Patent Publication Number: US-2022214679-A1

Title: Dynamic Prediction of Risk Levels for Manufacturing Operations through Leading Risk Indicators: Dynamic Exceedance Probability Method and System

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
     This application is a continuation-in-part of and claims the priority and benefit of U.S. patent application Ser. No. 16/894,965, entitled “Dynamic Prediction of Risk Levels for Manufacturing Operations through Leading Risk Indicators: Dynamic Risk Sloping Trend Method and System”, filed Jun. 8, 2020, which is a continuation-in-part of and claims the priority and benefit of U.S. Pat. No. 10,705,516, entitled “Dynamic Prediction Of Risk Levels For Manufacturing Operations Through Leading Risk Indicators: Dynamic Risk Fault Tree Method And System”, filed Mar. 18, 2019, which is a continuation-in-part of and claims the priority and benefit of U.S. Pat. No. 10,268,962, entitled “Dynamic Prediction of Risk Levels for Manufacturing Operations through Leading Risk Indicators: Dynamic Risk Analyzer Engine”, filed Feb. 1, 2016 which is a continuation-in-part of and claims the priority and benefit of U.S. Pat. No. 9,495,863, entitled “Dynamic Prediction of Risk Levels for Manufacturing Operations through Leading Risk Indicators: Alarm-based Intelligence and Insights, filed Oct. 10, 2014. This application also claims the priority and benefit of U.S. Provisional Patent Application Ser. No. 62/109,865, entitled “Dynamic Prediction of Risk Levels for Manufacturing Operations through Leading Risk Indicators: Dynamic Risk Analyzer Engine,” filed on Jan. 30, 2015. The entireties of each application are incorporated herein by reference in their entireties. 
    
    
     FIELD OF THE INVENTION 
     The dynamic risk analyzer (DRA) of the present invention periodically assesses real-time or historic process data, or both, associated with an operations site, such as a manufacturing, production, or processing facility, including a plant&#39;s operations, and identifies hidden near-misses of such operation, when in real time the process data appears otherwise normal. The DRA assesses the process data in a manner that enables operating personnel including management at a facility to have a comprehensive understanding of the risk status and changes in both alarm and non-alarm based process variables. The hidden process near-miss data may be analyzed alone or in combination with other process data and/or data resulting from prior near-miss situations to permit users to not only be aware of issues that may occur in the future and also be informed of how quickly this future issue may arrive. As a result of this information, strategic action may be taken to: (a) reduce or avert the occurrence of adverse incidents or catastrophic failure of a facility operation; (b) delay an unnecessary shutdown; or (c) plan for future maintenance. 
     BACKGROUND OF THE INVENTION 
     Every low-probability, high-consequence adverse incident or catastrophic operational failure at any production or processing facility, such as a chemical plant, fluid-catalytic-cracking units (FCCU) at a petroleum refinery, nuclear energy production plant, or even a biological facility or waste management facility, is preceded by many high-probability, low-consequence events, which may or may not be recognized by alarms or are considered near-misses. Some of these events remain hidden in the background of normal operating conditions. An ideal risk management system at the plant will account for the near-misses, especially those that are hidden, and develop indicators to notify the operators in advance of undesirable incidents that are likely to happen. In particular, such knowledge becomes highly desirable for unmanned plants/facilities. 
     The public has been harmed by industrial accidents, adverse events, and/or catastrophic failures that could have been avoided with a DRA system. Indeed, the US government chemical safety board web site (www.csb.gov) is inundated with reports of accidents that took place in the chemical manufacturing facilities in the recent years that cost lives, and damaged property. The recurring themes in the outcome of analysis of these accidents are a) the lack of preventive maintenance, and b) the lack of attention to process near-misses. Moreover, every year billions of dollars are lost in the manufacturing industry due to “trips” (unexpected shutdowns due to malfunction of the equipment and/or control systems) at operational plants and facilities. For instance, there have been $6 billion/year losses recorded by US refineries from unexpected shutdowns and associated incidents of crude and fluidized catalytic cracking (FCC) units. 
     An additional condition, which is frequently observed in most manufacturing or processing facilities, is silencing (muting) the alarms that are considered to be nuisance. These are alarms that are activated so often that they are considered to be of such little significance by the operators, that they are regarded as unimportant disturbances resulting from normal operations, so they are turned off or ignored like fire drills in office buildings. But such actions negate the value of the alarm system. For example, at an offshore refinery facility visited in 2011 by the inventors, most of the “low priority” alarms had been silenced. In fact, one of the reasons that the BP off shore accident in Gulf of Mexico in 2010 (where 11 people died and 17 were injured) was not identified in its early stages was because an alarm had been silenced after it had been going off in the middle of the night and awaking the workers. 
     Most safety activities are reactive and not proactive, and as a result many organizations wait for losses to occur before taking preventative steps to prevent a recurrence. Near miss incidents often precede loss producing events but are either hidden within process operations and related data or are largely ignored because no injury, damage, or loss actually occurred. Thus, many opportunities to prevent an accident or adverse incident are lost. However, recognizing and reporting near miss incidents, particularly measurable near misses, such as, for example, by alarms in an alarm-monitored plant/facility or by comparative data, can make a major difference to the safety of workers within organizations, and often to the public at large, e.g., in the case of a nuclear-powered facility wherein in a systems failure poses a significantly high amount of risk. History has shown repeatedly that most loss producing events (accidents) were preceded by warnings or near-miss accidents. 
     Fault tree analysis (FTA) is a logical graphic method used to evaluate the reliability of complex engineering systems from qualitative and quantitative perspectives. Fault trees provide a graphical representation of combinations of component failures leading to an undesired system failure. However, in many situations, the behavior of components in a complex system and their interactions, such as failure priority, sequentially dependent failures, functional dependent failures, and dynamic redundancy management, cannot be adequately addressed by traditional fault trees due to their limited modeling capacity. 
     A major disadvantage of the traditional FTA is its inability to capture sequence dependencies in the system while still allowing an analytic solution. Dynamic gates may be employed to address this disadvantage. There are four major types of dynamic gates: (1) priority-AND gates (PAND gates); (2) functional dependency gates (FDEP gates); (3) sequence enforcing gates (SEQ gates); and (4) spare gates. 
     PAND gates have two inputs, A and B, both of which may be basic events or the output of other logic gates. The output of this gate is true if both inputs have occurred and A occurred before B. 
     FDEP gates include a trigger input (either a basic event or an output of another gate) and one or more dependent events. The dependent events rely upon the trigger event. When the trigger event occurs, the dependent basic events follow, and the output becomes true. 
     SEQ gates do not open unless the inputs fail in a particular order. They are not true if the failure sequence occurs in a different order than that specified. The difference between SEQ gates and PAND gates is SEQ gates allow events to occur only in a pre-specified order and states that a different failure sequence is impossible. PAND gates do not impose such a strong assumption: they simply detect the failure order, and a failure is triggered upon the match with the order. 
     Spare gates often include one principal component that can be substituted by one or more backups that have the same function as the principal component. If the primary unit fails, the first alternate component begins to function. The output does not become true until all the replacements fail. 
     Simply observing known parameters may not be enough to evaluate the reliability of complex engineering systems from qualitative and quantitative perspectives. Subtle trends should be considered to predict out over future time horizons. However, such subtle linear trends may be deceiving or tricky to project. Indeed, what may appear to be a subtle trend over a designated time period may be nothing more than statistical noise (i.e., a phantom trend). Similarly, just because a trend appears to be reversing does not mean that a negative event will not occur. Predicting a variable&#39;s probability of exceeding a specified threshold over a given time horizon window in the future is difficult or impossible without a modeling approach that can account for the complex relationships among the various types of data. Especially when some of the parameters are, as here, unobservable (e.g., near misses). 
     Thus, there is a need, not met until the present invention, for a “dynamic risk analyzer” (DRA) system that provides probabilistic estimates for process variables exceeding their critical thresholds in the future via periodically analyzing real time and historic data and delivers this information to the users via the DRA system dashboard, allowing them to conduct further analysis. Such an ability to predict when process variables will likely exceed their critical thresholds in the future would permit the system to provide more accurate: (a) assessments of operational risks, and (b) identifications of near misses of alarm and non-alarm based process variables, which are hidden as normal operating conditions. In addition, these probabilities can help direct attention to developments that may give rise to critical adverse events, including shutdown trips, in the future. Based on such information, the system could send alert signals and/or reports to identify hidden risk thereby enabling managers to plan proactive action, including maintenance and possibly avoid incidents, rather than requiring costly unplanned maintenance or clean-ups—in case of severe events. 
     SUMMARY 
     The DRA may incorporate a dynamic exceedance probability system for analyzing risk levels for manufacturing operations. The components of a DEP system work in concert to automatically process a large number (often 1000 or more) tags on a scheduled basis and alert DRA system users to a variable&#39;s probability of exceeding a specified threshold over a given time horizon window in the future. In doing so, the users can be aware of not only issues that may occur later, but also be informed of how quickly a given tag may reach a critical value (e.g. a product pressure which is dipping, and once it reaches a critical threshold, the final product will have major quality problems). 
     The system includes a server that receives automatically measured process data from a real-time data source and/or a historical archive data source and long-term process data for a period preceding the measured process data. A processor analyzes the data. Specifically, a two-stage Bayesian inference model is used to analyze the values of parameters P and/or groups G of the parameters P of the measured process data at time interval T which determines a final dynamic exceedance probability value for the variable given the real-time data source, the historical archive data source or long-term process data source, and the variable threshold. Based on the final dynamic exceedance probability the system identifies operational risk and/or near-miss risk that would otherwise be unknown or concealed in parameters P. This identified operational risk and/or near-miss risk is used for strategic corrective action. A display presents the information the operational risk and/or near-miss risk in a graphic that visually depicts the final dynamic exceedance probability value for the variable over a future time horizon designated by the user or an agent or employee of the user. Furthermore, this system operates continuously. 
     In certain embodiments, the two stage Bayesian inference model first uses a time-based likelihood method to determine an initial posterior probability. This initial posterior probability serves as a prior distribution probability for the second-stage of the Bayesian inference model which determines the final posterior probability using an event-based likelihood method. Kalman filters may also be used. The process data may be either an analog signal or a two-state signal. Furthermore, the system may not communicate the process data outside the manufacturing operation and the system may operate autonomously. 
     A method for analyzing risk levels in a manufacturing operation. The method includes collecting: (1) measured process data, comprising: data automatically collected by a data collection component, located within the manufacturing operation, in either: (a) real-time or (b) from an archive server or both; and (2) long-term process data for a period preceding the collecting measured data. The data is used to identify risk and/or near-miss risk of the manufacturing operation that would otherwise be unknown or concealed in parameters P and/or groups G of the parameters P of process data by using a two-stage Bayesian inference model wherein an initial posterior probability is determined in a first-stage of the Bayesian inference model using a time-based likelihood method and the initial posterior probability serves as a prior distribution probability for a second-stage of the Bayesian inference model that determines the final posterior probability using an event-based likelihood method, wherein the final posterior probability is automatically updated over time to identify operational risk and/or near-miss risk that would otherwise be unknown or concealed in parameters P. Displaying the risk or near-miss risk in a graphic that visually depicts the final dynamic exceedance probability value for the variable over a future time horizon designated by the user or an agent or employee of the user. Furthermore, the method is performed continuously and autonomously. 
     A display system for risk indicators for a manufacturing operation is also disclosed. The display requires the identification of risk and/or near-miss risk of the manufacturing operation that would otherwise be unknown or concealed in parameters P and/or groups (of the parameters P of measured process data, in real-time, periodically, and/or historically. The measured process data is obtained by using a data collection component located within the manufacturing operation. Operational risk and/or near-miss risk that would otherwise be unknown or concealed in parameters P is identified using a two-stage Bayesian inference model wherein an initial posterior probability is determined in a first-stage of the Bayesian inference model by using a time-based likelihood method and the initial posterior probability serves as a prior distribution probability for a second-stage of the Bayesian inference model that determines the final posterior probability using an event-based likelihood method. A display depicts the risk or near-miss risk in a graphic that visually the final dynamic exceedance probability value for the variable over a future time horizon designated by the user or an agent or employee of the user. Again, the system is performed continuously and autonomously. 
    
    
     
       BRIEF DESCRIPTION OF THE FIGURES 
       The description discloses the invention that is illustrated with reference to the accompanying figures to advise one of ordinary skill in the art of the characteristics and benefits of the invention. In the various views of the figures, like reference characters designate like or similar parts, whereby: 
         FIG. 1  shows a DRA system of the present invention. 
         FIG. 2  shows a DRA system within a secured network with no remote access where connectivity with the OPC server allows the DRA system to obtain continuous process data, as it gets measured and channeled out, without requiring any direct communication with the industrial controls system (such as DCS, SCADA, or PLC devices). 
         FIG. 3  shows a petal chart for parameter P indicating its 7 values over 7 time periods (days) where the value of P for March-5 is equal to r, which is indicated by the petal with length r. 
         FIGS. 4A, 4B, 4C  show a presentation of a variation of parameter P over 7 consecutive time intervals on the petal chart ( FIG. 4A ) having a comparative distinct visual advantage over a bar chart ( FIG. 4B ), and line chart ( FIG. 4C ) showing. 
         FIG. 5  shows an embodiment of a dynamic fault tree at a single designated time period. 
         FIG. 6  shows a flowchart of one embodiment of the components of the dynamic risk sloping trend system. 
         FIG. 7A  shows a variable charted over 60 days. 
         FIG. 7B  shows the variable of  FIG. 7A  charted over 180 days along with a linear trendline identified using the dynamic risk sloping trend system. 
         FIG. 8  shows a flowchart of one embodiment of the components of the dynamic exceedance probability system. 
         FIG. 9A  shows a variable charted over 7 days with the dynamic exceedance probability system and an assigned low threshold of 5. 
         FIG. 9B  shows the continuously updated associated dynamic exceedance probability for the variable depicted in  FIG. 9A  to cross the low threshold of 5 over the following 30 days. 
     
    
    
     DESCRIPTION OF THE INVENTION 
     In general, and unless otherwise indicated, singular elements may be in plural and vice versa with no loss of generality. 
     Definitions 
     As used herein, each of the following terms has the meaning associated with it in this application. 
     The phrase “process data” is used to refer to data resulting from real-time measurements of both alarm and non-alarm-based process variables associated with a plant/facility including temperature, pressure, and the like. More specifically, “process data” is the collection of all or at least some of the values of process parameters that are measured, recorded, and reported by the distributed control system (DCS) for a process or plant, wherein a hierarchy of controllers is connected by communications networks for command and monitoring of control elements distributed throughout the system, or any other device that automatically measures the value of one or more variables and reports the data either in-real time or periodically, or both. For example, process data can include, but not be limited to, values including temperature measured in a reactor, at an inlet stream or an outlet stream, pressure of a reactor, flow rate of a liquid or gas going into or out of a reactor, liquid level in a reactor or a tank, and the like. In large industrial operations, there are hundreds of process variables that can be measured and reported. An industrial manufacturing operation centered around a reactor would have several parameters that are associated with that “reactor unit” (reactor and its associated peripheral equipment). Also, there are, for example, several parameters associated with a liquid flowing into a reactor including its temperature, pressure, viscosity, etc. Together the values of all these parameters comprise “process data.” 
     The phrase “real time” is used in its plain and ordinary meaning. 
     The phrase “distributed control system” or alternatively “DCS” is used to refer to a system of processors used as controllers that implement proprietary interconnections, control strategies, and standard communications protocol for communication. Input and output modules form component parts of the DCS. The processor receives information from input modules and sends information to output modules. Linked into the wired and/or wireless network, the input modules receive information from input instruments in the process or field and the output modules transmit instructions to the output instruments in the field. The inputs and outputs can be, for example, either analog signal which are continuously changing or discrete signals which are 2 state either on or off. Computer buses or electrical buses connect the processor and modules through multiplexer or demultiplexers. Buses also connect the distributed controllers with the central controller and finally to the Human-machine interface (HMI) or control consoles. The elements of a DCS may connect directly to physical equipment such as switches, pumps and valves and to Human Machine Interface (HMI) via SCADA. The differences between a DCS and SCADA is often subtle, especially with advances in technology allowing the functionality of each to overlap. 
     The phrase “near-miss” is used herein to refer to something narrowly avoided; a lucky escape. More specifically, a “near miss” for safety purposes is an unplanned event that did not result in actual injury, illness, or damage—but had the potential to do so, especially if left unaddressed. 
     The term “group” is used to refer to a collection of parameters that typically share one or more common characteristic(s). 
     The phrase “hidden process near-miss” is used to refer to a near-miss event or a series of events (often not obvious to the plant/facility operators through naked eye) that can be identified within process data of an operation. These events can be treated as precursors to accidents, hence, can be utilized by plant/facility operators as well as management to improve the system performance and prevent potential accidents. 
     The phrase “risk results” is used to refer to information on hidden near misses that indicate events or variables or their groups that exhibit risky or abnormal behavior. 
     The phrase “open platform communication” or alternatively “OPC” is used to refer to interoperability standards for reliable and secure exchange of data, between industrial hardware devices in the automation industry, developed by third-party vendors and solution providers. OPC standards define protocols for accessing real-time data, alarms and events, historical data and other applications. The OPC Foundation (opcfoundation.org) is responsible for the development and maintenance of the standards. 
     The phrase “OPC server” is used to refer to a commercially available server that is configured and functions in accordance with OPC standards and protocols and allows easy access to process data and alarms without the need to write vendor-specific programs. 
     The term “processor” is used to refer to a processor or processing unit, multiple processors, or multiple processing units, or other suitably configured computing element. 
     Dynamic Risk Analyzer 
     This description of the invention is intended to be read in connection with the accompanying figures depicting embodiments of the invention. 
     Referring to  FIGS. 1-2 , the dynamic risk analyzer (DRA) comprises a system for analyzing process data periodically (at a specific calculation interval) to identify risk results in connection with risk analysis processes for an operations site. The DRA system is useful for analyzing the process risk levels of an operations site, e.g., a manufacturing, production, or processing facility, on a periodic basis (e.g., minute, hourly, daily, etc.) in real-time or historically, and identifies hidden process near-misses. The DRA system is designed specifically to address the needs of plant managers, engineers, and other operating personnel, who review risk status on a periodic basis and take strategic actions as needed. 
     An overview of the DRA system is shown generally in  FIG. 1 . The DRA system is a computer-based system that includes (1) a data collection component, to connect to data source such as OPC server or historian, etc.; (2) a computer-readable data storage medium consisting of a relational database and a key-value storage (NoSQL) solution; (3) a data processor component, consisting of risk analysis methods and a processor such as a personal computer, a laptop computer, a workstation, a tablet computer, a smart-phone, and/or portable electronic device; and (4) a data presentation platform, such as a website, e.g., Internet or Intranet. The DRA system includes an integrated wired and/or wireless communication network that links all of the components of the system. 
     The collection component functions by receiving process data from a data source, such as an OPC server, historian, etc., in real-time or periodically and storing the process data in the system&#39;s computer readable data storage medium. DRA receives “process data” from an OPC server or Historian at scheduled intervals (every second/minute/hour or other). The data from an OPC server can be stored in an archival server and later accessed for online/offline analyses. An archival server can be a historian system. Commercial historian systems are available in the market (see http://en.wikipedia.org/wiki/Operational_historian), which have the capability to store large volumes of data, anywhere from a few hundred data points per second to hundreds of thousands of data points per second. In addition, the archival server permits end-users to browse and retrieve the historical data for several years. 
     The computer-readable data storage medium comprises a database, such as a relational database, and a key-value storage (NoSQL) solution. The computer readable storage medium functions by storing relevant process data and risk results and subsequently making stored data available for access by other components of the DRA system. Standard commercial or open-source packages can be used as the data storage medium. For example, MySQL, Microsoft SQL Server, and Oracle are suitable relational database solutions. Redis, MongoDB, or Oracle NoSQL can be used as key-value storage. The combination of relational and NoSQL databases allows DRA system to handle large volumes of data reliably. Alternatively, the data storage medium can include, but not be limited to, volatile memory, non-volatile memory, magnetic and optical storage devices such as disk drives, magnetic tape, CDs (compact discs), DVDs (digital versatile discs or digital video discs), removable storage, or other media capable of storing code and/or data, now known or later developed. All the process data and risk results can reside on the computer-readable data storage medium related to a company&#39;s secured server and network that is in communication with the DRA system and are not communicated to the external world. The DRA system is designed to continue operation perpetually, without any user intervention. 
     The data processor functions by analyzing collected and/or stored data to identify hidden near-miss risks. The data processor may be any electronic device cable of processing, receiving, and/or transmitting instructions. For example, the processor may be a microprocessor or a microcomputer. The data processing component begins calculations starting at every T intervals (where the value of T is between 1-minute to 1-month, with the typical value being 1-day)—based on the methods, such as DRA100, DRA200, DRA300, LI100, and LI200, among others, as described in U.S. Pat. No. 8,884,759, the entirety of which is incorporated herein by reference, to obtain the risk results that are used to alter or correct a problem in an operation. Depending upon the number of variables and/or groups being analyzed, length of time interval ‘T’, and server speed, the data processing can take anywhere from a few seconds to several minutes or hours or days. 
     The data presentation platform, such as an Internet or Intranet website, functions by visually presenting risk results identified by the data processor on a computer display. The data presentation component comprises a web application that serves different web pages (dashboards) within DRA to allow the user to browse the risk results. The latest risk results are added once the data processing is complete. There are several system-based services that run continuously to support user (client) interaction with the DRA system. In an embodiment, the data presentation component can include a petal chart, which comprises a new method of presenting variation of risk values with time. 
     The petal chart is introduced to show variation of a parameter P over discrete time periods, which can be any measurable time period, such as minutes, hours, days, weeks, months, years, etc. The different values of the parameter P are graphically displayed as petals next to each other relative to the discrete time period. The total number of petals in a given chart can range anywhere from 1 to 360, which a value being 7, for example. The length of a given petal indicates the value of the parameter for a given time value. If we assume that Pϵ[0, R], where R is a positive real number, then the radii of the outer and inner semicircles are equal to R+R 0 , where R 0  is a real number greater than zero and can be chosen by an analyst. The maximum value of P is shown by a petal whose edge touches the outer circle of the Petal Chart. The inclusion of an outer circle depicted on a petal chart is optional. Also, in reference to  FIG. 3 , the angle spread of the petal chart around the center of the petal chart is 180 degrees which can be a typical value. However, petal charts can have an angle spread equal to 90° around the center of the petal chart, or alternatively an angle value of between 30° to 180° can also be plotted on a petal chart. 
     For example,  FIG. 3  shows a petal chart for parameter P indicating 7 values for parameter P calculated for 7 time periods, which in this case each time period equals one day. Note that the value of parameter P for March 5 (3/5) is equal to r, which is indicated by the petal with length r. Using this concept, the calculated metrics identified in U.S. Pat. No. 8,884,759 such as the dynamic risk index, the compounded risk score, the number of abnormal events, the time segment values, etc., can be plotted with a petal chart. 
     Referring now to  FIGS. 4 a -4 c   , the petal chart has a distinct visual advantage over bar charts and line charts. The variation of parameter P for 7 consecutive time intervals, wherein each time interval is a day, is plotted using a petal chart ( FIG. 4 a   ), a bar chart ( FIG. 4 b   ), and a line chart ( FIG. 4 c   ). In  FIG. 4 a   , the area displayed by each petal, e.g., for March 5 (3/5), is equal to θ(r 1   2 +2r 1 R 0 ), wherein 0 is the angle spread for the petal, with origin at the center point of the petal chart. Thus, the ratio of areas of petals for March 5 (3/5) and March 4 (3/4) is equal to (r 1   2 +2r 1 R 0 )/(r 2   2 +2r 2 R 0 ). For the special case when R 0 &lt;&lt;r 1 , r 2 , this ratio is equal to r 1   2 /r 2   2 . In comparison, the bar chart shown in  FIG. 4 b    shows the ratio of areas of bars for March 5 (3/5) and March 4 (3/4) with heights equal to r 1  and r 2 , is equal to r 1 /r 2 . Similarly, the line chart shown in  FIG. 4 c    shows the ratio of heights of data points for March 5 (3/5) and March 4 (3/4) is equal to r 1 /r 2 . This means that the relative visual impact of the value of parameter P for March 5 (3/5) with respect to that of March 4 (3/4) is more visually significant in the petal chart, when compared to the presentation of the same values for parameter P in a bar chart and a line chart. Hence, the petal chart highlights the relative difference between data points better than that depicted with traditional bar charts and line charts. The petal chart is especially beneficial for operations sites, where the end-users are busy engineers and operators who benefit from quickly viewing the relative difference between consecutive data points. 
     The DRA system integrated into an operations environment is shown in  FIG. 2 . Connectivity with the OPC server allows DRA system to obtain continuous process data, as it gets measured and channeled out, without requiring any direct communication with the industrial controls system, such as DCS, SCADA, or PLC devices. Alternatively, the DRA system can extract the process data from the Historian in real-time or at periodic intervals, e.g., every second, minute, hour, or any other time interval. Once the process data begins to arrive, the DRA system calculates “risk results” at every T interval, where the value of T can be between 1-minute to 1-month or other time parameter, with the value being 1-day in an embodiment. 
     The DRA can automatically identify hidden process near-misses that can potentially lead to accidents having a major impact on safety, operability, quality, and/or business. 
     The methods to obtain process data are defined in U.S. Pat. No. 8,884,759, the entirety of which is incorporated herein by reference, and more specifically can include methods such as DRA100, DRA200, DRA300, LI100, and LI200, among others. The DRA functions to analyze process data to identify hidden process near-misses and to report, record, and use the identified information, e.g., risk results, for system improvement purposes. 
     Often, in industrial operations, the number of process parameters is large. To facilitate the review and analysis of their risk results, the DRA system allows the users to aggregate the process parameters in “groups” which enables the busy operating personnel to obtain a quick high-level view of developing risks in the operations. The parameters in a group may or may not be causally related to each other. For example, in a typical plant operation, groups such as reactors, vessels, pumps, condensers, etc., can be defined. 
     The risk results are available via a web interface to operating team members, also known as end-users, who have access to a company&#39;s intranet portal. Operating team member can include plant managers, operational engineers, supervisors, operators, etc. The risk results can be presented using intuitive charts/dashboards in the DRA system that allow the end-users to identify hidden risks or hidden near-misses at their early stages and take strategic corrective actions to avoid adverse incidents, shutdowns, and catastrophes. Many times, the hidden risks or hidden near-misses are not patently obvious or readily available to the human eye, in spite of the operating personnel conducting daily process monitoring including shift logs review, communications with field operators, trend visualization of key process parameters, etc. The risk results calculated and communicated by the DRA system to the operating personnel present a new dimension of knowledge that not only allows the savings in time of identifying where the attention is needed, but also makes risks transparent among the entire operations staff—which is often times, not clear, nor well understood. 
     Dynamic Risk Fault Tree 
     A Dynamic Risk Fault Tree (DRFT) is an on-line, deductive analytical method and system developed to identify the causal factors of an undesired state in an industrial manufacturing process. The data and risk indicators provided by the DRA system may be one of the inputs for DRFT analysis. The other inputs may include, but not limited to, time-series data for process variables that are part of the industrial manufacturing process under consideration. A key benefit of DRFT analysis is that the results are available to the users autonomously and periodically. Furthermore, the results of all current and past calculations associated with dynamic risk fault trees are available for review at any time (without any limitation of the number of concurrent users). DRFT is not a standard FTA nor it is similar to other ‘dynamic fault tree analysis’ which is either based on probabilistic calculations, such as Monte Carlo analysis or simulation results. “Standard fault trees” used regularly in industrial settings are typically static in nature and often conducted for one-time use. DRFT, instead, not only points out the status of the problem based on actual measured time-series results but also the trajectory of its development over time, by conducting fault tree calculations periodically and autonomously using real-time live or periodic data. Furthermore, its capability can be enhanced by reference of DRA results and calculations in its analysis. 
     The DRFT system obtains input data via a DRFT Data Acquisition component. Clients use a DRFT Editor to build new DRFTs and modify existing ones. Results are displayed on a DRFT dashboard, which is a visual, user-friendly dashboard that presents the results of a specific DRFT. Furthermore, access to past information for a set of DRFTs may be displayed on a dashboard known as DRFT Overview. 
     With regard to the DRFT data acquisition component, DRFT can be an integral part of the DRA software system or another risk analysis system or process data analysis system. The DRA system assesses the process risk levels of an operations site, e.g. a manufacturing, production or processing facility, on a periodic basis (e.g., daily) and points to hidden near-misses (as defined in the parent patent). DRA is designed to cater to the needs of plant managers, engineers and other operating personnel, who review risk status on a periodic basis and take strategic actions as needed. 
     DRFT utilizes the “process data” the DRA or another risk analysis system or process data analysis system receives from an Open Platform Communications (OPC) server or Historian at scheduled intervals (every second/minute/hour or other) and processes to identify risk status as well as the potential causal factors and root causes. OPC refers to interoperability standard for reliable and secure exchange of data, between industrial hardware devices in the automation industry, developed by third-party vendors and solution providers. The data from an OPC server can be stored in an archival server, for storage and online/offline analyses. This archival server serves as a Historian. Historian systems have the capability to store large volumes of data, anywhere from a few hundred data points per second to hundreds of thousands of data points per second. In addition, the Historians permit the end-users to browse and retrieve the historical data for several years. 
     DRFT presents the results in a tree format and is made up of several “nodes”, each consisting an expression or criterion to be satisfied (based on the state functions used in the node). The first node is referred as a “Main node” and it states the overall purpose of the fault tree. For example, identification of potential causal factors when the product yield becomes less than 95%. Other nodes, called “child nodes”, stem from the main node (and other nodes) and are related to the main node through various branches. The purpose of DRFT calculations is to process the nodes and identify time periods when the expressions specified for each node is satisfied. 
     Nodes contain one or more of valid expressions, such as the ones listed, but not limited to, in Table 1. A valid expression typically is a Boolean expression which references process variables, numbers, and other nodes. Nodes are connected to each other via parent-child relationship. 
     Process variables such as temperature, pressure, etc., can be used in expressions to identify the status of a problem. These process variable values or any combination of them, as well as the results of DRA risk calculations, and any combination of them, can be used as state functions in node expressions. 
     Each Node can also include additional text information, such as an explanation(s) and/or recommendation(s) related to the conditions identified in that node or in other nodes. 
     Each fault tree can have anywhere from one to thousands of nodes with a typical fault tree consisting of somewhere between 20-200 nodes. 
     Although DRFT is complimentary to a DRA system, the DRFT method and system described herein can be expanded as a stand-alone method and system which can receive time series data from any automatic data collection system and obtain results using the criteria listed in the nodes. 
     DRFTs can be developed with a user interface. The interface may permit the user to name the node (e.g., high reactor temperature), provide an expression within the node that may be either true or false (e.g., the reactor temperature is greater than 100° C.), or provide operator recommendations such as instructions to add coolant to reduce the reactor temperature. Once more than one node is created, the user may designate parent and child relationships between the nodes. 
     Node expression could include, but not be limited to, the following in Table 1: 
     
       
         
           
               
             
               
                 TABLE 1 
               
             
            
               
                   
               
               
                 Examples of node expressions and associated remarks 
               
            
           
           
               
               
            
               
                 Expression 
                 Remarks 
               
               
                   
               
               
                 TI100.PV &gt; 100 
                 Indicate when this temperature  
               
               
                   
                 variable exceeds 100 
               
               
                 (TI100.PV &gt; 100) AND 
                 Indicate when both the temperature  
               
               
                 (TI200.PV &gt; 100) 
                 variables exceed 100 
               
               
                 (TI100.PV &gt; 100) OR  
                 Indicate when either of the temperature  
               
               
                 (TI200.PV &gt; 100) 
                 variables exceed 100 
               
               
                 DRA(TI100.PV) &gt; 0 
                 Indicate when risk metric in DRA  
               
               
                   
                 for this temperature exceeds 0 
               
               
                   
               
            
           
         
       
     
     Each DRFT stems from a main event for which the potential root causes are expressed as nodes as “leaves” of branches. This main event is expressed using a “main node”. Once the development of a DRFT is completed, it starts evaluation of node expressions periodically, which can range from every few minutes to few hours and even few days. The results of the calculations indicate when the expressions listed in its nodes are satisfied by changing the shape or the color of a node. For example, the nodes for which the expressions are true may be depicted in blue color with a bold font. This is called an “Active Fault Tree” indicating its full functionality which can be seen following its branches, as part of a new dashboard. 
     A full DRFT system can have multiple DRFTs associated with it. The nodes of DRFTs can be satisfied one or more times in a given time period such as a day, a week, a month, etc. A summary of the number of times when a given DRFT&#39;s main node condition is satisfied can be shown as a graphical table indicating the number of activations of its main node for each time period. Each DRFT can be updated and recomputed by the user any time—giving significant flexibility and power to them to conduct an online and automated root cause analysis. 
     In certain embodiments a node expression is essentially a time-series Boolean value (true or 1 for some time instants and false or 0 for remaining time instants). The advantage is that a user can build complex node expressions and cross-reference different nodes easily, which is not possible in traditional fault tree structures. 
     For example, say for Node-A, the expression is: (TI100.PV&gt;100) OR ((TI200.PV&gt;200) AND (TI300.PV&gt;200)) OR (DRA(TI100.PV)&gt;0) OR (Node-B). TI100.PV, TI200.PV, TI300.PV are different temperature sensors and Node-B is another node, which may or may not be part of this DRFT. When the above condition is satisfied (say it is satisfied from 5-6 pm yesterday), the value of the expression becomes TRUE or 1 during that time, otherwise, it remains FALSE or 0. Another node is referenced also—so when Node-B is true, Node-A will be also true. Within an expression, each condition is treated equally. Furthermore, in alternate embodiments, the nodes may be assigned priority. Also, a user can refer multiple operations (OR, AND, &gt;, &lt;, =, +, −, *, /, custom-DRA operations, etc.) in an expression. 
     Furthermore, because of the flexibility and scalability associated with the disclosed node expressions, the utility of this method extends beyond just building cause-and-effect fault trees, instead such nodes also allow the user to create “dynamic risk trees” and/or other visual tree structures where one can capture and monitor risk performance and relationships between different equipment, process areas, plant operations, etc., over time. 
     Dynamic Risk Sloping Trend 
     Dynamic Risk Sloping Trend (DRST) is an on-line, statistical method and system developed to identify slow, consistent trends or changes in any continuously measured, calculated or monitored parameter or variable in a chemical or manufacturing process. These variables can be any sensor or calculated value recorded by the process control system or historian or input manually, in relation to a chemical or manufacturing process. The main benefit of the DRST system is to detect the existence of subtle and ongoing trends in variables, which may indicate potential undesirable process issues, delivered autonomously to the users via the DRA system dashboard. DRST is different from other linear modeling and fault detection methods in that it not only detects subtle trends via linear modeling, but also applies a series of filters to measure trend quality (e.g., how closely a best-fit line tracks the linear trendline). The filter used may be a Bayesian model-based filter. One type of a Bayesian model-based filter is, for example, a Kalman or Kalman-like filter. It is noted, however, that other Bayesian model-based filters exist. 
     Using both current and historical data, the DRST points out the status of the problem based on actual measured time-series results along with the potential speed and likelihood with which the problem will continue to develop over time by filtering the data to not only identify trend direction but also the likelihood the trajectory at which the trend will continue. The DRST displays all this information, ordered by different classification levels, for users to view. The viewing system is built to display detected trends, overlaid on the source data, excluding shutdown periods, which are not included in analysis. 
     Detecting these trends can offer a vital benefit to process facilities for several reasons. First, as with the DRA system, these trends represent that maintenance may be needed in the near future, and enables the managers to plan this maintenance, rather than requiring costly unplanned maintenance. Conversely, if a maintenance is planned, the DRST system may indicate that such maintenance can be delayed, hence saving production by reducing downtime. Second, where the DRA system detects sudden spikes in the upward and downward direction, the DRST system helps fill in the gaps of slow, but steady progression towards excessively high or low values—which otherwise is not easy to identify unless someone is specifically looking for it. Finally, by providing an easy, at a glance interface, these findings are spotlighted, and can be quickly triaged by plant management and handled at the time of their choosing. 
     The DRST system obtains input data via a DRST Data Acquisition component. 
     DRST is built to work alongside an existing DRA system. As mentioned above, the DRA system provides analysis at a glance of the process risk levels in a continuous operation plant. To do this, the system connects to an on-site data source (typically a historian or OPC server or sometimes an industrial control system) and extracts the data, transforms it to a uniform format, and loads it into the DRA database. This process may be referred to as an extract, transform, load (“ETL”) process. This time series data shows a sensor (“variable” or “tag”) and its reading at a given time (e.g. the temperature of the furnace at 1 pm is 234.5° C.). By collecting this data over long time periods, the DRST system can extract long term trends. 
     Once the data is loaded into the DRST system, it must be analyzed. Specifically, the data collected and loaded into the DRST system is used to detect the presence of trends over an extended period. Broadly speaking, this system identifies periods of time in which a tag exhibits consistent linear behavior in an upward or downward direction. Often, this can indicate a latent and ongoing issue in a continuous processing plant, such as a leakage, or a buildup. These trends are frequently hidden and are especially difficult to detect based on spot checks by plant operators and managers. Such issues are often missed because these readings appear to be static over short time frames, but when viewed over longer time frames are clearly trending upwards or downwards. For example, compare  FIG. 7A  wherein a variable viewed over 60 days appears static with  FIG. 7B  wherein the same variable viewed over 180 days shows a subtle upward trend. Simply put, the DRST system detects trends which span several different time ranges, using several measures of fit quality, and marks these trends for display through the DRA system. 
     The DRST system uses an algorithm based on statistical analysis of long term trends to detect when this is occurring and calls attention to it using the DRA system. These trends are evaluated using several statistical measures including quality of fit, residual error, and a steepness and flatness measure. This ensures that the presented trends represent a latent phenomenon with a high probability. 
     A trend can also be associated with a strength, which indicates its quality of fit. The strength value can be measured: (a) numerically (e.g. a value is assigned out of maximum 10 or 100 points), or (b) qualitatively (e.g. a level is assigned based on pre-defined strong, medium, low, insignificant brackets). The DRA may prioritize the display of trends with higher strength. Importantly, as new data becomes available periodically (every few minutes, hourly, daily, weekly, monthly), the trends are evaluated periodically by the DRST system. If an existing trend grows over time, its strength is re-evaluated periodically. 
     Furthermore, most continuous processing facilities go through downtimes, typically known as shutdowns, which can be planned or unplanned. During these periods, the plants might perform troubleshooting, or other maintenance tasks, which may generate irrelevant data. The DRA system allows admins to input shutdown conditions, which automatically determine if a plant is in shutdown during that time. DRST in turn removes these shutdown periods from the analysis, as well as visually, and prevents times of disuse from causing analysis to miss trends which were present both before and after a shutdown period. 
     Finally, the results of the DRST system are displayed via a DRST visualizer. The DRST visualizer is a part of the DRA frontend which allows the user to view at a glance all of the variables, currently exhibiting trends, classified according to their length or strength. If classified based on length, the buckets can be long-term, medium-term and short-term trends. The minimum trend lengths for short-term, medium-term and long-term trends are 60 days, 90 days and 180 days, however, they can vary depending upon the process and can be anywhere from 15 days (short-term) to 3 years (long-term). Furthermore, the DRA may include a graphical user interface for quickly seeing which tags are undergoing a trend and whether that trend is classified as short, medium, or long term. Indeed, the DRA may include a “Show Trend” button which displays the trends 
     In the DRST visualizer, the trends are often color coded, for example, long term trends may be highlighted in red, medium term trends may be highlighted in orange, and short-term trends may be highlighted in yellow. The DRST Visualizer allows the user to view trends over different time periods such as 60 days, 180 days, 1 year, 2 years, all data, etc. During these views, the shutdown periods are removed automatically so the user can visualize and understand the trends clearly. Optionally, the DRST can also display any anomalies detected by the DRA system. 
     Dynamic Exceedance Probability Method and System 
     Dynamic Exceedance Probability (DEP) is a statistical method and system developed to determine a variable&#39;s probability of exceeding a specified threshold over a given time horizon window in the future. These variables can be any sensor or calculated value recorded by the process control system or historian, in relation to a chemical or manufacturing process. These variables may also be input manually. The thresholds are inputted by the user or their employee or agent and can be either on the high or low end (of the normal operation). Often these thresholds indicate safety and quality limits in the process which, when exceeded, can result in a shutdown, lost productivity, equipment damage or potentially even more dangerous situations which may cost lives. These time horizon windows allow the users their employees or agents to see the probability of an exceedance in a future time period and can be set to any value. For example, the time horizon may be 1 day or 365 days. The main benefit of the DEP system is that it is a predictive tool that provides probabilistic estimates for process variables exceeding their critical thresholds in the future and delivers this information to the users their agents or employees via the DRA system dashboard, allowing them to conduct further analysis. 
     DEP is different from normal monitoring systems because it uses a Bayesian inference model, consisting of an ensemble of statistical measures, to automatically model the exceedances that occurred in the history and then using both current and historical data, it generates probability estimates for future time horizon windows even when there may not be any previous exceedances in the history. The Bayesian inference model typically has 3 components: the prior, the likelihood, and the posterior. Bayesian inference uses the likelihood of an event occurring together with prior information to calculate the posterior probability (i.e., the likelihood of an event occurring). The only input required is the identified threshold information. Everything else is done autonomously by the system. 
     Generating these posterior probabilities can offer major benefits to processing facilities. Just as with the DRA system, these probabilities can help direct attention to developments that may give rise to critical adverse events in the future, including shutdown trips. This early notification enables managers to plan proactive action(s), including maintenance and possibly avoid incidents, rather than requiring costly unplanned maintenance or clean-ups—in case of severe events. Additionally, these probabilities can be generated over more than one time horizon window, providing users the ability to see the chances of an exceedance over, for example, 7 days, 30 days, 90 days, 180 days, or even 365 days. Finally, by providing an easy, at a glance interface, these findings are spotlighted, and can be quickly triaged by plant management and handled at the time of their choosing. 
       FIG. 8  depicts one embodiment of the flowchart of the DEP system. The DEP system includes: (1) a data acquisition module that extracts input data from compatible data sources and loads the extracted data into the system; (2) a threshold input module where a user, or their agents or employee, enters applicable variable thresholds for the system to perform analysis on; (3) an analysis platform that obtains a dynamic exceedance probability values for a variable given the data and threshold provided above; and (4) a display on which the dynamic exceedance probabilities for a variable over different time horizon windows are presented. 
     For the data acquisition module, the DEP is integrated with an existing DRA system. As mentioned in the parent patents, the DRA system provides results of analysis of process variable data from a continuous operation plant. This system connects to an existing on-site data source that provides historical data archives (either a historian or an OPC server). This data is extracted, transformed to a uniform format, and loaded into the DRA database (DRA DB). This is time series data meaning each row corresponds to a timestamp, value, and a specific sensor (known as a variable or a tag). For instance, the data may indicate that temperature of the furnace at 1 pm on Jan. 17, 2022 was 234.5° C. By collecting and analyzing this data along with the threshold input (discussed next), the DEP system is able to provide probability estimates of variables exceeding certain thresholds over a given future time horizon. 
     To identify when a variable is likely to cross a threshold, the DEP requires the user or their agent or employee to identify threshold(s) for any variables that need to be analyzed. These threshold(s) may have several attributes. These attributes may include location (high end or low end), threat level(s) (level 1, level 2, level 3, etc.; higher levels typically indicate more severity), and limit value(s). For instance, the user may want to know the probability of a furnace temperature exceeding 300° C. which is its level 3 high-end threshold. These thresholds and their levels are typically well understood by the users, and correspond closely to critical safety, quality, and equipment integrity related limits. For example, a level 3 exceedance may lead to an automatic shutdown in the system. Another example might be to set up some critical extreme limits that may go beyond currently used limits, where any probability of greater than 10% (example) may not be tolerable and may lead to a broader set of measures to be taken. Once the thresholds are identified, the DEP system can automatically import them from a spreadsheet provided by the user, or they can be input individually directly into the system. 
     Once the data to be acquired and threshold(s) to monitor have been identified, The DEP system uses an algorithm based on Bayesian inference that analyses both the historical and the current data. As outlined above, the Bayesian inference model typically has 3 components: the prior, the likelihood, and the posterior. The prior and likelihood are estimated by parameterizing a model based on an ensemble of statistical distributions using the long-term history of process variable and its behavior with respect to the configured threshold. The long-term history can be any amount of time. For example, it may be from 30 days to 3 years. Finally, the posterior probability (at time T) of crossing threshold in the next time horizon window is obtained by combining the prior and likelihood. 
     One such method to obtain the posterior probability is to use a conjugate analysis. For example, given the likelihood p(y|θ), if the prior p(θ) results in a posterior y(θ|y) that has the same form as p(θ), then p(θ) is referred as a conjugate prior. For example, given a Binomial(n,k|θ) likelihood, and a Beta(a,b) prior on θ, where θ is the exceedance probability of crossing the configured threshold, a and b are prior hyperparameters, and n and k are likelihood parameters, the posterior distribution of θ will be Beta(a+k,b+n−k). Depending on the expert judgement, the prior can be chosen to be informed or uninformed. A Beta(1,1) prior would be considered an uninformed prior. An informed prior can be obtained by parameterizing a model based on general distribution of the process variable using the long-term history. The likelihood parameters n and k are obtained by modeling the distance of the process variable value with the respect to the configured threshold using the long-term history. Once the values for a, b, n, and k are available, the posterior probability is obtained. 
     A new system and method that calculates posterior probability in two stages to first create an informed prior followed by using this informed prior to calculate the final posterior probability is described herein. In stage 1, a first posterior probability is calculated using a time-based likelihood method. The posterior distribution obtained in stage 1 then serves as an informed prior distribution for stage 2. In stage 2, the posterior probability is calculated using an event-based likelihood method. The difference between time-based and event-based likelihoods is described below. 
     When using a time-based likelihood method, like in stage 1 of the system described herein, each instant in the long-term history is evaluated to see if there is a value in the next time horizon window that exceeds the threshold. If the outcome is a success, the system increments both n and k by 1. If the outcome is a failure, the system increments n by 1 but do not increment k. This evaluation is performed for each instant in the long-term history to obtain the total values of n and k, which are then used to calculate a first posterior distribution. 
     When using an event-based likelihood method, like in stage 2 of the system described herein, the threshold may define a reference band. For example, the band may be below/above a certain value, or between two values. These values determine the start and end times of events in the long-term history. In certain embodiments, the threshold value(s) may be designated by the user or their employee or agent and uploaded to the system server. In other embodiments, the reference band is independent of the threshold(s) designated by the user. In such embodiments, the reference band may be part of the algorithm. Regardless, the reference band determines the start and end times of events in the long-term history. The reference band can be set to 75 th  percentile and 25 th  percentile (or 80 th  percentile and 20 th  percentile, etc.) obtained using the long-term history values. The events in the long-term history are calculated next. An event starts when the variable value goes outside of the reference band and ends when it is within the reference band. Next, for each event in the long-term history, the system evaluates if there is a value in the next time horizon window that exceeds the threshold (user specified). If the outcome is a success, the system increments both n and k by 1. If the outcome is a failure, the system increments n by 1 but do not increment k. This evaluation is performed by the system for each event in the long-term history to obtain the total values of n and k, which are then used to calculate the posterior distribution. The posterior distribution obtained in stage 2 serves as the final posterior distribution. 
     As new data becomes available periodically (every few seconds, minutes, hourly, daily, weekly, monthly, continuously), the probability values are evaluated and revised by the DEP system. 
     Regardless, it is understood that that most continuous processing facilities go through downtimes, typically known as shutdowns, which can be planned or unplanned. During these periods, the plants might perform troubleshooting, or other maintenance tasks, which may generate data that is not useful for the DEP analysis. The DRA system allows administrators to input shutdown conditions, which allows the system to automatically determine if a plant is in shutdown during that time. Hence, the DEP system is configured to automatically excludes these shutdown periods from the analysis. 
     Finally, the DEP visualization is integrated into the DRA frontend through the “Operating Fitness” module. This visualization part has advanced filtering capabilities and shows variation of dynamic exceedance probability values over time in a user friendly way. This allows the user to quickly examine any variables with a high probability of exceeding their thresholds within a user-designated time period (e.g., the next 30 days, 90 days and so on). Additionally, since this is integrated with a DRA system, these probabilities can be sent to users in form of easy-to-read pdf reports. 
       FIGS. 9A and 9B  show how the visualization part is configured to depict probability values over time in a user friendly way.  FIG. 9A  shows a pressure variable over a 7-day period, along with a previously designated low threshold of 5 psia.  FIG. 9B  shows the dynamic exceedance probability values over the following 30 days, obtained from DEP system, for the same date range. As one can see, although lately the pressure is fluctuating and is even going up sometimes—away from the low threshold—the probability of crossing the low threshold is still increasing based on historical performances. Such a hidden insight can be useful to the mangers in making proactive decisions. As can be seen, the DEP system computes the probability estimates automatically and brings attention to variables which are exhibiting high values. Specifically, the DEP visualization module allows the user to view such trends over long time periods such as 60 days, 180 days, 1 year, 2 years, all data, etc. Optionally, it can also display any anomalies detected by the DRA system. 
     In summary, the components of a DEP system work in concert to automatically process a large number (often 1000 or more) variables on a scheduled basis and alert DRA system users to the occurrence of escalating probabilities of exceeding their important thresholds. In doing so, the users can be aware of not only issues that may occur later, but also be informed of how quickly a given variable may reach a critical value (e.g. a product pressure which is dipping, and once it reaches 5 psia, the final product will have major quality problems). 
     The methods and processes described in the disclosure of the invention can be embodied as code and/or data, which can be stored in the computer-readable storage medium as described above. When a computer system reads and executes the code and/or data stored on the computer-readable storage medium, the computer system performs the methods and processes embodied as data structures and code and stored within the computer-readable storage medium. 
     While the invention is described in conjunction with specific embodiments, many alternatives, modifications, permutations and variations will become apparent to those skilled in the art in light of the foregoing description. Accordingly, it is intended that the invention embraces all such alternatives, modifications, permutations and variations as falling within the scope of the claims below.