Problems: 1. On average there is a minor breakdown in a machine every 200 hours

Question

Problems: 1. On average there is a minor breakdown in a machine every 200 hours of production at a large facility. The number of accidents can be modeled by a Poisson random variable.

a) What is the parameter for this variable?

b) The machine is currently taken off-line for several preventive maintenance tasks once every two weeks. This takes 1.5 hours to complete. Assume 40 hour weeks. What is the probability of a minor breakdown before the next scheduled preventive maintenance?

c) The line supervisor has decided there are too many breakdowns between scheduled maintenance times. He wants the probability of a breakdown before the next maintenance to be no more than 2%. How often should the maintenance tasks be performed to meet this goal of reduced breakdowns? (Hint: You want the probability of one or more failure to be 0.02.)

d)Do you think the proposed revision of the preventive maintenance schedule is practical? Why or why not?

2. A large software company has discovered the average number of programming errors in a first attempt is 2.8 per 100 lines of code. The number of coding errors follows an approximately Poisson distribution.

a) How many coding errors would be expected in a program with 355 lines of code?

b) What is the probability that a program of 500 lines will have at least 12 errors?

Explanation / Answer

SOlution:-

2)

= 2.8 per 100

a) Coding errors would be expected in a program with 355 lines of code is 9.38.

Expected number of error in 335 lines = (2.8 × 335)/100 = 9.38

b) The probability that a program of 500 lines will have at least 12 errors is 0.816.

= (2.8 × 500)/100 = 14

= 14

By applying poisons distribution:-

P(x; ) = (e-) (x) / x!

P(x > 12) = 0.816

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