Question

A logic circuit is known to have a decreasing failure rate of the form lambda(t) = 1/20 t ⁻¹/²/year, where t is in years. If the design life is one year, what is the reliability? If the component undergoes wear in for one month before being put into operation, what will the reliability be for a one-year design life?

Answer 1

To calculate the reliability of a logic circuit with a decreasing failure rate, integrate the given failure rate function over the desired time period. For a one-year design life, calculate the reliability using the formula and substitute the given failure rate. To account for one month of wear before operation, adjust the integration limits and recalculate the reliability.

Step-by-step explanation:

The reliability of a logic circuit with a decreasing failure rate can be calculated using the formula:

R(t) = e-∫[0,t](λ(u))du

For a one-year design life, the reliability can be calculated as:

R(1) = e-∫[0,1](λ(u))du

Substituting the given failure rate (λ(t) = 1/20 t-1/2/year) into the formula, we get:

R(1) = e-∫[0,1]((1/20)u-1/2)(du)

Integrating this expression gives the reliability for a one-year design life.

If the component undergoes wear for one month before being put into operation, the reliability for a one-year design life can be calculated as:

R(0.9167) = e-∫[0,0.9167]((1/20)u-1/2)(du)

Integrating this expression gives the reliability for a one-year design life with one month of wear.