Length of life of a halogen bulb. For a certain type of halogen light bulb, an old bulb that has been in use for a while tends to have a longer life than a new bulb. Let x represent the life (in hours) of a new halogen light bulb, and assume that x has an exponential distribution with mean u = 250 hours. According to Microelectronics and Reliability (Jan.

1986), the“ life” distribution of x is considered new better than used (NBU) if

Alternatively, a “life” distribution is considered new worse than used (NWU) if P1x 7 a + b2 Ú P1x 7 a2P1x 7 b2

a. Show that when a = 300 and b = 200, the exponential distribution is both NBU and NWU.

b. Choose any two positive numbers a and

b, and repeat part a.

c. Show that, in general, for any positive a and

b, the exponential distribution with mean u is both NBU and NWU. Such a “life” distribution is said to be new same as used, or memoryless. Explain why.

Transcribed Image Text:

P(x > a+b) P(x > a)P(x > b)