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OpenPit System Reliability AnalysisTable of Contents:
Nowadays, the selection of equipment for modern openpit 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 evergrowing 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, openpit mines’ each element (i.e., shovel, dumper, working face, dumping point, etc.) may be considered as an independent link to the openpit mine chain system. The chain system’s reliability analyses when it forms parallel and series networks are presented below [4]. OpenPit Parallel SystemThis type of network is formed when there is more than one unit of an openpit 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 R_{pn} 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. R_{2} (/) 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 R_{pn} (/) 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 MTTF_{pn} is the shovel parallel network mean time to failure. Example 10.1 Assume that an openpit system has two independent and nonidentical 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 openpit system reliability for a 100hours 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 openpit system reliability and mean time to failure are 0.8702 and 338.88 hours, respectively. OpenPit Series SystemIn this case, the openpitmine 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 R_{os} is the openpit series system reliability. R_{sh} is the shovel reliability. R_{du} is the dumper or drumtruck reliability. R_{dp} is the dumpingplace reliability. R_{w}f is the workingface 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. X_{sh} is the shovel constant failure rate. R_{du}(t) is the dumper or dumptruck reliability at time t. X_{du} is the dumper or dumptruck constant failure rate. R_{Jp}{t) is the dumpingplace reliability at time t. Яф is the dumpingplace constant failure rate. R_{w}f(t) is the workingface reliability at time t. Ais the workingface constant failure rate. By inserting Equations (10.12)—(10.15) into Equation (10.11), we obtain where R_{os} (r) is the openpit series system reliability at time t. By integrating Equation (10.16) over the time interval [0,oo], we get the following equation for the openpit series system mean time to failure:
where MTTF_{()S} is the openpit series system mean time to failure. Example 10.2 Assume that an openpit 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 openpit 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 openpit 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 openpit series system reliability for a 100hour 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 openpit series system reliability for a 100hour mission and mean time to failure are 0.0497 and 33.33 hours, respectively. 
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