My father asked me to submit a question about the so-called 'bathtub
        curve'. If you cut a bathtub in half lengthwise down it's middle, the
        edge of the tub would describe the 'bathtub curve' which can be used 
        to demonstrate typical failure rates of products. This curve is 
        characterised by high initial (infant mortality) failure rates at 
        it's beginning, which drop quickly to a very low level. Failures then
        increase gradually to the "end of life" stage where the failure rate 
        takes off dramatically again.
      If anyone in the math department knows about the so-called 'bathtub 
        curve' my father would really appreciate the equation.