Question

A manufacturer has determined that a model of its washing machine has an expected life that is Exponential with a mean of four years to failure and irrelevant board burn-in period. He wants to testthe system and complete data collection. Find the probability that one of these washing machines will have a life that ends: (Note you can find the reliability of the washing machine life)

Answer 1

Complete question:

A manufacturer has determined that a model of its washing machine has an expected life that is Exponential with a mean of four years to failure and irrelevant board burn-in period. He wants to testthe system and complete data collection. Find the probability that one of these washing machines will have a life that ends: (Note you can find the reliability of the washing machine life)

a) After an initial four years of washing machine service

b) Before four years of washing machine service are completed

c) Not before six years of washing machine service.

Answer:

a) 0.3679

b) 0.6321

c) 0.2231

Explanation:

Given:

Mean, u= 4

/\ = 1/u

= 1/4 = 0.25

The cummulative distribution function, will be:

For x≥0,

`F(x) = 1 - e^-^0^.^2^5^X`

`P(x<X) = F(X)`

a) After an intial four years:

`P(x>4) = 1-(1-e^-^0^.^2^5^*^4^.^0)`

P(x>4) = 0.3679

b) Before four years:

`P(x<4) = 1-(e^-^0^.^2^5^*^4^.^0)`

P(x<4) = 0.6321

c) Not before 6 years:

`P(x>6) = 1-(1-e^-^0^.^2^5^*^4^.^0)`

P(x>6) = 0.2231