How Many Trucks / Shovels?
1. Sufficient number to secure the required production, or
2. Sufficient number to meet the blending requirements, or
3. Sufficient number to provide required production rate with desired probability, or
4. Sufficient number to meet company objectives (cost, reliability, other)
Example: Binomial Distribution
Assume the shovel availability is 80%. Then the
probability that the shovel is available is:
(P) is 0.80 or 80%
The probability the shovel is not available:
(Q) is 0.20 or 20%
i.e. P = 0.80, Q = 0.20, and P + Q = 1.00
If there is more than one shovel in the fleet, say n units, then the probabilities of shovels being available and not available are given by the Binomial Distribution
Polynomial ------> (P + Q)n
Binomial Distribution
(P + Q)n
Let’s assume: P = 0.8, Q = 0.2
For two units: n = 2
(P + Q)n becomes (0.8 + 0.2)2
Worked out:
(0.8 + 0.2)2 = 0.64 + 0.32 + 0.04
Meaning there is:
1st: 64% probability that all two units are available
2nd: 32% prob. that exactly one units are available
3rd: 4% prob. that no units is available
Another conclusion: for 96% of time at least one unit is available
(meaning: either one or two units are available)
For three units: n = 3
(P + Q)n becomes (0.8 + 0.2)3
Worked out:
(0.8)3 + [3 x (0.8)3 x 0.2] + [3 x 0.8 x (0.2)2 ] + (0.2)3
Or (in “round figures”):
0.512 + 0.384 + 0.096 + 0.008
Meaning that there is:
1. 51.2% prob. that all three units are available
2. 38.4% prob. That exactly two units are available
3. 9.6% prob. That exactly one unit is available
4. 0.8% prob. That no units are available
Use polynomial formulas (math handbook?) to define probability distribution for larger fleets!
Probability That Exact No. of Trucks is available for a Fleet of 10 units & Availability of 70%
Cumulative Probability of Available Trucks for a Fleet of 10 and the Availability of 70%
How Does Availability Help?
Fleet Management
1. Define objectives
a. Minimize number of units?
b. Maximize production?
c. Other?
2. Equipment match
a. Undertruck?
b. Overtruck?
3. Unit assignments: optimize
Support Equipment
1. Improves working conditions
2. Rolling resistance
3. Drainage, spillage
4. Bench & dump leveling
5. Allows the main equipment:
6. To be used for primary production
7. To fully utilize available time
A Motor Grader Articulation; Crab Movement
How Big a Blade?
