A problem with MTBF and cost....

[Steve]

Here is a problem I have found to be particularly disturbing since I believe the "official" answer to be wrong. Take a look and see what you think:

"You are considering the purchase of an piece of equipment for your company. Two are available. Unit A costs $150,000 and has an expected life of 20 years with a MTBF of 5 years. Unit B costs $141,000 and has an expected life of 15 years and a MTBF of 3 years. The expected cost of repair for each unit is $1,000. Assuming that there is no value at the end of the life and interest rate is 12%, which unit has the lowest life-cycle cost?"

Take a shot at it and see what you get. I got something different than what is said to be the "correct" answer, and I think that it is wrong.

[Steve]

Okay, with everybody clamoring to get the right answer, I suppose I should reveal what it is:

Either. Supposedly.

Total Life-Cycle Cost is: $25,650 for Unit A and $26,586.67.

My question is, what do I do when Unit B fails in the 15th year? I can either do without it or buy a new one. And yet, the "official" answer ignores this.

[Tarik El-Azzouzi]

System A is expected to fail (on average) every 5 years
and costs 1000$ for each failure. After 20 years, it will cost 150,000$ to purchase a new one. It will once again start failing every 5 years

System B is expected to fail (on average) every 3 years
and costs 1000$ for each failure. After 15 years, it will cost 141,000$ to purchase a new one. It will once again start failing every 3 years.

If you want to compare the 2 systems, you need to pick a certian mission period or operation period (for example 20 years) and consider the systems' overhall costs and apply the interest rate you mentioned to obtain the current value of money.

[Rui Assis]

Steve,

I would like to add the following comment to what Tarik said:

If you intend to stop the business as soon as the equipment reaches its useful life (regardless of which equipment you decided upon), then, use the present worth as the decision criteria – in which case alternative B is the best choice (despite the difference is minimal). If that is not the case and the business must go on, then, use the annual worth as the criteria – in which case you pick up the alternative A (despite the difference is again minimal).

I attach an Excel file with the calculus.

Regards,

Rui