the breakdown field of 10 MV/cm and at 105 °C? Assume an exponential TF model with a field acceleration parameter of
γ = 4.0 cm/MV.
2.
A randomly selected sample of capacitors was rampedtofailure using a ramp rate of
R = 1 MV/cm/sec at 105 °C. What is the timetofailure
\( {t}_0^{\ast } \) at the breakdown field of 10 MV/cm and at 105 °C? Assume a powerlaw TF model with an exponent of
n = 44.
3.
For the capacitors described in Problem 1 above, calculate the screeninginduced degradation Δ
E
_{BD} for a capacitor with a prescreen breakdown strength of 10 MV/cm. Assume that the screen is conducted with stressing field of 9 MV for 5 s.
4.
For the capacitors described in Problem 2 above, calculate the screeninginduced degradation Δ
E
_{BD} for a capacitor with a prescreen breakdown strength of 10 MV/cm. Assume that the screen is conducted with stressing field of 9 MV for 5 s.
5.
Toxic gas lines/pipes are expected to operate at a normal pressure of 4 kpsi. To insure that the metal pipes can reliably withstand the normal operating pressure, a random selection of such pipes was taken and the pressure was rampedtorupture with a ramp rate of 1 kpsi/min at the expected operating temperature. The median prescreen rupture strength was determined to be 12 kpsi. Calculate the expected screeninginduced degradation to the median prescreen rupture strength if a screening stress of 6 kpsi is applied for 1 min.
(a)
Assume a powerlaw exponent of
n = 4.
(b)
Assume a powerlaw exponent of
n = 7.
Answers: (a) Δ
P
_{BD} = 0.063 kpsi and (b) Δ
P
_{BD} = 0.0078 kpsi
6.
Using the information found in Table
17.1, determine the screening effectiveness of using a 23 V screen and the degradation impact to the good/strong devices.
Answer: Comparing the 9 and 23 V screens, with the exponential TF model, the 23 V screen is excessive—it does not eliminate anymore defects than does the 9 V screen; in addition, the 23 V screen produces more degradation (ΔV
_{BD}) for the good/strong devices.
7.
Using the details found in Table
17.2, describe the screening effectiveness of using a 23 V screen and the degradation impact to the good/strong devices.
Answer: Comparing the 10 and 23 V screens, with the powerlaw TF model, the 23 V is excessive—it does not eliminate anymore weak devices than does the 10 V screen; in addition, the 23 V screen produces more degradation (Δ
V
_{BD}) for the good/strong devices.
8.
Using the details found in Example Problem 3, describe the screening effectiveness of using a 14 psi stress and the degradation impact to the good/strong devices.
(a)
Assume a powerlaw exponent of
n = 4.
(b)
Assume a powerlaw exponent of
n = 7.
Answers: (a) Δ
P
_{BD} = 0.063 kpsi and (b) Δ
P
_{BD} = 0.0078 kpsi
9.
A randomly selected group of 28 gas cylinders was rampedtorupture (using a ramp rate of 0.50 kpsi/min at the expected operational temperature) and the following rupture values (in units of kpsi) were obtained: 26.50, 1.00, 26.25, 2.00, 26.00, 2.50, 25.75, 3.50, 25.25, 9.00, 25.00, 9.50, 25.50, 10.00, 26.75, 28.00, 30.00, 27.00, 27.25, 29.75, 29.50, 29.25, 29.00, 28.75, 28.50, 28.25, 27.75, and 27.50. Assuming an operational pressure of 2 kpsi and a powerlaw. TF model with an exponent of
n = 5, evaluate the screening impact/effectiveness of applying a screening pressure of 1, 2, 3, or 4 kpsi for 1 min.
(b)
Identify the gas cylinder rupture values that represent a yield loss.
(c)
Identify the gas cylinder rupture values that represent a reliability risk.
(d)
What is the screening effectiveness when using a 1, 2, 3, or 4 kpsi screen for 1 min? Which is the optimal screen for this group of cylinders?
Answers:
(b)
Five rupture values less ≤2 kpsi represent a yield loss.
(c)
Three rupture values between 2 and 6 kpsi represent a reliability risk.
(d)
A screen of at least 4 kpsi for 1 min is needed to eliminate all weak components without producing significant degradation to the good/strong components. This represents the optimal screen for the four screening conditions presented.
1
2
A yield strength
ξ
_{Yield} (see Chap.
13) has not been included in this powerlaw model. Since we are screening for defects, the assumption is made here that the defective units are unlikely to have a yield point.
Recall from Chap.
6––to convert the standard deviation Zvalue to cumulative fraction
F of devices, use the Excel Function:
F = NORMSDIST(Z).
 Titel
 Screening
 DOI
 https://doi.org/10.1007/9783319936833_17
 Autor:

J. W. McPherson
 Sequenznummer
 17
 Kapitelnummer
 Chapter 17