Solder joints are widely used in the electronic packaging industry to provide a connection between wafer level chips and a printed circuit board (PCB). The most common failure of the connection is caused by cracks in the bulk solder joint close to the wafer package-pad. Researchers at National Semiconductor Corporation estimated the failure time (in hours) of the solder joint connections for a 64L bump micro SMD package using the Weibull distribution (Electronic Components and Technology Conference, May 2003). The median failure time was estimated at 590 hours.

a. Write an expression for the median failure time as a function of the Weibull distribution parameters α and β.

b. Find the value of β when α = 1 and the median is 590 hours.

c. Find the value of β when α = 2 and the median is 590 hours.

d. Find the hazard rate when α = 2 and the median is 590 hours.