math

posted by .

A machine has four components, A, B, C, and D, set up in such a manner that all four parts must work for the machine to work properly. Assume the probability of one part working does not depend on the functionality of any of the other parts. Also assume that the probabilities of the individual parts working are P(A) = P(B) = 0.93, P(C) = 0.95, and P(D) = 0.92. Find the probability that the machine works properly.


My possible answers are:
.7559
.2441
.8217
.8128

I have tried and asked and no one is getting any of these. Help, please!

  • math -

    My understanding of your question means that you have a fault tree with 'machine unavailable' as the top event and the Boolean algebra expression for the top event being

    A OR B OR C OR D

    because failure of any one of the four components results in machine failure.

    As an approximation (because it will be missing the AB components and therefore slightly too high - the probability of A OR B is [P(A)+P(B)-P(A)*P(B)])

    is 0.07+0.07+0.05+0.08 = 0.27, which is slightly high so the unavailability is likely to be the 0.2441 value, hence the probability that it is working is

    1-0.2441 = 0.7559.

    You will need to workout an exact value for your answer and the best way to do this is to sequentially use the [P(A)+P(B)-P(A)*P(B)] expression. What I mean is combine A OR B, then combine the result of this with C and so on.

  • math -

    Just to confirm.

    If you go through the maths steps as I indicated I got

    0.2439854, so allowing for the occasion rounding error this is close to 0.2441.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. science

    percentages: to use a machine,u must do the work on the machine called input work. the machine then foes the work on and object called output work. not all the input work gets transmitted to output work. some work is lost due to friction …
  2. Health Physics

    A machine is used to either do work or to convert energy. To find the efficiency of a machine, one must compare the power input to the machine to the power output of the machine. What does thepower take into account in addition to …
  3. Physics

    A machine is used to either do work or to convert energy. To find the efficiency of a machine, one must compare the power input to the machine to the power output of the machine. What does thepower take into account in addition to …
  4. stat

    a machine has 7 identical components which function independently. the probability that a component will fail is 0.2. the machine will stop working if more than three components fail. find the probability that the machine will be working.
  5. discrete probability distribution (help please!)

    a machine has 7 identical components which function independently. the probability that a component will fail is 0.2. the machine will stop working if more than three components fail. find the probability that the machine will be working.
  6. Statistics

    Half of a set of the parts are manufactured by machine A and half by machine B. Four (.04) of all the parts are defective. Six percent (6%) of the parts manufacture on machine A are defective. Find the probability that a part was manufactured …
  7. Elementary Statistics

    A machine has 7 identical components which function independently. The probability that a component will fail is .2. The machine will stop working if more than three components fail. Find the probability that the machine will be working?
  8. Statistics

    The production process of computer parts uses two machines one old & one new. If the old machine is used the probability that the defected part is produced is .13 if the new machine is used the probability that the defective part is …
  9. Quantitative, stastics and business

    A company has three machines A, B and C which all produce the same two parts, X and Y. of all the parts produced, machine A produces 60%, machine B produces 30%, and machine C produces the rest. 40% of the parts made by machine A are …
  10. Statistics

    In a particular manufacturing plant, two machines (A and B) produce a particular part. One machine (B) is newer and faster. In one five-minute period, a lot consisting of 32 parts is produced. Twenty-two are produced by machine B and …

More Similar Questions