Consider a 50-pin module such that the probability of failure upon inserting it into a mating connector is [latex]1.8 \times 10^{-3}[/latex] % per pin. What is the probability of failure of the module?

In this problem the module is the system (s), and the pins (p) are the elements. If we assume that a single pin failure causes the module to fail, then by Eqn (4.21), [latex]F_{s}(t)=1-\prod\limits_{i=1}^{n} (1-F_{i}(t))[/latex], (4.21) [latex]F_{s}=1-(1-F_{p})^{n}[/latex] , where n is the number of pins per module. Substituting, [latex]F_{p}=1.8 \times 10^{-5}[/latex] and n = 50 yields [latex]F_{s}=1-(1-1.8\times10^{-5})^{50}=0.00090[/latex]. Therefore, the failure probability is predicted to be 0.09%, or 9 module failures in 10,000 insertions.

Question 4.4: Consider a 50-pin module such that the probability of failur...

Reliability and Failure of Electronic Materials and Devices

Consider a 50-pin module such that the probability of failure upon inserting it into a mating connector is $1.8 \times 10^{-3}$ % per pin. What is the probability of failure of the module?

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In this problem the module is the system (s), and the pins (p) are the elements. If we assume that a single pin failure causes the module to fail, then by Eqn (4.21),

$F_{s}(t)=1-\prod\limits_{i=1}^{n} (1-F_{i}(t))$ , (4.21)

$F_{s}=1-(1-F_{p})^{n}$ , where n is the number of pins per module. Substituting, $F_{p}=1.8 \times 10^{-5}$ and n = 50 yields $F_{s}=1-(1-1.8\times10^{-5})^{50}=0.00090$ .
Therefore, the failure probability is predicted to be 0.09%, or 9 module failures in 10,000 insertions.

A collection of 60 laser diodes were tested, and 7 failures occurred after 1000 h. The lifetimes obtained are tabulated below. 1. Plot the results in both Weibull and lognormal fashion. 2. What is the MTTF for each? 3. For the lognormal plot, what is the value of σ? 4. For the Weibull plot, what ...

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First,

F(t_{i})

is calculated for n...

Question: 4.1

Suppose that a population of 525,477 solid-state devices is burned in at elevated temperature, and the number of failed devices are weeded out as a function of time is recorded in the following table. Determine the failure rates, λ(t), at the indicated times. ...

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Results of the calculations are tabulated. Tim...

Question: 4.6

Suppose that ICs are used in a critical application at 40°C. The manufacturer selects a sample population of 1000 chips, ages them at 150°C for 2 years (ta = 1.75 × 10^4 h) and no failures are observed. Typical data for other similar products suggest that the activation energy for failure is 0.4 eV ...

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First the AF is evaluated from Eqn (4.36):

...

Question: 4.2

Suppose the population of devices is described by the life distribution F(t) = 1 – exp(-0.0001t). 1. What is the probability that a new device will fail after 1000 h? After 5000 h? Between these times? 2. What is the failure rate at 1000 h? After 5000 h? ...

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By substitution,

F(t)=1-exp[-0.0001(1000)]=...

Question: 4.5

Tantalum capacitors were tested at elevated temperature, and the failure times were Weibull distributed with scale parameter α = 2.5 × 10^5 h and a shape parameter β = 0.5. If the AF is estimated to be 1 × 10^4 , what is the probability that the capacitors will last 1 year? ...

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The failure probability is given by

F(t)=1-...

Question 4.4: Consider a 50-pin module such that the probability of failur...

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Suppose the population of devices is described by the life distribution F(t) = 1 – exp(-0.0001t). 1. What is the probability that a new device will fail after 1000 h? After 5000 h? Between these times? 2. What is the failure rate at 1000 h? After 5000 h? ...

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Tantalum capacitors were tested at elevated temperature, and the failure times were Weibull distributed with scale parameter α = 2.5 × 10^5 h and a shape parameter β = 0.5. If the AF is estimated to be 1 × 10^4 , what is the probability that the capacitors will last 1 year? ...

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