Patent Publication Number: US-10776706-B2

Title: Cost-driven system and method for predictive equipment failure detection

Description:
TECHNICAL FIELD 
     This disclosure relates generally to techniques for identifying faulty equipment. More specifically, this disclosure relates to a cost-driven system and method for predictive equipment failure detection. 
     BACKGROUND 
     Industrial process control and automation systems are routinely used to automate large and complex industrial processes. Maintaining the equipment in industrial processes can be financially burdensome due to things like the costs of equipment replacements and lost operating times when equipment fails. Predictive algorithms can be used to predict whether a piece of equipment is experiencing a problem or about to fail, allowing maintenance to be scheduled for that piece of equipment. However, when designing an algorithm to predict whether a piece of equipment requires maintenance, the algorithm&#39;s developer is often faced with a dilemma. Algorithms typically use a threshold value to determine whether maintenance for a piece of equipment is needed. If the threshold value is too low, the algorithm results in too many service calls for equipment that is functional. If the threshold value is too high, the algorithm may not schedule adequate maintenance for faulty equipment. 
     SUMMARY 
     This disclosure provides a cost-driven system and method for predictive equipment failure detection. 
     In a first embodiment, a method includes identifying costs associated with different outcomes of a failure prediction algorithm. The failure prediction algorithm is configured to predict one or more faults with at least one piece of industrial equipment, and the different outcomes include both successful and unsuccessful predictions by the failure prediction algorithm. The method also includes identifying a threshold value for the failure prediction algorithm using the costs, where the threshold value is used by the failure prediction algorithm to identify whether maintenance of the at least one piece of industrial equipment is needed. The method further includes providing the threshold value to the failure prediction algorithm. In addition, the method can include receiving equipment data associated with operation of the at least one piece of industrial equipment, calculating an indicator value based on the equipment data using the failure prediction algorithm, comparing the indicator value to the threshold value, and generating a signal indicating whether maintenance is needed based on the comparison. The threshold value is selected such that a net positive economic benefit is obtained from use of the threshold value with the failure prediction algorithm. 
     In a second embodiment, an apparatus includes at least one processing device configured to identify costs associated with different outcomes of a failure prediction algorithm. The failure prediction algorithm is configured to predict one or more faults with at least one piece of industrial equipment, and the different outcomes include both successful and unsuccessful predictions by the failure prediction algorithm. The at least one processing device is also configured to identify a threshold value for the failure prediction algorithm using the costs, where the threshold value is used by the failure prediction algorithm to identify whether maintenance of the at least one piece of industrial equipment is needed. The at least one processing device is further configured to provide the threshold value to the failure prediction algorithm. The at least one processing device is configured to select the threshold value such that a net positive economic benefit is obtained from use of the threshold value with the failure prediction algorithm. 
     In a third embodiment, a non-transitory computer readable medium contains instructions that, when executed by at least one processing device, cause the at least one processing device to identify costs associated with different outcomes of a failure prediction algorithm. The failure prediction algorithm is configured to predict one or more faults with at least one piece of industrial equipment, and the different outcomes include both successful and unsuccessful predictions by the failure prediction algorithm. The medium also contains instructions that, when executed by the at least one processing device, cause the at least one processing device to identify a threshold value for the failure prediction algorithm using the costs, where the threshold value is used by the failure prediction algorithm to identify whether maintenance of the at least one piece of industrial equipment is needed. In addition, the medium contains instructions that, when executed by the at least one processing device, cause the at least one processing device to provide the threshold value to the failure prediction algorithm. The threshold value is selected such that a net positive economic benefit is obtained from use of the threshold value with the failure prediction algorithm. 
     Other technical features may be readily apparent to one skilled in the art from the following figures, descriptions, and claims. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       For a more complete understanding of this disclosure, reference is now made to the following description, taken in conjunction with the accompanying drawings, in which: 
         FIG. 1  illustrates an example industrial process control and automation system according to this disclosure; 
         FIG. 2  illustrates an example device for cost-driven predictive equipment failure detection according to this disclosure; 
         FIG. 3  illustrates an example cost-driven predictive equipment failure detection technique according to this disclosure; 
         FIGS. 4 and 5  illustrate example receiver operating characteristic (ROC) curves according to this disclosure; 
         FIGS. 6, 7, 8A, and 8B  illustrate an example application of a failure prediction algorithm according to this disclosure; and 
         FIG. 9  illustrates an example method for cost-driven predictive equipment failure detection according to this disclosure. 
     
    
    
     DETAILED DESCRIPTION 
       FIGS. 1 through 9 , discussed below, and the various embodiments used to describe the principles of the present invention in this patent document are by way of illustration only and should not be construed in any way to limit the scope of the invention. Those skilled in the art will understand that the principles of the invention may be implemented in any type of suitably arranged device or system. 
       FIG. 1  illustrates an example industrial process control and automation system  100  according to this disclosure. As shown in  FIG. 1 , the system  100  includes various components that facilitate production or processing of at least one product or other material. For instance, the system  100  is used here to facilitate control over components in one or multiple plants  101   a - 101   n . Each plant  101   a - 101   n  represents one or more processing facilities (or one or more portions thereof), such as one or more manufacturing facilities for producing at least one product or other material. In general, each plant  101   a - 101   n  may implement one or more processes and can individually or collectively be referred to as a process system. A process system generally represents any system or portion thereof configured to process one or more products or other materials in some manner. 
     In  FIG. 1 , the system  100  is implemented using the Purdue model of process control. In the Purdue model, “Level 0” may include various sensors  102   a , actuators  102   b , and pieces of industrial equipment  102   c . The sensors  102   a  could measure a wide variety of characteristics in the process system, such as temperature, pressure, or flow rate. Often times, the sensors  102   a  are used to measure one or more characteristics associated with the industrial equipment  102   c . The actuators  102   b  could alter a wide variety of characteristics in the process system, such as by altering operation of the industrial equipment  102   c . Each of the sensors  102   a  includes any suitable structure for measuring one or more characteristics in a process system. Each of the actuators  102   b  includes any suitable structure for operating on or affecting one or more conditions in a process system. The industrial equipment  102   c  includes one or more pieces of equipment that perform the function(s) required for at least one industrial process. For instance, the equipment  102   c  could include any suitable manufacturing or processing equipment to support one or more industrial processes. As specific examples, the equipment  102   c  could include components supporting oil and gas refining, pulp paper processing, pharmaceutical manufacturing, or chemical processing. 
     At least one network  104  is coupled to the components  102   a - 102   c . The network  104  can facilitate interaction with the components  102   a - 102   c . For example, the network  104  could transport measurement data from the sensors  102   a  and provide control signals to the actuators  102   b . The network  104  could represent any suitable network or combination of networks. As particular examples, the network  104  could represent an Ethernet network, an electrical signal network (such as a HART or FOUNDATION FIELDBUS network), a pneumatic control signal network, or any other or additional type(s) of network(s). 
     In the Purdue model, “Level 1” may include one or more controllers  106 , which are coupled to the network  104 . Among other things, each controller  106  may use the measurements from one or more sensors  102   a  to control the operation of one or more actuators  102   b  in order to modify the operation of the industrial equipment  102   c . For example, a controller  106  could receive measurement data from one or more sensors  102   a  and use the measurement data to generate control signals for one or more actuators  102   b . Multiple controllers  106  could also operate in redundant configurations, such as when one controller  106  operates as a primary controller while another controller  106  operates as a backup controller (which synchronizes with the primary controller and can take over for the primary controller in the event of a fault with the primary controller). Each controller  106  includes any suitable structure for controlling one or more pieces of equipment. Each controller  106  could, for example, represent a multivariable controller, such as a Robust Multivariable Predictive Control Technology (RMPCT) controller or other type of controller implementing model predictive control (MPC) or other advanced predictive control (APC). As a particular example, each controller  106  could represent a computing device running a real-time operating system. 
     Two networks  108  are coupled to the controllers  106 . The networks  108  facilitate interaction with the controllers  106 , such as by transporting data to and from the controllers  106 . The networks  108  could represent any suitable networks or combination of networks. As particular examples, the networks  108  could represent a pair of Ethernet networks or a redundant pair of Ethernet networks, such as a FAULT TOLERANT ETHERNET (FTE) network from HONEYWELL INTERNATIONAL INC. 
     At least one switch/firewall  110  couples the networks  108  to two networks  112 . The switch/firewall  110  may transport traffic from one network to another. The switch/firewall  110  may also block traffic on one network from reaching another network. The switch/firewall  110  includes any suitable structure for providing communication between networks, such as a HONEYWELL CONTROL FIREWALL (CF9) device. The networks  112  could represent any suitable networks, such as a pair of Ethernet networks or an FTE network. 
     In the Purdue model, “Level 2” may include one or more machine-level controllers  114  coupled to the networks  112 . The machine-level controllers  114  perform various functions to support the operation and control of the controllers  106  and related components  102   a - 102   c . For example, the machine-level controllers  114  could log information collected or generated by the controllers  106 , such as measurement data from the sensors  102   a  or control signals for the actuators  102   b . The machine-level controllers  114  could also execute applications that control the operation of the controllers  106 , thereby controlling the operation of the actuators  102   b . In addition, the machine-level controllers  114  could provide secure access to the controllers  106 . Each of the machine-level controllers  114  includes any suitable structure for providing access to, control of, or operations related to a machine or other individual piece of equipment. Each of the machine-level controllers  114  could, for example, represent a server computing device running a MICROSOFT WINDOWS operating system. Although not shown, different machine-level controllers  114  could be used to control different pieces or collections of equipment in a process system. 
     One or more operator stations  116  are coupled to the networks  112 . The operator stations  116  represent computing or communication devices providing user access to the machine-level controllers  114 , which could then provide user access to the controllers  106  (and possibly the components  102   a - 102   c ). As particular examples, the operator stations  116  could allow users to review the operational history of the equipment  102   c  using information collected by the controllers  106  and/or the machine-level controllers  114 . The operator stations  116  could also allow the users to adjust the operation of the components  102   a - 102   c , controllers  106 , or machine-level controllers  114 . In addition, the operator stations  116  could receive and display warnings, alerts, or other messages or displays generated by the controllers  106  or the machine-level controllers  114 . For example, the operator stations  116  could allow users to review failure potentials of the equipment  102   c  and determine when maintenance on the equipment  102   c  is needed. Each of the operator stations  116  includes any suitable structure for supporting user access and control of one or more components in the system  100 . Each of the operator stations  116  could, for example, represent a computing device running a MICROSOFT WINDOWS operating system. 
     At least one router/firewall  118  couples the networks  112  to two networks  120 . The router/firewall  118  includes any suitable structure for providing communication between networks, such as a secure router or combination router/firewall. The networks  120  could represent any suitable networks, such as a pair of Ethernet networks or an FTE network. 
     In the Purdue model, “Level 3” may include one or more unit-level controllers  122  coupled to the networks  120 . Each unit-level controller  122  is typically associated with a unit in a process system, which represents a collection of different machines operating together to implement at least part of a process. The unit-level controllers  122  perform various functions to support the operation and control of components in the lower levels. For example, the unit-level controllers  122  could log information collected or generated by the components in the lower levels, execute applications that control the components in the lower levels, and provide secure access to the components in the lower levels. Each of the unit-level controllers  122  includes any suitable structure for providing access to, control of, or operations related to one or more machines or other pieces of equipment in a process unit. Each of the unit-level controllers  122  could, for example, represent a server computing device running a MICROSOFT WINDOWS operating system. Although not shown, different unit-level controllers  122  could be used to control different units in a process system. 
     Access to the unit-level controllers  122  may be provided by one or more operator stations  124 . Each of the operator stations  124  includes any suitable structure for supporting user access and control of one or more components in the system  100 . Each of the operator stations  124  could, for example, represent a computing device running a MICROSOFT WINDOWS operating system. 
     At least one router/firewall  126  couples the networks  120  to two networks  128 . The router/firewall  126  includes any suitable structure for providing communication between networks, such as a secure router or combination router/firewall. The networks  128  could represent any suitable networks, such as a pair of Ethernet networks or an FTE network. 
     In the Purdue model, “Level 4” may include one or more plant-level controllers  130  coupled to the networks  128 . Each plant-level controller  130  is typically associated with one of the plants  101   a - 101   n , which may include one or more process units that implement the same, similar, or different processes. The plant-level controllers  130  perform various functions to support the operation and control of components in the lower levels. As particular examples, the plant-level controller  130  could execute one or more manufacturing execution system (MES) applications, scheduling applications, or other or additional plant or process control applications. Each of the plant-level controllers  130  includes any suitable structure for providing access to, control of, or operations related to one or more process units in a process plant. Each of the plant-level controllers  130  could, for example, represent a server computing device running a MICROSOFT WINDOWS operating system. 
     Access to the plant-level controllers  130  may be provided by one or more operator stations  132 . Each of the operator stations  132  includes any suitable structure for supporting user access and control of one or more components in the system  100 . Each of the operator stations  132  could, for example, represent a computing device running a MICROSOFT WINDOWS operating system. 
     At least one router/firewall  134  couples the networks  128  to one or more networks  136 . The router/firewall  134  includes any suitable structure for providing communication between networks, such as a secure router or combination router/firewall. The network  136  could represent any suitable network, such as an enterprise-wide Ethernet or other network or all or a portion of a larger network (such as the Internet). 
     In the Purdue model, “Level 5” may include one or more enterprise-level controllers  138  coupled to the network  136 . Each enterprise-level controller  138  is typically able to perform planning operations for multiple plants  101   a - 101   n  and to control various aspects of the plants  101   a - 101   n . The enterprise-level controllers  138  can also perform various functions to support the operation and control of components in the plants  101   a - 101   n . As particular examples, the enterprise-level controller  138  could execute one or more order processing applications, enterprise resource planning (ERP) applications, advanced planning and scheduling (APS) applications, or any other or additional enterprise control applications. Each of the enterprise-level controllers  138  includes any suitable structure for providing access to, control of, or operations related to the control of one or more plants. Each of the enterprise-level controllers  138  could, for example, represent a server computing device running a MICROSOFT WINDOWS operating system. In this document, the term “enterprise” refers to an organization having one or more plants or other processing facilities to be managed. Note that if a single plant  101   a  is to be managed, the functionality of the enterprise-level controller  138  could be incorporated into the plant-level controller  130 . 
     Access to the enterprise-level controllers  138  may be provided by one or more operator stations  140 . Each of the operator stations  140  includes any suitable structure for supporting user access and control of one or more components in the system  100 . Each of the operator stations  140  could, for example, represent a computing device running a MICROSOFT WINDOWS® operating system. 
     Various levels of the Purdue model can include other components, such as one or more databases. The database(s) associated with each level could store any suitable information associated with that level or one or more other levels of the system  100 . For example, a historian  141  can be coupled to the network  136 . The historian  141  could represent a component that stores various information about the system  100 . The historian  141  could, for instance, store information used during production scheduling and optimization. The historian  141  represents any suitable structure for storing and facilitating retrieval of information. Although shown as a single centralized component coupled to the network  136 , the historian  141  could be located elsewhere in the system  100 , or multiple historians could be distributed in different locations in the system  100 . 
     In particular embodiments, the various controllers and operator stations in  FIG. 1  may represent computing devices. For example, each of the controllers and operator stations could include one or more processing devices and one or more memories for storing instructions and data used, generated, or collected by the processing device(s). The instructions and data may comprise a software package for use in operating and controlling MPCs, such as PROFIT SUITE by HONEYWELL INTERNATIONAL INC. Each of the controllers and operator stations could also include at least one network interface, such as one or more Ethernet interfaces or wireless transceivers. 
     As noted above, predictive algorithms typically use a threshold value to determine whether maintenance for a piece of equipment is needed. If the threshold value is too low, the algorithm results in too many service calls for equipment that is functional, meaning the algorithm identifies that maintenance is needed when it is actually not needed. If the threshold value is too high, the algorithm may not schedule adequate maintenance for faulty equipment, meaning the algorithm identifies that maintenance is not needed when it actually is needed. 
     In accordance with this disclosure, the system  100  supports a prediction tool  144  at one or more locations within the system  100 . The prediction tool  144  is configured to determine a cost-effective threshold value for identifying when maintenance (such as repair or replacement) is needed for one or more components within the system  100  (such as one or more pieces of equipment  102   c ). For example, the prediction tool  144  can determine a cost associated with each possible outcome of an equipment failure prediction. Example outcomes include a true positive, a true negative, a false positive, and a false negative. A true positive means the equipment failure prediction accurately predicts that maintenance is needed, while a true negative means the equipment failure prediction accurately predicts that maintenance is not needed. A false positive means the equipment failure prediction predicted that maintenance is needed when it was not needed, while a false negative means the equipment failure prediction predicted that maintenance is not needed when it was needed. The prediction tool  144  determines a threshold value for identifying when maintenance is needed based on these costs in order to maximize the cost savings of the algorithm&#39;s operation. 
     One conventional approach to setting a prediction threshold value involves setting an acceptable error rate, meaning the detection of true equipment failures versus false alarms, and implementing a prediction algorithm with a threshold that meets the error rate. A Receiver Operating Characteristic (ROC) curve is often used to display the performance of the algorithm at different thresholds and the error rates to which the performance corresponds. 
     In contrast, the prediction tool  144  operates to include additional information into the threshold value selection, such as the cost associated with each possible outcome of an equipment failure prediction (true positive, true negative, false positive, and false negative). This enables the prediction tool  144  to increase or maximize cost savings of the prediction algorithm&#39;s deployment and to select threshold values based on economic considerations rather than just on error rates. In some embodiments, the prediction tool  144  can incorporate a cost calculation into an ROC graph in the form of a “break-even” line. The prediction tool  144  uses the break-even line to evaluate whether an equipment failure prediction algorithm has a better cost benefit than simply repairing equipment after the equipment fails. This allows the prediction tool  144  or personnel to determine (such as by visual inspection or with an automated algorithm) at what threshold cost benefits can be maximized. Additional details regarding this functionality are provided below. 
     Note that the prediction tool  144  could be implemented in a number of ways and at a number of locations within a system. For example, the prediction tool  144  could be implemented on any of the various controllers or operator stations shown in  FIG. 1 . The prediction tool  144  could also be implemented on one or more stand-alone devices, such as a prediction device  146 . The prediction device  146  could include any suitable structure facilitating the cost-based identification of threshold values, such as a computing device executing a suitable operating system. 
     Although  FIG. 1  illustrates one example of an industrial process control and automation system  100 , various changes may be made to  FIG. 1 . For example, a system could include any number of plants, sensors, actuators, equipment, controllers, servers, operator stations, networks, historians, and prediction tools and devices. Also, the makeup and arrangement of the system  100  in  FIG. 1  is for illustration only. Components could be added, omitted, combined, or placed in any other suitable configuration according to particular needs. Further, particular functions have been described as being performed by particular components of the system  100 . This is for illustration only. In general, process control systems are highly configurable and can be configured in any suitable manner according to particular needs. In addition, while  FIG. 1  illustrates one example environment in which cost-based identification of equipment failure prediction threshold values can be used, this functionality can be used in any other suitable device or system. 
       FIG. 2  illustrates an example device  200  for cost-driven predictive equipment failure detection according to this disclosure. The device  200  could, for example, represent the prediction device  146  or other device providing the prediction tool  144  in  FIG. 1 . However, the device  200  could be used in any other suitable system, and the prediction tool  144  could be used with any other suitable device. 
     As shown in  FIG. 2 , the device  200  includes a bus system  202 , which supports communication between at least one processing device  204 , at least one storage device  206 , at least one communications unit  208 , and at least one input/output (I/O) unit  210 . The processing device  204  executes instructions that may be loaded into a memory  212 . For example, the processing device  204  can execute instructions to determine a cost-effective threshold value for use in determining when equipment may require maintenance. The processing device  204  may include any suitable number(s) and type(s) of processors or other devices in any suitable arrangement. Example types of processing devices  204  include microprocessors, microcontrollers, digital signal processors, field programmable gate arrays, application specific integrated circuits, and discrete circuitry. 
     The memory  212  and a persistent storage  214  are examples of storage devices  206 , which represent any structure(s) capable of storing and facilitating retrieval of information (such as data, program code, and/or other suitable information on a temporary or permanent basis). The memory  212  may represent a random access memory or any other suitable volatile or non-volatile storage device(s). The persistent storage  214  may contain one or more components or devices supporting longer-term storage of data, such as a read only memory, hard drive, Flash memory, or optical disc. 
     The communications unit  208  supports communications with other systems or devices. For example, the communications unit  208  could include a network interface card that facilitates communications over at least one Ethernet or serial connection. The communications unit  208  could also include a wireless transceiver facilitating communications over at least one wireless network. The communications unit  208  may support communications through any suitable physical or wireless communication link(s). 
     The I/O unit  210  allows for input and output of data. For example, the I/O unit  210  may provide a connection for user input through a keyboard, mouse, keypad, touchscreen, or other suitable input device. The I/O unit  210  may also send output to a display, printer, or other suitable output device. 
     Although  FIG. 2  illustrates one example of a device  200  for cost-driven predictive equipment failure detection, various changes may be made to FIG.  2 . For example, various components in  FIG. 2  could be combined, further subdivided, or omitted and additional components could be added according to particular needs. Also, computing devices can come in a wide variety of configurations, and  FIG. 2  does not limit this disclosure to any particular configuration of computing device. 
       FIG. 3  illustrates an example cost-driven predictive equipment failure detection technique  300  according to this disclosure. The detection technique  300  could, for example, be implemented using the prediction tool  144  in the system  100  of  FIG. 1 . However, the detection technique  300  could be used with any suitable device and in any suitable system. 
     As shown in  FIG. 3 , equipment information (such as sensor or other instrumentation data) associated with equipment  302  is provided to the prediction tool  144 . The equipment  302  could, for example, denote the equipment  102   c  in the system  100  of  FIG. 1 . The prediction tool  144  can receive the information in any suitable manner, such as directly from sensors, controllers, or other components or indirectly through historians or other components. 
     When the prediction tool  144  receives the equipment information, a machine learning classifier  304  analyzes the received information to identify an indicator value y, which ranges from zero to one in this example. The indicator value varies and is indicative of the possibility of a fault or other problem with the equipment. A number of classification algorithms are known in the art for analyzing equipment information and calculating an indicator value. The machine learning classifier  304  includes any suitable logic for calculating indicator values for equipment. The machine learning classifier  304  could, for example, implement classification algorithms such as logistic regression, random forest, or support vector machine algorithms. The machine learning classifier  304  could also implement regression algorithms such as Bayesian Ridge Regression or Kernel Ridge Regression algorithms. 
     A threshold decision unit  306  calculates a suitable threshold value t for comparison with the indicator value y. If the indicator value y exceeds the threshold value t, a decision  308  can be made that maintenance is needed with the equipment. If the indicator value y does not exceed the threshold value t, a decision  310  can be made that maintenance is not needed with the equipment. The threshold decision unit  306  includes any suitable logic for identifying a threshold value. 
     The threshold decision unit  306  uses costs associated with both successful and unsuccessful predictions, such as a true positive (TP), a false positive (FP), a true negative (TN), and a false negative (FN), to calculate a suitable threshold value. The costs can be compared to a baseline cost associated with only performing maintenance and repairs when a defect occurs. As such, a much more informed and economically motivated selection of the threshold value can be made, which increases or maximizes the savings obtainable through predictive equipment failure detection systems. 
     The threshold decision unit  306  can identify a threshold value based on an economic cost of operating at least one piece of equipment (while described below as a unit, the economic cost can be related to a single piece of equipment or any collection of multiple pieces of equipment). The economic cost of operating equipment can include a summation of the costs of the four potential outcomes (TP, FP, TN, and FN). In particular embodiments, the economic cost can be calculated using the following equation: 
             CostPerUnit   =               CostPerTP   *   TP     +     CostPerFP   *   FP     +                 CostPerTN   *   TN     +     CostPerFN   *   FN               TP   +   FP   +   TN   +   FN             
where CostPerTP, CostPerFP, CostPerTN, and CostPerFN denote the costs of the four potential outcomes and TP, FP, TN, and FN denote the number of occurrences of the four potential outcomes.
 
     The CostPerUnit value can also be refactored in terms of a true positive rate (TP/(TP+FN))=1−β, a false positive rate (FP/(FP+TN))=α, and Q. Q is the ratio of the number of faults to the number of non-faults and can be expressed as (TP+FN)/(TN+FP). Refactoring the CostPerUnit value could then be done as follows: 
     
       
         
           
             CostPerUnit 
             = 
             
               
                 
                   Q 
                   
                     Q 
                     + 
                     1 
                   
                 
                 ⁢ 
                 
                   ( 
                   
                     CostPerTP 
                     - 
                     CostPerFN 
                   
                   ) 
                 
                 ⁢ 
                 
                   ( 
                   
                     1 
                     - 
                     β 
                   
                   ) 
                 
               
               + 
               
                 
                   1 
                   
                     Q 
                     + 
                     1 
                   
                 
                 ⁢ 
                 
                   ( 
                   
                     CostPerFP 
                     - 
                     CostPerTN 
                   
                   ) 
                 
                 ⁢ 
                 α 
               
               + 
               
                 
                   1 
                   
                     Q 
                     + 
                     1 
                   
                 
                 ⁢ 
                 
                   ( 
                   
                     CostPerTN 
                     + 
                     
                       Q 
                       × 
                       CostPerFN 
                     
                   
                   ) 
                 
               
             
           
         
       
     
     As illustrated in figures described below, an ROC curve for the machine learning classifier  304  can plot α versus (1−β) and thereby provide a cost for each threshold of a prediction. A cost baseline can be determined without predictive models so that failures are not predicted and equipment is only repaired or replaced after the equipment has already experienced a fault. In some embodiments, the cost baseline can be expressed as (CostPerFN×(TP+FN))+(CostPerTN×(TN+FP)). The baseline cost can also be divided by a number of units and can be refactored for Q. Thus, a base cost per unit can be expressed as (CostPerFN×Q)+(CostPerTN/(Q+1)). The baseline cost can be set equal to a prediction CostPerUnit to obtain a break-even line. The break-even line for bounce back scenarios can be expressed as follows: 
     
       
         
           
             
               ( 
               
                 1 
                 - 
                 β 
               
               ) 
             
             = 
             
               
                 1 
                 Q 
               
               ⁢ 
               
                 
                   ( 
                   
                     CostPerFP 
                     - 
                     CostPerTN 
                   
                   ) 
                 
                 
                   ( 
                   
                     CostPerFN 
                     - 
                     CostPerTP 
                   
                   ) 
                 
               
               ⁢ 
               α 
             
           
         
       
     
     The break-even line can be plotted on an ROC graph. Points on the ROC curve that lie above or to the left of the break-even line are points where cost savings can be realized by implementing a predictive maintenance system. The point that is furthest above the break-even line could denote the point that maximizes cost savings, and that point can be used to determine the threshold value t. 
     Although  FIG. 3  illustrates one example of a cost-driven predictive equipment failure detection technique  300 , various changes may be made to  FIG. 3 . For example, the detection technique  300  could involve any other suitable mechanism for identifying the indicator value y. 
       FIGS. 4 and 5  illustrate example receiver operating characteristic (ROC) curves according to this disclosure. As shown in  FIG. 4 , an ROC curve  400  illustrates a break-even cost line  402  and plotted points  404  that reflect true positive rates relative to false positive rates of a particular piece of equipment. A vertical distance  406  between the break-even cost line  402  and the plotted points  404  indicates the profit or loss for a particular piece of equipment. In this example, a point  408  has the largest positive difference above the break-even cost line  402 , indicating the maximum cost benefit for a particular piece of equipment. 
     The prediction tool  144  can identify the break-even cost line  402  in any suitable manner. As described above, in some embodiments, the cost baseline can be expressed as (CostPerFN×(TP+FN))+(CostPerTN×(TN+FP)) or as (CostPerFN×Q)+(CostPerTN/(Q+1)). The prediction tool  144  can identify the point  408  highest above the break-even cost line  402  once the break-even cost line  402  is calculated, and the threshold value t could be calculated using that point  408 . For example, since the point  408  lies above the break-even cost line  402 , the point  408  can be used to identify a TP rate and an FP rate that can be mapped back to the threshold value t corresponding to the TP and FP rates. 
     As shown in  FIG. 5 , an ROC curve  500  illustrates a break-even cost line  502 , a curve  504  indicating a weak classifier design, and a curve  506  indicating a strong classifier design. The curve  504  remains at or below (to the right of) the break-even cost line  502 , indicating that the weak classifier design provides little or no benefit. In contrast, a significant portion of the curve  506  remains above (to the left of) the break-even cost line  502 , indicating that the strong classifier design can provide significant cost benefits. Again, a point  508  having the greatest vertical distance above the break-even cost line  502  indicates the economic optimal decision threshold value, and the point  508  can be used to determine the threshold value t. 
     Among other things, this approach allows users to evaluate if a classifier is economically viable or not by determining whether points are above or below the break-even line. When a classifier is viable, this approach also gives users the ability to choose a threshold value for increased or maximum economic benefit. 
     Although  FIGS. 4 and 5  illustrates example ROC curves, various changes may be made to  FIGS. 4 and 5 . For example, any other suitable curves, points, and lines could be used depending on the equipment being monitored. 
       FIGS. 6, 7, 8A, and 8B  illustrate an example application of a failure prediction algorithm according to this disclosure.  FIG. 6  shows an example system  600  containing multiple pieces of industrial equipment  602 - 620 , which in this example denote compressors. Some of the compressors shown in dashed lines (equipment  604 ,  608 ,  612 , and  614 ) denote equipment that will fail, while the remaining compressors will not.  FIG. 6  also includes indicator values y computed for the pieces of industrial equipment  602 - 620  using a classifier. 
     Selecting different threshold values t will affect the classifier&#39;s TP and FP rates. The behavior of a classifier with a specific threshold value t can be expressed using an outcome matrix.  FIG. 7  illustrates a generic outcome matrix  700 , which indicates the four possibilities of determining if and when a failure is detected. For example, a prediction that a failure has occurred when the failure has actually occurred is a true positive. A prediction that a failure has occurred when the failure has not actually occurred is a false positive. A prediction that a failure has not occurred when the failure has actually occurred is a false negative. A prediction that a failure has not occurred when the failure has not actually occurred is a true negative. Specific values in an outcome matrix can be used as the TP, IN, FP, and FN values described above. 
       FIGS. 8A and 8B  illustrate specific outcome matrices  800 A and  800 B for classifiers that analyze data from the pieces of equipment  602 - 620  in  FIG. 6  using different threshold values t. In  FIG. 8A , the outcome matrix  800 A is generated using a threshold value of 0.25. In this case, a true positive value is 4.0, a false positive value is 5.0, a false negative value is 0.0, and a true negative value is 1.0. Accordingly, a true positive rate is 4/4 (defined as TP/(TP+FN)) and a false positive rate is 5/6 (defined as FP/(FP+TN)). In  FIG. 8B , the outcome matrix  800 B is generated using a threshold value of 0.65. In this case, a true positive value is 3.0, a false positive value is 2.0, a false negative value is 1.0, and a true negative value is 4.0. Accordingly, a true positive rate is 3/4 (defined as TP/(TP+FN)) and a false positive rate is 2/6 (defined as FP/(FP+TN)). 
     As can be seen here, the threshold value of 0.25 provides a better true-positive rate and a worse false positive rate, while the threshold value of 0.65 provides a worse true-positive rate and a better false positive rate. By taking into account the costs of the different possible outcomes of the failure prediction algorithm, an ideal threshold value can be selected that can increase or maximize the economic benefit of the failure prediction algorithm. 
     Although  FIGS. 6, 7, 8A, and 8B  illustrate one example of an application of a failure prediction algorithm, various changes may be made to  FIGS. 6, 7, 8A, and 8B . For example, any other suitable industrial equipment, thresholds, and outcome matrices could be used depending on the application. 
       FIG. 9  illustrates an example method  900  for cost-driven predictive equipment failure detection according to this disclosure. For ease of explanation, the method  900  is described as being performed by the prediction tool  144  in the system  100  of  FIG. 1 . However, the method  900  could be used with any suitable device or system. 
     Equipment information indicating one or more characteristics of a piece of equipment is received at step  902 . This could include, for example, the prediction tool  144  receiving the equipment information from any suitable source(s), such as one or more sensors, actuators, controllers, or process historians. An indicator value indicative of a potential fault for the piece of equipment is identified at step  904 . This could include, for example, the prediction tool  144  calculating an indicator having a value between zero and one indicating a likelihood of a fault. 
     A decision threshold value is determined at step  906 . This could include, for example, the prediction tool  144  incorporating a cost calculation into an ROC graph in the form of a break-even line. Points that reflect true positive rates relative to false positive rates of a particular piece of equipment can be plotted on the ROC graph, and the point having the maximum vertical distance above the break-even line can be identified. This point can be used to identify the threshold value. 
     The indicator value is compared to the threshold value at step  908 , and a signal is transmitted indicating whether maintenance is to be performed at step  910 . This could include, for example, the prediction tool  144  transmitting a signal to an operator station, maintenance scheduler, or other device or system when the indicator value exceeds the threshold value. 
     Although  FIG. 9  illustrates one example of a method  900  for cost-driven predictive equipment failure detection, various changes may be made to  FIG. 9 . For example, while shown as a series of steps, various steps shown in  FIG. 9  could overlap, occur in parallel, occur in a different order, or occur multiple times. As a particular example, the threshold value for a particular piece of equipment could be calculated at any suitable time and need not be calculated after equipment information is received and an indicator value is calculated. Moreover, some steps could be combined or removed and additional steps could be added according to particular needs. 
     In some embodiments, various functions described in this patent document are implemented or supported by a computer program that is formed from computer readable program code and that is embodied in a computer readable medium. The phrase “computer readable program code” includes any type of computer code, including source code, object code, and executable code. The phrase “computer readable medium” includes any type of medium capable of being accessed by a computer, such as read only memory (ROM), random access memory (RAM), a hard disk drive, a compact disc (CD), a digital video disc (DVD), or any other type of memory. A “non-transitory” computer readable medium excludes wired, wireless, optical, or other communication links that transport transitory electrical or other signals. A non-transitory computer readable medium includes media where data can be permanently stored and media where data can be stored and later overwritten, such as a rewritable optical disc or an erasable memory device. 
     It may be advantageous to set forth definitions of certain words and phrases used throughout this patent document. The terms “application” and “program” refer to one or more computer programs, software components, sets of instructions, procedures, functions, objects, classes, instances, related data, or a portion thereof adapted for implementation in a suitable computer code (including source code, object code, or executable code). The term “communicate,” as well as derivatives thereof, encompasses both direct and indirect communication. The terms “include” and “comprise,” as well as derivatives thereof, mean inclusion without limitation. The term “or” is inclusive, meaning and/or. The phrase “associated with,” as well as derivatives thereof, may mean to include, be included within, interconnect with, contain, be contained within, connect to or with, couple to or with, be communicable with, cooperate with, interleave, juxtapose, be proximate to, be bound to or with, have, have a property of, have a relationship to or with, or the like. The phrase “at least one of,” when used with a list of items, means that different combinations of one or more of the listed items may be used, and only one item in the list may be needed. For example, “at least one of: A, B, and C” includes any of the following combinations: A, B, C, A and B, A and C, B and C, and A and B and C. 
     The description in the present application should not be read as implying that any particular element, step, or function is an essential or critical element that must be included in the claim scope. The scope of patented subject matter is defined only by the allowed claims. Moreover, none of the claims is intended to invoke 35 U.S.C. § 112(f) with respect to any of the appended claims or claim elements unless the exact words “means for” or “step for” are explicitly used in the particular claim, followed by a participle phrase identifying a function. Use of terms such as (but not limited to) “mechanism,” “module,” “device,” “unit,” “component,” “element,” “member,” “apparatus,” “machine,” “system,” “processor,” or “controller” within a claim is understood and intended to refer to structures known to those skilled in the relevant art, as further modified or enhanced by the features of the claims themselves, and is not intended to invoke 35 U.S.C. § 112(f). 
     While this disclosure has described certain embodiments and generally associated methods, alterations and permutations of these embodiments and methods will be apparent to those skilled in the art. Accordingly, the above description of example embodiments does not define or constrain this disclosure. Other changes, substitutions, and alterations are also possible without departing from the spirit and scope of this disclosure, as defined by the following claims.