The chief design engineer for Colonial Warning Systems wants to know the reliability of a two-lamp device intended to warn the operator of potential problems with a commercial steam kettle. One (either) lamp is to be lit if steam pressure drops below the desired level and two (both) are to be lit if temperature drops below a desired level. His supplier estimates that a lamp has a failure rate of .2 per hour of operation, and a mean wear-out time of seven years with a standard deviation of eight months.
What warranty period for a lamp would give a probability of .9987 that it would not require warranty service?
5.67 years
9 years
6.33 years
7 years
5 years