Question

In a process, the number of cycles to failure decreases exponentially with an increase in load. At a load of 80 units, it takes 100 cycles for failure. When the load is halved, it takes 10000 cycles for failure. The load for which the failure will happen in 5000 cycles is ________.

Answer 1

When load will be 46.02 units, process will fail at 5000 cycles.

• In a given process,  the number of cycles to failure decreases exponentially with an increase in load

• General mathematical equation for such a process is given by:

       y = a$e^{-bx}$

      where y is number of cycles to failure, and x is load.

• When load is 80 units, process fails in 100 cycles.

        100 = a$e^{-80b}$     ...(1)

• When load is halved, process fails in 10000 cycles.

       10000 = a$e^{-40b}$  ...(2)

• Solving (1) & (2),

        b = 0.1151

        a = 1000000

• At 5000 cycles to failure

        5000 = a$e^{-bx}$  ...(3)

• Put above values of a & b in equation (3)

• Then,  we will get x = 46.02
• Hence, when load will be 46.02 units, process will fail at 5000 cycles.