Mining & Mineral Economics

Maintainability, Availability & Decision Trees

MTBF, MTTR and machine availability, plus the expected-monetary-value logic of decision trees under uncertainty.

PART 1

Topic Breakdown & Traps

The Engineering Principle

Equipment economics hinges on availability — the fraction of scheduled time a machine is fit to run. It is built from two reliability measures: MTBF (mean time between failures), a measure of reliability, and MTTR (mean time to repair), a measure of maintainability. Higher MTBF and lower MTTR both raise availability. For investment and operating choices under uncertainty, decision trees lay out decisions (squares) and chance events (circles) with probabilities and payoffs; each branch is rolled back using expected monetary value (EMV) — the probability-weighted average payoff — and the highest-EMV decision is chosen.

The Core Formula Matrix

Availability:

A = \frac{M T B F}{M T B F + M T T R}

Failure rate:

λ = \frac{1}{M T B F}

; repair rate

μ = \frac{1}{M T T R}

Expected monetary value:

E M V = \sum_{i} p_{i} V_{i}

(probability

p_{i}

× payoff

V_{i}

\sum p_{i} = 1

)

Decision rule: choose the alternative with the highest EMV (or lowest expected cost).

The ‘IIT Traps’

⚠
Availability puts MTBF over (MTBF + MTTR) — not MTBF over MTTR. Mixing these is the classic slip.
⚠
MTBF and MTTR must share units (both hours, say) before combining.
⚠
EMV weights *all* outcomes by probability — don't just take the best-case payoff.
⚠
Probabilities at a chance node sum to 1. If they don't, an outcome is missing.

PART 2

Progressive 3-Tier Question Suite

Q1BASIC1 Mark · MCQ

Mean Time To Repair (MTTR) is primarily a measure of a machine's:

Q2MEDIUM2 Marks · NAT

A shovel has a mean time between failures of

90 h

and a mean time to repair of

10 h

. Its availability is ______ %. (Round to the nearest whole number.)

Q3HARD2 Marks · NAT

A decision has two outcomes: a

0.6

chance of a

\

50{,}000

p r o f i t an d a

0.4

c han ceo f a

20, 000

loss. The expected monetary value (EMV) of the decision is ______ dollars. (Round to the nearest whole number.)