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Open-Pit System Reliability Analysis

Nowadays, the selection of equipment for modern open-pit mines has become a quite challenging issue in terms of availability, maintainability, reliability, productivity, etc. The overall system has grown to the level where the application of reliability principles has been considered to be very useful for satisfying the ever-growing technological requirements. The system has various types of loading and dumping machinery that, in turn, are arranged in different arrays. These arrays result in various types of sequencing systems. The malfunction of a single element in the sequences can cause part or total system failure.

Nonetheless, open-pit mines’ each element (i.e., shovel, dumper, working face, dumping point, etc.) may be considered as an independent link to the open-pit mine chain system. The chain system’s reliability analyses when it forms parallel and series networks are presented below [4].

Open-Pit Parallel System

This type of network is formed when there is more than one unit of an open-pit system’s components/units functioning simultaneously and at least one of these units/components must work normally for the system to succeed. For example, there are two shovels functioning simultaneously and at least one of the shovels must work normally for the system to succeed. In this case, both shovels form a parallel network and the network’s reliability, if both shovels fail independently, using Chapter 3 and Dhillon [5], is expressed by

where

Rpn is the shovel parallel network reliability.

Л, is the reliability of shovel number one.

R-, is the reliability of shovel number two.

For constant failure rates of both the shovels, using Chapter 3 and Dhillon [5], we write

where

/?! (r) is the reliability of shovel number one at time t.

Aj is the constant failure rate of shovel number one.

R2 (/) is the reliability of shovel number two at time t.

Л2 is the constant failure rate of shovel number two.

By substituting Equations (10.7) and (10.8) into Equation (10.6), we get where

Rpn (/) is the shovel parallel network reliability at time t.

By integrating Equation (10.9) over the time interval [0,~], we get the following equation for the shovel parallel network mean time to failure:

where

MTTFpn is the shovel parallel network mean time to failure.

Example 10.1

Assume that an open-pit system has two independent and non-identical shovels forming a parallel network (i.e., at least one shovel must operate normally for the system to succeed). The shovel number 1 and 2 constant failure rates are 0.004 failures per hour and 0.005 failures per hour, respectively.

Calculate the open-pit system reliability for a 100-hours mission and mean time to failure.

By substituting the given data values into Equation (10.9), we obtain

Similarly, by substituting the given data values into Equation (10.10), we obtain

Thus, the open-pit system reliability and mean time to failure are 0.8702 and 338.88 hours, respectively.

Open-Pit Series System

In this case, the open-pit-mine components/units, i.e., shovel, dumper, dumping place, and working face, form a series network. This means all components/units must function normally for the system to succeed.

For independent components/units, the system reliability is expressed by [4,5]

where

Ros is the open-pit series system reliability.

Rsh is the shovel reliability.

Rdu is the dumper or drum-truck reliability.

Rdp is the dumping-place reliability.

Rwf is the working-face reliability.

For constant failure rates of the shovel, dumper or dump truck, dumping place, and working face, using Chapter 3 and Dhillon [5], we get

where

RJt) is the shovel reliability at time t. Xsh is the shovel constant failure rate.

Rdu(t) is the dumper or dump-truck reliability at time t.

Xdu is the dumper or dump-truck constant failure rate.

RJp{t) is the dumping-place reliability at time t.

Яф is the dumping-place constant failure rate.

Rwf(t) is the working-face reliability at time t.

Ais the working-face constant failure rate.

By inserting Equations (10.12)—(10.15) into Equation (10.11), we obtain where

Ros (r) is the open-pit series system reliability at time t.

By integrating Equation (10.16) over the time interval [0,oo], we get the following equation for the open-pit series system mean time to failure:

where

MTTF()S is the open-pit series system mean time to failure.

Example 10.2

Assume that an open-pit system is composed of four components: shovel, dumper, dumping place, and working face and each component’s reliability is 0.95, 0.98, 0.96, and 0.92, respectively. Calculate the open-pit system reliability if all its components fail independently and form a series network.

By substituting given data values into Equation (10.11), we obtain Thus, the open-pit system reliability is 0.8222.

Example 10.3

Assume that in Example 10.2, the constant failure rates of shovel, dumper, dumping place, and working face are 0.009 failures per hour, 0.008 failures per hour, 0.007 failures per hour, and 0.006 failures per hour, respectively.

Calculate the open-pit series system reliability for a 100-hour mission and mean time to failure.

By substituting the given data values into Equation (10.16), we obtain

Similarly, by substituting the given data values into Equation (10.17), we obtain

Thus, the open-pit series system reliability for a 100-hour mission and mean time to failure are 0.0497 and 33.33 hours, respectively.

 
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