Method and system for determining an end-of-life parameter of a plurality of devices

Abstract

Disclosed is a method for determining an end-of-life parameter of a plurality of devices, the method comprising: obtaining, by a processor, current operation data of the plurality of devices and historical failure data associated with the plurality of devices; estimating, by the processor, a failure probability distribution of the plurality of devices based on the current operation data and the historical failure data; defining or obtaining a prediction horizon; predicting, by the processor, using the failure probability distribution and a plurality of candidate end-of-life parameters, a number of failures within the prediction horizon based on each of the candidate end-of-life parameters; defining or obtaining an observation window; calculating a number of operating devices within the observation window; calculating a normalized average number of failures across a defined base period within the observation window, based on the historical failure data and the number of operating devices within the observation window; comparing the normalized average number of failures with the predicted number of failures for the plurality of candidate end-of-life parameters; and determining the end-of-life parameter based on the comparison.

Description

METHOD AND SYSTEM FOR DETERMINING AN END-OF-LIFE PARAMETER OF A PLURALITY OF DEVICES TECHNICAL FIELD

[0001] Various aspects of this disclosure relate to a method and system for determining an end-of-life parameter of a plurality of devices, which may include a fleet of similar devices.BACKGROUND

[0002] The following discussion of the background art is intended to facilitate an understanding of the present disclosure only. It should be appreciated that the discussion is not an acknowledgement or admission that any of the material referred to was published, known or is part of the common general knowledge of the person skilled in the art in any jurisdiction as of the priority date of the disclosure.

[0003] The accurate projection of end-of-life (EOL) for devices is important in asset management across various engineering industries. A precise EOL projection enhances asset utilization, maintains reliability, and mitigates unexpected failures as well as downtime. Concurrently, the application of mitigation actions is crucial for improving the reliability of the targeting devices. The optimization of when and how these mitigation actions should be executed forms a primary objective.

[0004] Statistical models have traditionally been employed for estimating survival functions or reliability functions of devices, which indicate the survival probability or reliability against operational time. Recent advancements in sensor technology have enabled the collection of condition data from these assets. However, due to practical constraints in many engineering sectors, regularly acquiring condition data from sensors installed on devices remains challenging. As a result, statistical modeling of reliability based on the life-time data, which consists of both failure data and survival data, continues to be the most effective approach for fleet- level analysis and decision-making.

[0005] There exists a need to improve on decision making by leveraging current statistical modeling to better predict or determine end-of-life parameters of a fleet of devices, inter alia, for improved maintenance of the fleet of devices.SUMMARY

[0006] The present disclosure was conceptualized to provide a technical solution for projecting (estimating or predicting) the end-of-life (EOL) parameter of a plurality of devices, such as a fleet of devices, using statistical models.

[0007] The statistical model may be constructed using a population of devices operating currently (or current operating devices) and historical failure records, i.e., the life-time data of a plurality (fleet) of devices, and may be used to predict the number of failures.

[0008] The present disclosure also offers an alternative method to improve the EOL parameter projection under the circumstance that historical failure records arc relatively sufficient, i.e., failures densely recorded across operational time.

[0009] The present disclosure also relates to a method for projecting the end-of-life (EOL) of a fleet of devices, and a method for improving the EOL when sufficient historical failure records are available to ensure the optimal utilization of the devices.

[0010] According to an aspect of the present disclosure there is provided a method for determining an end-of-life parameter of a plurality of devices, the method comprising: obtaining, by a processor, current operation data of the plurality' of devices and historical failure data associated with the plurality of devices; estimating, by the processor, a failure probability distribution of the plurality of devices based on the current operation data and the historical failure data; defining or obtaining a prediction horizon; predicting, by the processor, using the failure probability distribution and a plurality of candidate end-of-life parameters, a number of failures within the prediction horizon based on each of the plurality of candidate end-of-life parameters; defining or obtaining an observation window; calculating, by tire processor, a number of operating devices within the observation window; calculating, by the processor, a normalized average number of failures across a defined base period within the observation window, based on the historical failure data and the number of operating devices within the observation window; comparing, by the processor, the normalized average number of failures with the predicted number of failures for each of the plurality of candidate end-of-life parameters; and determining, by the processor, the end-of-life parameter based on the comparison.

[0011] In some embodiments, the current operation data comprises a number of devices of the plurality of devices currently in operation, and the historical failure data comprises a number of failed devices of the plurality of devices.

[0012] In some embodiments, defining the prediction horizon includes specifying a current operating year corresponding to the number of devices currently in operation, and a predefined number of future years h following the current operating year.

[0013] In some embodiments, predicting the number of failures within the prediction horizon includes predicting an average yearly number of failures based on a conditional probability representing a probability of failure happening to a number of devices operating at an age t within the predefined number of future years h.

[0014] In some embodiments, defining the observation window further comprises defining a length of calendar years, and normalized average number of failures across a defined base period is a normalized average yearly number of failures.

[0015] In some embodiments, calculating the normalized average yearly number of failures include calculating a proportion of failure in each calendar year until the end of the length of calendar years.

[0016] In some embodiments, calculating the proportion of failure for calculating the normalized average yearly number of failures comprises collecting historical total number of failures in each calendar year and total number of operating devices in each calendar year within the observation window.

[0017] In some embodiments, determining the end-of-life parameter further comprises obtaining a weighted sum average of the normalized average number of failures and the predicted number of failures within the prediction horizon.

[0018] In some embodiments, the failure probability distribution is a cumulative distribution function.

[0019] In some embodiments, the cumulative distribution function comprises one of the following baseline models: an exponential distribution, a two-parameter Weibull distribution.

[0020] According to another aspect of the present disclosure there is provided a system for determining an end-of-life parameter of a plurality of devices, the system comprising at least one sensor, the at least one sensor configured to obtain current operation data of the plurality of devices and historical failure data associated with the plurality of devices; a processor, the processor configured to: estimate a failure probability distribution of the plurality of devices based on the current operation data and the historical failure data; define or obtain a prediction horizon; predict, using the failure probability distribution and a plurality of candidate end-of-life parameters, a number of failures within the prediction horizon based on each of the plurality of candidate end-of-life parameters; define or obtain an observation window; calculate anumber of operating devices within the observation window; calculate a normalized average number of failures across a defined base period within the observation window, based on the historical failure data and the number of operating devices within the observation window; compare the normalized average number of failures with the predicted number of failures for each of the plurality of candidate end-of-life parameters; and determine the end-of-life parameter based on the comparison.

[0021] In some embodiments, the current operation data comprises a number of devices of the plurality of devices currently in operation, and the historical failure data comprises a number of failed devices of the plurality of devices.

[0022] In some embodiments, the processor is configured to define the prediction horizon by specifying a current operating year corresponding to the number of devices currently in operation, and a predefined number of future years h following the current operating year.

[0023] In some embodiments, the processor is further configured to predict an average yearly number of failures based on a conditional probability representing a probability of failure happening to a number of devices operating at an age t within the predefined number of future years h.

[0024] In some embodiments, the processor is configured to define the observation window based on defining a length of calendar years, and normalized average number of failures across a defined base period is a normalized average yearly number of failures.

[0025] In some embodiments, the processor is configured to calculate the normalized average yearly number of failures based on a calculation of a proportion of failure in each calendar year until the end of the length of calendar years.

[0026] In some embodiments, the processor is configured to collect historical total number of failures in each calendar year and total number of operating devices in each calendar year within the observation window.

[0027] In some embodiments, the processor is configured to determine the end-of-life parameter based on obtaining a weighted sum average of the normalized average number of failures and the predicted number of failures within the prediction horizon.

[0028] In some embodiments, the failure probability distribution is a cumulative distribution function.

[0029] In some embodiments, the cumulative distribution function comprises one of the following baseline models: an exponential distribution, a two-parameter Weibull distribution.

[0030] According to another aspect of the present disclosure there is provided a computer program element comprising program instructions, which, when executed by one or more processors, cause the one or more processors to perform any of the aforementioned methods.

[0031] According to another aspect of the present disclosure there is provided a non-transitory computer-readable medium comprising program instructions, which, when executed by one or more processors, cause the one or more processors to perform any of the aforementioned methods.

[0032] According to another aspect of the present disclosure there is provided a reliability monitoring system, the system arranged to receive the end-of-life parameter from any of the aforementioned systems.BRIEF DESCRIPTION OF THE DRAWINGS

[0033] The disclosure will be better understood with reference to the detailed description when considered in conjunction with the non-limiting examples and the accompanying drawings, in which:- FIG. l is a flow chart of a method for determining an end-of-life parameter of a plurality of devices.- FIG. 2A and FIG. 2B are block diagrams of a server apparatus and system for determining an end-of-life parameter of a plurality of devices.- FIG. 3 illustrates examples of life-time data of a fleet or group of similar' devices, including a current age distribution with number of currently operating devices and the age distribution of a number of failed devices as historical records.- FIG. 4 illustrates a flow chart of a method for projecting the end-of-life (EOL) parameter of a fleet of devices based on the life-time data of the targeting devices, employing a statistical model with a cumulative distribution function (CDF) for predicting the number of failures with different candidate EOL parameters. It also illustrates the concept of normalized average yearly number of failures based on past observation.- FIG. 5 illustrates an example or instance of a cumulative distribution function (CDF) estimated, denoted as F(t), using life-time data with the current population of operating devices and historical failure records. This CDF represents the cumulative probability of failures against ages as a non-limiting example.- FIG. 6 illustrates the historical number of failure records, historical number of operating devices or approximated historical number of operating devices using current age distribution of operating devices, and the yearly proportion of failure by each calendar year. The yearly proportion of failure is calculated with the yearly number of failures and the actual or approximated number of operating devices in the past years.- FIG. 7 displays the predicted average yearly number of failures within the prediction horizon given different candidate EOL parameters from 1 to 25 as examples. Additionally, it showcases the normalized average yearly number of failures calculated based on the average yearly proportion of failure within the given observation window and the current number of operating devices.DETAILED DESCRIPTION

[0034] The following detailed description refers to the accompanying drawings that show, by way of illustration, specific details, and embodiments in which the disclosure may be practiced. These embodiments are described in sufficient detail to enable those skilled in the art to practice the disclosure. Other embodiments may be utilized, and structural and logical changes may be made without departing from the scope of the disclosure. The various embodiments are not necessarily mutually exclusive, as some embodiments can be combined with one or more other embodiments to form new embodiments.

[0035] Features that are described in the context of an embodiment may correspondingly be applicable to the same or similar features in the other embodiments. Features that arc described in the context of an embodiment may correspondingly be applicable to the other embodiments, even if not explicitly described in these other embodiments. Furthermore, additions and / or combinations and / or alternatives as described for a feature in the context of an embodiment may correspondingly be applicable to the same or similar feature in the other embodiments.

[0036] In the context of various embodiments, the articles “a”, “an” and “the” as used with regard to a feature or element include a reference to one or more of the features or elements. As used herein, the term “and / or” includes any and all combinations of one or more of the associated listed items.

[0037] While such terms as "first," "second," etc., may be used to describe various elements, such elements must not be limited to the above terms. The above terms are used only to distinguish one element from another, and do not define corresponding elements, for example,an order and / or significance of the elements. Without departing from the scope of rights of the specification, a first element may be referred to as a second element, and similarly, the second element may be referred to as the first element.

[0038] As used herein, the term “data” may be understood to include information in any suitable analog or digital form, for example, provided as a file, a portion of a file, a set of files, a signal or stream, a portion of a signal or stream, a set of signals or streams, and the like. The term data, however, is not limited to the aforementioned examples and may take various forms and represent any information as understood in the art.

[0039] As used herein, the term “processor” refers to a circuit, including analog circuits, digital circuits, or hybrid circuits, or their constituent components. Any other kind of implementation of the respective functions which will be described in more detail below may also be understood as a “circuit” in accordance with an alternative embodiment. A digital circuit may be understood as any kind of a logic implementing entity, which may be special purpose circuitry or a processor executing software stored in a memory, or a firmware.

[0040] As used herein, the term “module” refers to, forms part of, or includes an Application Specific Integrated Circuit (ASIC); an electronic circuit; a combinational logic circuit; a field programmable gate array (FPGA); a processor (shared, dedicated, or group) that executes code; other suitable hardware components that provide the described functionality; or a combination of some or all of the above, such as in a system-on-chip. The term module may include memory (shared, dedicated, or group) that stores code executed by the processor. A single module or a combination of modules may be regarded as a device. A processor may include one or more modules. For example, multiple modules described in this disclosure may form a processor.

[0041] As used herein, the term “associate”, “associated”, and “associating” indicate a defined relationship (or cross-reference) between two items.

[0042] As used herein, “memory” may be understood as a non-transitory computer-readable medium in which data or information can be stored for retrieval. References to “memory” included herein may thus be understood as referring to volatile or non-volatile memory, including random access memory (“RAM”), read-only memory (“ROM”), flash memory, solid-state storage, magnetic tape, hard disk drive, optical drive, etc., or any combination thereof. Furthermore, it is appreciated that registers, shift registers, processor registers, data buffers, etc., are also embraced herein by the term memory. It is appreciated that a single component referred to as “memory” or “a memory” may be composed of more than one different type of memory, and thus may refer to a collective component including one or moretypes of memory. It is readily understood that any single memory component may be separated into multiple collectively equivalent memory components, and vice versa. Furthermore, while memory may be depicted as separate from one or more other components (such as in the drawings), it is understood that memory may be integrated within another component, such as on a common integrated chip.

[0043] As used herein, the term “device” may be understood to refer to any apparatus, equipment, or component, whether standalone or integrated, that performs a specific function or set of functions. This includes, but is not limited to, mechanical, electrical, electronic, optical, or electromechanical systems, subsystems, and assemblies. A device may comprise one or more components, modules, or units that are designed to interact with each other to achieve a particular purpose. The term "fleet of devices" refers to a collection or group of multiple devices that are managed, operated, or monitored collectively as a unit. For example, operation data of the fleet can be collected. The devices within the fleet may be of the same type or a combination of different types and can be geographically distributed or co-located. A fleet of devices may be interconnected, communicate with a central management system, or operate autonomously while being grouped based on shared characteristics, purpose, ownership, or operational goals. A fleet of devices may share a common characteristic, such as operational lifespan before failure. In obtaining data from a fleet of devices for the purpose of the present disclosure to generate various statistical models, a sufficient number of devices, i.e. fleet size (population size) may be required. The fleet size may be determined according to different operation conditions and / or device type. For example, a fleet of power transformers at a common voltage level of 22 kilo-volts (kV) may have a fleet size of 20,000, or in a range of 100 to 10,000 assuming the devices arc from the same manufacturer.

[0044] As used herein, the term “sensor” includes any device, apparatus, system, or software component that detects, measures, monitors, or records physical, environmental, or operational conditions, phenomena, or properties, and generates output indicative of those conditions. The output may be in the form of electrical, mechanical, optical, or other signals, and may be processed by hardware or software systems for further analysis or control purposes . A sensor may include both hardware components (e.g., transducers, detectors, circuits) and software components (e.g., algorithms, data processing modules) that together enable the detection, measurement, and interpretation of the desired parameters. Some non-limiting examples of sensors include voltage sensors, current sensors, power meters, frequency sensors,temperature sensors, fault detection sensors, power quality sensors, energy metering sensors, insulation resistance sensors, load sensors, surge protection sensors, capacitive sensors.

[0045] As used herein, the term “configured to” broadly refers to the design, arrangement, or adaptation of a system, device, component, or module to perform a specific function or achieve a particular outcome. The term includes both hardware and software implementations wherein in a hardware implementation, the physical components are arranged, programmed, or structured to carry out the intended function(s), and in the context of programming and software, a device is operable under executable instructions (e.g., software, firmware) to perform the specified function(s) when executed by one or more processors. The resultant configuration allows the system or component to perform the stated function, either inherently or after suitable programming or activation, without requiring substantial modifications to its structure or operational logic.

[0046] According to various embodiments, a circuit may include analog circuits or components, digital circuits or components, or hybrid circuits or components. Any other kind of implementation of the respective functions which will be described in more detail below may also be understood as a "circuit" in accordance with an alternative embodiment. A digital circuit may be understood as any kind of a logic implementing entity, which may be special purpose circuitry or a processor executing software stored in a memory, firmware, or any combination thereof. Thus, in various embodiments, a "circuit" may be a digital circuit, e.g. a hard-wired logic circuit or a programmable logic circuit such as a programmable processor, e.g. a microprocessor (e.g. a Complex Instruction Set Computer (CISC) processor or a Reduced Instruction Set Computer (RISC) processor). A "circuit" may also include a processor executing software, e.g. any kind of computer program, e.g. a computer program using a virtual machine code such as e.g. Java.

[0047] A method for projecting or determining the end-of-life (EOL) parameter of a fleet of devices based on life-time data is provided. The approach relies on statistical modeling based on the age distribution with the current number of operating devices at different ages and the age distribution with historical number of failure records at different ages.

[0048] The present disclosure may include using an estimated cumulative distribution function to predict number of failures with the establishment of a prediction horizon, and introducing an observation window for calculating the normalized average yearly number of failures. By comparing the normalized average yearly number of failures based on past observation with the predicted number of failures given different candidate EOL parameters,the method identifies the predicted or determined EOL parameter that can help maintain reliability of the current operating devices during a prediction horizon to the level equivalent to the historical performance within an observation window. This innovative framework enhances asset management in engineering industries by improving EOL parameter projection for targeting devices to ensure optimal utilization of the devices while preventing unexpected failures.

[0049] According to an aspect of the present disclosure, there is provided a method for determining an end-of-life parameter of a fleet of devices. Referring to FIG. 1, a method 100 may be implemented by a processor. The processor may be configured to implement the method comprising the steps of:

[0050] Step S 101 : obtaining, by a processor, current operation data of a plurality of devices and historical failure data associated with the plurality of devices;

[0051] Step S102: estimating, by the processor, a failure probability distribution of the plurality of devices based on the current operation data and the historical failure data;

[0052] Step S 103: defining or obtaining a prediction horizon;

[0053] Step S 104: predicting, by the processor, using the failure probability distribution and a plurality of candidate end-of-life parameters, a number of failures within the defined prediction horizon based on each of the candidate end-of-life parameters;

[0054] Step SI 05: defining or obtaining an observation window;

[0055] Step S106: calculating, by the processor, a number of operating devices within the observation window;

[0056] Step S107: calculating, by the processor, a normalized average number of failures across a defined base period within the observation window, based on the historical failure data and the number of operating devices within the observation window;

[0057] Step S 108: comparing, by the processor, the normalized average number of failures with the predicted number of failures for each of the plurality of candidate end-of-life parameters; and

[0058] Step S109: determining, by the processor, the end-of-life parameter based on the comparison.

[0059] FIG. 2A illustrates a server apparatus for receiving sensor data and processing the sensor data according to the method 100.

[0060] The server apparatus may comprise a processor and a memory, the processor is capable of being configured to execute instructions stored in the memory to receive a requestfor resources. In the embodiment illustrated in FIG. 2A, the server apparatus may be a communications server apparatus. The communications server apparatus may be in the form of a server computer 200, the server computer 200 may be a single server as illustrated schematically in FIG. 2A, or have the functionality performed distributed across multiple server components.

[0061] In some embodiments, the server computer 200 includes a communication interface 202 (e.g. configured to receive or obtain sensor data, historical data of one or more components, etc.). The communication interface 202 may include a transmitter module and / or a receiver module allowing the server computer 200 to communicate over a communications network. The communication interface 202 may include one or more user interfaces configured to provide users with user control and may include, for example, one or more computing peripheral devices such as display monitors, computer keyboards and the like.

[0062] The server computer 200 may further include a processor in the form of processing unit 204 and a memory 206. The memory 206 may be used by the processing unit 204 to store, for example, data to be processed, such as the current operation data of a plurality of devices and historical failure data associated with the plurality of devices. It is contemplated that the term “operation data” may include, but is not limited to, operation status. In some embodiments, such operation status may include an “normal operation” status and an “failed” status. In some embodiments, the “on” status and “off’ status may be represented as binary data. For example, a normal operation status may be represented by a binary 1, and failed status may be represented by a binary 0.

[0063] As shown in FIG. 2B, the processing unit 204 may configured to receive, from one or more sensors 210 or databases 230, current operation data 211 of the plurality of devices and historical failure data 212 of failed devices, within a time period. The current operation data 211 and historical failure data 212 may be of a structured or unstructured data format.

[0064] The server computer 200 and one or more sensors 210, databases 230 may be connected via a network 280 to form a system 250 for determining an end-of-life parameter of a fleet of devices. In addition, the system 250 may comprise one or more reliability monitoring system 260, the reliability monitoring system 260 configured to receive the determined parameter for further processing. The network 280 may be an internet or intranet network.

[0065] Upon receipt of the data from the one or more sensors 210, the processing unit 204 may be configured to determine or project the end-of-life parameter 213 of a fleet of devices.

[0066] In some embodiments, the end-of-life parameter may be used for the determination of replacement of one or more of the devices within the fleet of devices. In some embodiments, the end-of-life parameter may be utilized for real-time monitoring to improve the reliability of the fleet of devices by making timely changes.

[0067] In some embodiments, the determination of the end-of-life parameter 213 is based on a statistical model, the statistical model estimated using the current operation data of a plurality of devices and historical failure data associated with the plurality of devices.

[0068] FIG. 3 illustrates the current operation data of the fleet of devices, denoted as 301, and the historical failure data denoted as 302. The current operation data 301 may also be regarded as an age profile of the fleet of devices. The age is from age 1 to 39. The age profile 301 indicates that most current operating units are in the age of between 19 to 21. The failed unit profile 302 indicates that most failed units are in the age of 33 and 34. Such a result may be due to proactive actions to replace old equipment for prevention of an increasing number of unexpected failures for older equipment, and / or may be a reflection of from the number of operating units, with much fewer equipment operating above 35 years old. It is contemplated that one or more statistical measures, including, but not limited to, average, median, and / or mode, may be derived from the profiles. The data forms the foundation for the end-of-life parameter determination method for the targeted components or equipment, as illustrated in FIG. 4.

[0069] FIG. 4 is a flow chart of a method for projecting the End-of-Life (EOL) parameter 400 of a fleet of devices based on the life-time data of a target group or fleet of devices.

[0070] In step S401, the data for 301 and 302 may be obtained, with no prerequisite for any condition data or complex information to facilitate subsequent steps. The current operation data 301 may comprise a number of devices currently in operation, of the plurality of devices, and the historical failure data 302 may comprise a number of failed devices, of the plurality of devices. In some embodiments, the data may be pre-processed into an acceptable form to be processed by the processor. In the present disclosure, an assumption is that the one or more components or equipment is either operating, or it has failed (only one time in its life), and the one or more components or equipment can only experience at most one repair throughout its lifetime. As such, each equipment has only one failure information if the equipment has failed, or there is no failure information if the equipment is still operating.

[0071] In step S402, a cumulative distribution function (CDF), denoted as F(t), is estimatedbased on the collected data 301 and 302. To estimate the CDF, a baseline model can be selected. In some embodiments, the baseline model may be an exponential distribution, a two-parameter Weibull distribution, or similar options. In general, a baseline model may be selected from continuous probability distributions used in reliability analysis, survival analysis, and various fields of engineering and statistics. For example, a log-normal distribution, three-parameter Weibull model, Gamma distribution, etc., may be contemplated. In some embodiments, mixture distributions such as a mixture of exponentials which combines multiple exponential distributions to model heterogeneous populations, or mixture of Weibull distributions, may be contemplated. Maximum likelihood estimation (MLE) is employed for estimating the parameters of these underlying distributions.

[0072] An example of the estimated F(t) based on a two-parameter Weibull distribution is presented in FIG. 5. The estimated CDF model F(t) characterizes the failure probability of the fleet of devices. It is appreciable that the estimated CDF model describes the time distribution to the first failure occurrence of the equipment (i.e., age).

[0073] In step S403, a prediction horizon h is determined before predicting the number of failures. Defining the prediction horizon may include specifying a current operating year yo corresponding to the total number of devices presently in operation, and a predefined number of future years following the current operating year. In other words, the prediction horizon h begins at the current calendar year (denoted as yo corresponding to a current number of operating devices (see data 301).

[0074] In step S404, a plurality of candidate end-of-hfe (EOL) parameters are utilized for predicting the number of failures denoted as Nyo(ft, EOL') within the upcoming h years, given by the prediction horizon. In some embodiments, the prediction of average yearly number of failures is mathematically expressed and calculated using Equation (1) as follows:ft, EOL)(1) wherein Nt,yo is the number of operating devices at a particular age t with reference to profile 301, and P(t, h, EOL) is the conditional probability, representing the probability of failure happening to operating devices currently at age t within the upcoming ft years. In summary, predicting the number of failures within the defined prediction horizon includes predicting an average yearly number of failures based on a conditional probability representing the probability of failure happening to a number of devices operating at an age t within the predefined number of future years ft.

[0075] The calculation of P(t, h, EOL) may be computed based on F(t) and Equation (2), mathematically expressed as follows:Wherein the mathematical function max(t, EOL) ensures that devices aged above the given EOL in the current operating devices (reference age profile 301) are considered as having reached EOL and no failure is predicted from these devices, and the mathematical function min(t + h, max(t, EOL)) ensures that devices aged above the EOL after h years are replaced early when they have reached EOL. The principle condition is that when a unit exceeds the given EOL, it is replaced.

[0076] In step S405, and with reference to FIG. 6, an observation window 621 may be determined, with length of w calendar years, prior to computing the normalized average yearly number of failures 701 in FIG. 7 from the historical data. Defining the observation window 621 may further comprise defining a length of calendar years, and normalized average number of failures across a defined base period is a normalized average yearly number of failures.

[0077] In step S406, historical data may be presented along the calendar year as shown in FIG. 6. The number of failures in each calendar year based on the failure records 611 shows the number of failures in each of the corresponding calendar years. The number of operating devices in each calendar year 622 records the total number of operating devices by the corresponding calendar year, which can be recorded with actual values if recorded by each calendar year or approximated from the age distribution of the current number of operating devices 301. The proportion of failure py623 within each calendar year y can be calculated using the Equation (3) mathematically expressed as follows:

[0078] Tn Equation (3), y represents the calendar year within an observation window 621, N’yis the number of failures that occurred within calendar year y, and Nyis the number of operating devices by calendar year y as shown in graph 622. Subsequently, the average proportion of failure 631 within the observation window 621 is computed using Equation (4), which is mathematically expressed as follows:

[0079] In step S406, the normalized average yearly number of failures can be calculated using Equation (5), which is mathematically expressed as follows:

[0080] where Nyo = t t,yo is the total number of operating devices within the current calendar year yo. This calculation of Equation (5) provides a reference of the expected yearly failures according to the historical performance observed within the observation window 621. By comparing this reference number Nyo with the predicted average yearly number of failures within prediction horizon Nyo(h, EOL) based on different candidate EOL parameters, the projected or determined EOL 702 (see FIG. 7) can be selected as:Projected

[0081] In some embodiments, projected EOL 702 is determined when it closely matches the normalized average yearly number of failures 701 within the observation window 621. The selected choice ensures that the projected EOL maintains a similar level of reliability or failure probability among the current operating devices during the prediction horizon.

[0082] In the steps S405 and S406, an average proportion of failure, denoted as Pyo(vv) within the observation window 621 using the proportion of failure pywithin each calendar year y was computed. This considers the proportion of failure in total. However, the number of predicted failures is related to the age distribution of operating devices. For example, when the function F(t) shows an accelerated increase of cumulated failure probability, the targeted fleet of devices may be exposed to a relatively higher probability of failure when the fleet of devices are getting older. In such instances, the number of failures happening to a number of 30-year-old devices and a number of brand-new devices in the upcoming years may be different. Therefore, it may be important to understand the historical proportion of failure by ages. The challenge is that failure records can be rare and get even more limited by ages when dealing with highly reliable devices. In these cases, the proportion of failure pyin total provided in the above-mentioned steps S405 and S406 may be more insightful and reliable to represent the historical performance, as in the case with limited data the proportion of failures by different ages will be dominated by 0%.

[0083] However, when the failure records are adequate at different ages, an alternative approach for calculating the normalized average yearly number of failures 701 may be contemplated.

[0084] In step S406, historical numbers may be generated along the calendar years as shown in FIG. 6. The number of failures in each calendar year as shown in graph 611 records the number of failures within the corresponding calendar year. The number of operating devices in each calendar year as graph 622 records the total number of operating devices within the corresponding calendar' year'. In addition, the total number of operating devices may be grouped or divided into numbers by ages. The proportion of failure 623 happening to devices at age of t within the calendar year y, denoted as pt,y, (see for example label P 1,2005 indicating a proportion of failure at a particular calendar year 2005 of an arbitrary age t) can be calculated using Equation (7), mathematically expressed as follows:Wherein N't,yis the number of failures that occurred at age of t within calendar year y (see for example label N't, 2005 indicating the total number of failures at the age of t at the particular calendar year 2005), and Nt,y is the total number of operating devices at the age of t within calendar year y from a base reference calendar year yo (see for example label Nt,2oos indicating the total number of operating devices at the age of t at the particular calendar' year' 2005). Subsequently, the average proportion of failure 631 at age of t within the observation window 621 is computed using the equation (8), mathematically expressed as follows:

[0085] This approximates the average level of failure probability P at age of t over the past w years within the observation window 621. Then, the normalized average yearly number of failures 701, as shown in FIG. 7, can be calculated with equation (9), mathematically expressed as follows:

[0086] When the failure records are adequate at different ages, the normalized average yearly number of failures 701 introduced in equation (9) can better represent the historical performance on reliability of the targeting devices.

[0087] In various instances, there may comprise a reliability monitoring system, such as the reliability monitoring system 260, for interface with the system 250. The reliability monitoring system may be configured to enhance the operational efficiency and lifecycle management of the fleet of devices. The system 260 may leverage predictive analytics to optimize device utilization and maintenance.

[0088] In some embodiments, the reliability monitoring system may be configured to receive end-of-life (EOL) parameters of the plurality (fleet) of devices in the fleet. These EOL parameters are generated by an integrated prediction system to estimate the remaining useful life (RUL) of individual devices.

[0089] In some embodiments, the reliability monitoring system may include an optimizer designed to manage the fleet of devices based on the received EOL parameters. The optimizer may be capable of: prioritizing maintenance or replacement schedules, allocating resources efficiently to maximize fleet uptime, and adjusting operational parameters of devices to extend their service life where possible.

[0090] In some embodiments, the reliability monitoring system may include a dynamic fleet management system. By incorporating real-time or periodic updates from the system 250, the reliability monitoring system 260 may be configured to dynamically adjust management strategies to adapt to changing conditions in the fleet. For instance, high-priority interventions may be triggered for devices nearing critical EOL parameter thresholds. Such high-priority interventions may be in the form of replacements of devices and components; non-critical devices with extended remaining useful life estimates may have deferred maintenance to conserve resources.

[0091] In some embodiments, the reliability monitoring system may be scalable, and may be capable of managing fleets ranging from a few devices to thousands. The reliability monitoring system may also be compatible with a wide range of devices, regardless of their functional domain, making it applicable across industries such as manufacturing, transportation, and energy.

[0092] In some embodiments, the reliability monitoring system may include a data-driven decision-making module. The reliability monitoring system may aggregate data from the prediction system 250 and other sources, for example, historical maintenance logs, operational performance metrics, etc., to enable data-driven decision-making. Advanced visualization tools and dashboards may allow stakeholders to monitor fleet health and make informed decisions.

[0093] The present disclosure provides a statistical based model to determine an end-of-life (EOL) parameter, the EOL parameter utilized for reliability improvement and asset management improvement. By determining the optimal EOL parameter of the fleet of devices, the usage of the devices can be maximized, and the number of unexpected failures with associated costs minimized.

[0094] It is contemplated that the outcome of the present disclosure, i.e. the determined EOL parameter, can be directly used in the daily operation by the engineers from certain industries, e.g., utility industry, where the determined EOL parameter can be further incorporated with their mitigation measure optimization procedures.

[0095] While the disclosure has been particularly shown and described with reference to specific embodiments, it should be understood by those skilled in the art that various changes in form and detail may be made therein without departing from the spirit and scope of the disclosure as defined by the appended claims. The scope of the disclosure is thus indicated by the appended claims and all changes which come within the meaning and range of equivalency of the claims are therefore intended to be embraced.

Claims

CLAIMS1. A method for determining an end-of-life parameter of a plurality of devices, the method comprising:obtaining, by a processor, current operation data of the plurality of devices and historical failure data associated with the plurality of devices;estimating, by the processor, a failure probability distribution of the plurality of devices based on the current operation data and the historical failure data;defining or obtaining a prediction horizon;predicting, by the processor, using the failure probability distribution and a plurality of candidate end-of-life parameters, a number of failures within the prediction horizon based on each of the plurality of candidate end-of-life parameters;defining or obtaining an observation window;calculating, by the processor, a number of operating devices within the observation window;calculating, by the processor, a normalized average number of failures across a defined base period within the observation window, based on the historical failure data and the number of operating devices within the observation window;comparing, by the processor, the normalized average number of failures with the predicted number of failures for each of the plurality of candidate end-of-life parameters; and determining, by the processor, the end-of-life parameter based on the comparison.

2. The method of claim 1, wherein the current operation data comprises a number of devices of the plurality of devices currently in operation, and the historical failure data comprises a number of failed devices of the plurality of devices.

3. The method of claim 2, wherein defining the prediction horizon includes specifying a current operating year corresponding to the number of devices currently in operation, and a predefined number of future years h following the current operating year.

4. The method of claim 3, wherein predicting the number of failures within the prediction horizon includes predicting an average yearly number of failures based on a conditionalprobability representing a probability of failure happening to a number of devices operating at an age t within the predefined number of future years h.

5. The method of any one of the preceding claims, wherein defining the observation window further comprises defining a length of calendar years, and normalized average number of failures across a defined base period is a normalized average yearly number of failures.

6. The method of claim 5, wherein calculating the normalized average yearly number of failures include calculating a proportion of failure in each calendar year until the end of the length of calendar years.

7. The method of claim 6, wherein calculating the proportion of failure for calculating the normalized average yearly number of failures comprises collecting historical total number of failures in each calendar year and total number of operating devices in each calendar year within the observation window.

8. The method of any one of the preceding claims, wherein determining the end-of-life parameter further comprises obtaining a weighted sum average of the normalized average number of failures and the predicted number of failures within the prediction horizon.

9. The method of any one of the preceding claims, wherein the failure probability distribution is a cumulative distribution function.

10. The method of claim 9, wherein the cumulative distribution function comprises one of the following baseline models: an exponential distribution, a two-parameter Weibull distribution.

11. A system for determining an end-of-life parameter of a plurality of devices, the system comprisingat least one sensor, the at least one sensor configured to obtain current operation data of the plurality of devices and historical failure data associated with the plurality of devices;a processor, the processor configured to:estimate a failure probability distribution of the plurality of devices based on the current operation data and the historical failure data;define or obtain a prediction horizon;predict, using the failure probability distribution and a plurality of candidate end-of-life parameters, a number of failures within the prediction horizon based on each of the plurality of candidate end-of-life parameters;define or obtain an observation window;calculate a number of operating devices within the observation window; calculate a normalized average number of failures across a defined base period within the observation window, based on the historical failure data and the number of operating devices within the observation window;compare the normalized average number of failures with the predicted number of failures for each of the plurality of candidate end-of-life parameters; anddetermine the end-of-life parameter based on the comparison.

12. The system of claim 11, wherein the current operation data comprises a number of devices of the plurality of devices currently in operation, and the historical failure data comprises a number of failed devices of the plurality of devices.

13. The system of claim 12, wherein the processor is configured to define the prediction horizon by specifying a current operating year corresponding to the number of devices currently in operation, and a predefined number of future years h following the current operating year.

14. The system of claim 13, wherein the processor is further configured to predict an average yearly number of failures based on a conditional probability representing a probability of failure happening to a number of devices operating at an age / within the predefined number of future years h.

15. The system of any one of claims 11 to 14, wherein the processor is configured to define the observation window based on defining a length of calendar years, and normalized average number of failures across a defined base period is a normalized average yearly number of failures.

16. The system of claim 15, wherein the processor is configured to calculate the normalized average yearly number of failures based on a calculation of a proportion of failure in each calendar year until the end of the length of calendar years.

17. The system of claim 16, wherein the processor is configured to collect historical total number of failures in each calendar year and total number of operating devices in each calendar year' within the observation window.

18. The system of any one of claims 11 to 17, wherein the processor is configured to determine the end-of-life parameter based on obtaining a weighted sum average of the normalized average number of failures and the predicted number of failures within the prediction horizon.

19. The system of any one of claims 11 to 18, wherein the failure probability distribution is a cumulative distribution function.

20. The system of claim 19, wherein the cumulative distribution function comprises one of the following baseline models: an exponential distribution, a two-parameter Weibull distribution.

21. A computer program element comprising program instructions, which, when executed by one or more processors, cause the one or more processors to perform the method of any one of claims 1 to 10.

22. A non-transitory computer-readable medium comprising program instructions, which, when executed by one or more processors, cause the one or more processors to perform the method of any one of claims 1 to 10.

23. A reliability monitoring system, the system arranged to receive the end-of-life parameter from the system of any one of claims 11 to 20.

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