Notice of Pre-AIA or AIA Status
The present application, filed on or after March 16, 2013, is being examined under the first inventor to file provisions of the AIA . In the event the determination of the status of the application as subject to AIA 35 U.S.C. 102 and 103 (or as subject to pre-AIA 35 U.S.C. 102 and 103) is incorrect, any correction of the statutory basis for the rejection will not be considered a new ground of rejection if the prior art relied upon, and the rationale supporting the rejection, would be the same under either status.
DETAILED ACTION
The following NON-FINAL Office Action is in response to application 18/440,256 filed on 02/13/2024. This communication is the first action on the merits.
Status of Claims
Claims 1-20 are currently pending and have been rejected as follows.
IDS
The information disclosure statements filed on 02/13/2024, 09/24/2025 and 08/04/2026 comply with the provisions of 37 CFR 1.97, 1.98 and MPEP § 609 and are considered.
Specification
The following is a quotation of 37 CFR 1.71(a):
The specification must include a written description of the invention or discovery and of the manner and process of making and using the same, and is required to be in such full, clear, concise, and exact terms as to enable any person skilled in the art or science to which the invention or discovery appertains, or with which it is most nearly connected, to make and use the same.
The specification is objected to because both the phrases “Bayesian Inference” (see [0008] and [0016]) and “Bayesian Interference” (see [0028], [0029], [0076], [0078], [00102], [00104], [00112], [00114], [00122], [00124], [00132], [00134]) are used throughout the specification. Though “Bayesian Inference” is a well-known statistical method, “Bayesian Interference” is not a well-defined term. The Examiner assumes it is a typo and all instances of “Bayesian Interference” should read “Bayesian Inference”.
Appropriate correction is required.
Claim Objections
Claims 2,4,12 and 14 are objected to because of the following informalities:
The term “Bayesian interference” should read “Bayesian inference”.
Appropriate correction is required.
Claim Rejections - 35 USC § 112
The following is a quotation of 35 U.S.C. 112(b):
(b) CONCLUSION.—The specification shall conclude with one or more claims particularly pointing out and distinctly claiming the subject matter which the inventor or a joint inventor regards as the invention.
The following is a quotation of 35 U.S.C. 112 (pre-AIA ), second paragraph:
The specification shall conclude with one or more claims particularly pointing out and distinctly claiming the subject matter which the applicant regards as his invention.
Claims 1-20 are rejected under 35 U.S.C. 112(b) or 35 U.S.C. 112 (pre-AIA ), second paragraph, as being indefinite for failing to particularly point out and distinctly claim the subject matter which the inventor or a joint inventor (or for applications subject to pre-AIA 35 U.S.C. 112, the applicant), regards as the invention.
Claim 1 recites the following limitations:
establishing a first conjugate prior or a second conjugate prior for a first distribution probability density function;
performing, based on the operation data and the first and second conjugate priors for the first distribution probability density function, a Maximum A Posteriori (MAP) estimation to determine distribution parameters for the first distribution probability density function, wherein the data are samples of the key performance indicator;
The second limitation of “… based on the first and second conjugate priors…” contradict with the first limitation of “establishing a first conjugate prior or a second conjugate prior” as the first limitation clearly states that only one of the two conjugate priors is established while the second limitation requires performing a Maximum A Posteriori (MAP) estimation based on both conjugate priors. Therefore, it is unclear how many established conjugate priors would be considered as falling within scope of the claim.
Claims 11 and 20 are rejected for the same reason. Claims 2-10 and claims 12-19 are rejected as for being dependent on the above rejected parent claims.
Claim Rejections - 35 USC § 101
35 U.S.C. 101 reads as follows:
Whoever invents or discovers any new and useful process, machine, manufacture, or composition of matter, or any new and useful improvement thereof, may obtain a patent therefor, subject to the conditions and requirements of this title.
Claims 1-20 are rejected under 35 U.S.C. 101 because the claimed invention is directed to a judicial exception and do not include additional elements that amount to significantly more than the judicial exception. A subject matter eligibility analysis is set forth below. See MPEP 2106.
Specifically, representative Claim 1 recites:
A method comprising:
receiving operation data about a collection of machines wherein the operation data characterizes one or more aspects of operation of at least one machine of the collection of machines;
establishing a first conjugate prior or a second conjugate prior for a first distribution probability density function;
performing, based on the operation data and the first and second conjugate priors for the first distribution probability density function, a Maximum A Posteriori (MAP) estimation to determine distribution parameters for the first distribution probability density function, wherein the data are samples of the key performance indicator;
predicting, based on the distribution parameters, a probability the key performance indicator will take a value for a number of the machines; and
scheduling maintenance for the machines based on the probability.
The claim limitations in the abstract idea have been highlighted in bold above; the remaining limitations are “additional elements.”
Similar limitations comprise the abstract idea of computing device claim 11 and non-transitory computer-readable medium claim 20.
Under Step 1 of the analysis, claim 1 belongs to a statutory category, namely it is a process claim. Likewise, claim 10 is a system claim and claim 20 a manufacture claim.
Under Step 2A, prong 1, this part of the eligibility analysis evaluates whether the claim recites a judicial exception. As explained in MPEP 2106.04, subsection II, a claim “recites” a judicial exception when the judicial exception is “set forth” or “described” in the claim.
In the instant case, claims 1, 11, and 20 are found to recite at least one judicial exception (i.e. abstract idea), that being a Mental Process and/or a Mathematical Concept. This can be seen in the claim limitations of “establishing” (understood as setting parameters in light of the specification) a first conjugate prior or a second conjugate prior; “performing” ... a Maximum A Posteriori (MAP) estimation to “determine” distribution parameters for the first distribution probability density function; “predicting” ...a probability the key performance indicator will take a value for a number of the machines; and “scheduling” maintenance for the machines based on the probability, which is the judicial exception of a mental process because these limitations are merely data observations, evaluations, judgements, and/or opinion, in order to perform predictive maintenance, and is capable of being performed mentally and/or with the aid of pen and paper. Additionally, the aforementioned limitations recite mathematical calculations, e.g. performing a Maximum A Posteriori (MAP) estimation in order to calculate the distribution parameters for the first distribution probability density function, e.g. see Spec. equations (11) and (17) describing the mathematical operation of MAP estimation of the parameter α for two different distributions and thus fall well within the mathematical concepts category of abstract idea.
Similar limitations comprise the abstract ideas of claims 11 and 20.
Step 2A, prong 2 of the eligibility analysis evaluates whether the claim as a whole integrates the recited judicial exception(s) into a practical application of the exception. This evaluation is performed by (a) identifying whether there are any additional elements recited in the claim beyond the judicial exception, and (b) evaluating those additional elements individually and in combination to determine whether the claim as a whole integrates the exception into a practical application.
In addition to the abstract ideas recited in claim 1, the claimed method recites additional elements including “receiving operation data about a collection of machines wherein the operation data characterizes one or more aspects of operation of at least one machine of the collection of machines”. However, the element is found to be data gathering step, which is recited at a high level of generality, and thus merely amount to “insignificant extra-solution” activity(ies). See MPEP 2106.05(g) “Insignificant Extra-Solution Activity”.
System claim 11 and manufacture claim 20 recite the same additional element as claim 1 and also recite “a hardware processor and a memory, the memory containing instructions executable by the hardware processor whereby the computing device is configured to:” and “A non-transitory computer-readable medium storing a computer program product, the computer program product comprising software instructions that, when run on a computing device, cause the computing device to:” respectively. However, the use of a generic “hardware processor”, “memory”, and “non-transitory computer-readable medium” to perform the method disclosed in claim 1 or store the software instructions of the method disclosed in claim 1 is similarly found to be insignificant extra-solution activity and is also considered as a tool to “apply” the abstract idea in a technological environment. See MPEP 2106.05(f) “Mere Instructions To Apply An Exception”.
The generic data gathering, processing, and/or output steps, are recited at such a high level of generality that it represents no more than mere instructions to apply the judicial exceptions on a computer. It can also be viewed as nothing more than an attempt to generally link the use of the judicial exceptions to the technological environment of a computer. Noting MPEP 2106.04(d)(I): “It is notable that mere physicality or tangibility of an additional element or elements is not a relevant consideration in Step 2A Prong Two. As the Supreme Court explained in Alice Corp., mere physical or tangible implementation of an exception does not guarantee eligibility. Alice Corp. Pty. Ltd. v. CLS Bank Int’l, 573 U.S. 208, 224, 110 USPQ2d 1976, 1983-84 (2014) ("The fact that a computer ‘necessarily exist[s] in the physical, rather than purely conceptual, realm,’ is beside the point")”.
Thus, under Step 2A, prong 2 of the analysis, even when viewed in combination, these additional elements do not integrate the recited judicial exception into a practical application and the claim is directed to the judicial exception. No specific practical application is associated with the claimed system.
Under Step 2B, the claims do not include additional elements that are sufficient to amount to significantly more than the judicial exception because the additional elements, as described above with respect to Step 2A Prong 2, merely amount to a general-purpose computer system that attempts to apply the abstract idea in a technological environment, limiting the abstract idea to a particular field of use, and/or merely performs insignificant extra-solution activit(ies) (claims 11 and 20). Such insignificant extra-solution activity, e.g. data gathering and output, when re-evaluated under Step 2B is further found to be well-understood, routine, and conventional as evidenced by MPEP 2106.05(d)(II) (describing conventional activities that include transmitting and receiving data over a network, electronic recordkeeping, storing and retrieving information from memory, and electronically scanning or extracting data from a physical document).
Therefore, similarly the combination and arrangement of the above identified additional elements when analyzed under Step 2B also fails to necessitate a conclusion that claims 1, 11 and 20 amount to significantly more than the abstract idea.
With regards to the dependent claims, claims 2-10 and 12-19, merely further expand upon the algorithm/abstract idea and do not set forth further additional elements that integrate the recited abstract idea into a practical application or amount to significantly more. Therefore, these claims are found ineligible for the reasons described for parent claims 1 and 11. Specifically:
With respect to dependent claims 2 and 12, the claims further recite “the first distribution probability density function is defined within a generalized-gamma distribution family; and applying a Bayesian interference to the first distribution probability density function when a gamma shape distribution parameter is unknown.”, which is further part of the abstract idea as applying a Bayesian interference to a specified distribution function is a mathematical concept.
With respect to dependent claims 3 and 13, the claims further recite, w.r.t. their parent claims, “wherein the first conjugate prior satisfies the following relation with (μ, δ) hyperparameters:
p
α
δ
,
μ
,
β
∝
β
∙
μ
δ
∙
α
Γ
α
δ
”, which is further part of the abstract idea as specifying the property of the first conjugate prior is the judicial exception of a mathematical concept.
With respect to dependent claims 4 and 14, the claims further recite, w.r.t. their parent claims, “wherein the first distribution probability density function is defined within a generalized-gamma distribution family; and applying a Bayesian interference to the first distribution probability density function when a gamma shape distribution parameter is unknown and a gamma rate distribution parameter is unknown.”, which is further part of the abstract idea as applying a Bayesian interference to a specified distribution function is the judicial exception of a mathematical concept.
With respect to dependent claims 5 and 15, the claims further recite, w.r.t. their parent claims, “wherein the second conjugate prior satisfies the following relation with (δ, η, μ) hyperparameters:
p
α
,
β
δ
,
η
,
μ
∝
β
∙
μ
δ
∙
α
e
δ
η
β
∙
Γ
α
δ
”}. .”, which is further part of the abstract idea as specifying the property of the second conjugate prior is the judicial exception of a mathematical concept.
With respect to dependent claims 6 and 16, the claims further recite, w.r.t. their parent claims, “wherein the operation data is collected in real-time during a commercial aircraft flight operation, a military aircraft maintenance procedure, a military aircraft flight operation, or during a commercial aircraft maintenance procedure”. However, this is a further part of the data gathering activity, as described above, and thus amounts to nothing more than insignificant extra-solution activity. Additionally, the recitation of a commercial aircraft flight operation, a military aircraft maintenance procedure, a military aircraft flight operation, and a commercial aircraft maintenance procedure is an attempt to limit the abstract idea to a particular technological environment, e.g. type of data values or source of data, and therefore fails to integrate the abstract idea into a practical application or amount to significantly more.
With respect to dependent claims 7-9 and 17-19, the claims further recite, w.r.t. their parent claims, “wherein the first distribution probability density function is a generalized-gamma distribution function including but not limited to gamma, inverse-gamma, or Nakagami distribution function”, “wherein the first distribution probability density function is an Erlang distribution function.”, and/or “wherein the first distribution probability density function is selected from the group consisting of a chi or chi-squared distribution function.”, which is further part of the same abstract idea as specifying the specific distribution function(s) is the judicial exception of a mathematical concept.
With respect to dependent claim 10, the claim further recites, w.r.t. its parent claim, “wherein the indicator is a repair time to fix a component of the machines.”. However, this is further part of the data gathering activity, as described above, and thus amounts to nothing more than insignificant extra-solution activity. Additionally, the recitation of the indicator being a repair time to fix a component of the machines is an attempt to limit the abstract idea to a particular technological environment, e.g. type of data values or source of data, and therefore fails to integrate the abstract idea into a practical application or amount to significantly more.
Claim Rejections - 35 USC § 103
The following is a quotation of 35 U.S.C. 103 which forms the basis for all obviousness rejections set forth in this Office action:
A patent for a claimed invention may not be obtained, notwithstanding that the claimed invention is not identically disclosed as set forth in section 102, if the differences between the claimed invention and the prior art are such that the claimed invention as a whole would have been obvious before the effective filing date of the claimed invention to a person having ordinary skill in the art to which the claimed invention pertains. Patentability shall not be negated by the manner in which the invention was made.
Claims 1,2,4,6,7,10,11,12,14,16,17, and 20 are rejected under 35 U.S.C 103 as being unpatentable over BLACK (US20090299789A1, (IDS filed on 02/13/2024, Cite No. 1)) in view of STANFORD (Stanford CS109 Maximum a Posteriori, winter 2021, Available at https://web.stanford.edu/class/archive/cs/cs109/cs109.1214/lectures/22-MaximumAPosteriori/22-MaximumAPosteriori.pdf, accessed on Aug. 15, 2026) and further in view of UBC (The University of British Columbia website, CPSC 440/450 Winter 2023. https://www.cs.ubc.ca/~dsuth/440/22w2/slides/7-bayesian.pdf accessed on Aug. 17, 2026)
Regarding claim 1, BLACK teaches on the following limitations of the claim:
A method comprising: receiving operation data about a collection of machines wherein the operation data characterizes one or more aspects of operation of at least one machine of the collection of machines (FIG. 1 , reference numbers 12 and 18, and [0023]: “… as well as information relating to the aircraft, such as the age, the flight time and prior maintenance activities performed upon the aircraft”);
predicting, based on the distribution parameters, a probability the key performance indicator will take a value for a number of the machines ([0043]: “… a measure of the relative state of readiness of an aircraft or other repairable system is generated based upon an analysis of the complete intensity function of a modulated power law process. … Since the solution … defines the probability of failure of the repairable system, ….” “);
and scheduling maintenance for the machines based on the probability. (Figure 3, element 66 and [0013]: “… the relative states of readiness of the reparable systems are then determined based upon the respective probabilities of failure of the repairable systems…”)
BLACK fails to teach, STANFORD, however, does teach the following limitation of claim 1:
establishing a first conjugate prior or a second conjugate prior for a first distribution probability density function (Slide 11: “Observe data, Choose model, Choose prior on 𝜃 . Slide 15: “Beta is a conjugate distribution for Bernoulli.” Slide 21: “MAP for Bernoulli, conjugate prior: …, choose a prior on 𝜃”);
performing, based on the operation data and the first and second conjugate priors for the first distribution probability density function, a Maximum A Posteriori (MAP) estimation to determine distribution parameters for the first distribution probability density function, wherein the data are samples of the key performance indicator (Slide 22: This slide shows how to determine the MAP estimation of the distribution parameter 𝜃MAP based on the observed data (flip a coin n + m times));
Since BLACK and STANFORD are both analogous art as they relate to parameter estimation of distribution functions, therefore, before the effective filing date of the claimed invention, it would have been obvious to a person having ordinary skill in the art to have modified BLACK’s teaching on predictive maintenance using a Maximum Likelihood Estimate (e.g. Black [0027]-[0028]), as discussed above, to include “establishing a first conjugate prior or a second conjugate prior for a first distribution probability density function” and “performing, based on the operation data and the first and second conjugate priors for the first distribution probability density function, a Maximum A Posteriori (MAP) estimation to determine distribution parameters for the first distribution probability density function, wherein the data are samples of the key performance indicator” in view of STANFORD with the motivation to improve the estimation accuracy (see UBC Slide 17: “With good hyperparameters, MAP usually outperforms MLE”) and to make the estimation computationally efficient (see STANFORD Slide 22: “If we choose a conjugate prior, we avoid calculus with MAP.”) by substituting the MLE estimation of Black with the better performing MAP approach known in the art (see MPEP 2143 G; also MPEP 2143B - simple substitution of one known technique for another).
Regarding claim 2, the combination of BLACK and STANFORD teaches the elements of the parent claim(s). BLACK further teaches the following limitation of the claim:
The method of claim 1 wherein the first distribution probability density function is defined within a generalized-gamma distribution family ([0038] “Then X1, X2,..., Xn, form a random sample of size n from the gamma distribution with parameters 𝜃 and k.” Equation (20) indicates that the parameters k and 𝜃 are the gamma shape parameter and the reciprocal of the gamma rate parameter.);
BLACK fails to teach, STANFORD, however, does teach the following element of the claim:
and applying a Bayesian interference to the first distribution probability density function when a gamma shape distribution parameter is unknown.( Slides 3-5 teach the use of Bayesian inference for MAP estimation.);
Since BLACK and STANFORD are both analogous art as they relate to parameter estimation of distribution functions; therefore, before the effective filing date of the claimed invention, it would have been obvious to a person having ordinary skill in the art to have modified BLACK’s teaching on predictive maintenance, as discussed above, to clearly include “and applying a Bayesian interference to the first distribution probability density function when a gamma shape distribution parameter is unknown” in view of STANFORD with the motivation to improve the estimation accuracy (see UBC Slide 17: “With good hyperparameters, MAP usually outperforms MLE” and MAP involves Bayesian inference.) (see MPEP 2143 G).
Regarding claim 4, the combination of BLACK and STANFORD teaches the elements of the parent claim(s). BLACK further teaches the following limitation of the claim:
The method of claim 1 wherein the first distribution probability density function is defined within a generalized-gamma distribution family ([0038] “Then X1, X2,..., Xn, form a random sample of size n from the gamma distribution with parameters 𝜃 and k.” Equation (20) indicates that the parameters k and 𝜃 are the gamma shape parameter and the reciprocal of the gamma rate parameter.);
BLACK fails to teach, STANFORD, however, does teach the following element of the claim:
and applying a Bayesian interference to the first distribution probability density function when a gamma shape distribution parameter is unknown and a gamma rate distribution parameter is unknown.( Slides 3-5 teach the use of Bayesian inference for MAP estimation.);
Since BLACK and STANFORD are both analogous art as they relate to parameter estimation of distribution functions; therefore, before the effective filing date of the claimed invention, it would have been obvious to a person having ordinary skill in the art to have modified BLACK’s teaching on predictive maintenance, as discussed above, to clearly include “and applying a Bayesian interference to the first distribution probability density function when a gamma shape distribution parameter is unknown and a gamma rate distribution parameter is unknown.” in view of STANFORD with the motivation to improve the estimation accuracy (see UBC Slide 17: “With good hyperparameters, MAP usually outperforms MLE and MAP involves Bayesian inference) (see MPEP 2143 G).
Regarding claim 6, the combination of BLACK and STANFORD teaches the elements of the parent claim(s). BLACK further teaches the following limitations of the claim:
The method of claim 1, wherein the operation data is collected in real-time during a commercial aircraft flight operation, a military aircraft maintenance procedure, a military aircraft flight operation, or during a commercial aircraft maintenance procedure ([0024]: “In addition, the maintenance management system will monitor maintenance activity and update the maintenance records associated with the aircraft as various maintenance operations are performed and completed. Based upon the data maintained by the maintenance management system, the method and system 10 of the present invention can therefore determine the aircraft that will be operational on the projected date of a mission.).
Regarding claim 7, the combination of BLACK and STANFORD teaches the elements of the parent claim(s). BLACK further teaches the following limitations of the claim:
The method of claim 1, wherein the first distribution probability density function is a generalized-gamma distribution function including but not limited to gamma, inverse-gamma, or Nakagami distribution function ([0027]: “… the process that describes the probability of failure of an aircraft is actually a more specific form of the modulated power law process, such as a gamma renewal process, a homogenous Poisson process or a power law process, …”)
Regarding claim 10, the combination of BLACK and STANFORD teaches the elements of the parent claim(s). BLACK further teaches the following limitations of the claim:
The method of claim 1, wherein the indicator is a repair time to fix a component of the machines. ([0027]: “…, the modulated power law process is a three parameter stochastic point process model that can be used to describe the failure times of a repairable system.”)
Regarding claim 11, BLACK teaches on the following limitations of the claim:
A computing device comprising: a hardware processor and a memory, the memory containing instructions executable by the hardware processor whereby the computing device is configured to ([0048]: “ The system 10 of the present invention is typically embodied by a processing element 20 and an associated memory device, both of which are commonly comprised by a computer or the like. As such, the system of the present invention generally operates under control of a computer program product according to another aspect of the present invention.” )
receive operation data about a collection of machines wherein the operation data characterizes one or more aspects of operation of at least one machine of the collection of machines (FIG. 1 , reference numbers 12 and 18, and [0023]: “… as well as information relating to the aircraft, such as the age, the flight time and prior maintenance activities performed upon the aircraft”);
responsive to performing the MAP estimation, predict, based on the distribution parameters, a probability the key performance indicator will take a value for a number of the machines ([0043]: “… a measure of the relative state of readiness of an aircraft or other repairable system is generated based upon an analysis of the complete intensity function of a modulated power law process. … Since the solution … defines the probability of failure of the repairable system, ….”);
and responsive to predicting the probability, scheduling maintenance for the machines based on the probability (Figure 3, element 66. [0013]: “… the relative states of readiness of the reparable systems are then determined based upon the respective probabilities of failure of the repairable systems.”).
BLACK fails to teach, STANFORD, however, does teach the following limitations of claim 11:
responsive to receiving operation data, establish a first conjugate prior or a second conjugate prior for a first distribution probability density function (Slide 11: “Observe data, Choose model, Choose prior on 𝜃 . Slide 15: “Beta is a conjugate distribution for Bernoulli.” Slide 21: “MAP for Bernoulli, conjugate prior: …, choose a prior on 𝜃”);
responsive to the establishing, perform, based on the operation data and the first and second conjugate priors for the first distribution probability density function, a Maximum A Posteriori (MAP) estimation to determine distribution parameters for the first distribution probability density function, wherein the data are samples of the key performance indicator (Slide 22: This slide shows how to determine the MAP estimation of the distribution parameter 𝜃MAP based on the observed data (flip a coin n + m times);
Since BLACK and STANFORD are both analogous art as they relate to parameter estimation of distribution functions, therefore, before the effective filing date of the claimed invention, it would have been obvious to a person having ordinary skill in the art to have modified BLACK’s teaching on predictive maintenance using a Maximum Likelihood Estimate (e.g. Black [0027]-[0028]), as discussed above, to include “establishing a first conjugate prior or a second conjugate prior for a first distribution probability density function” and “performing, based on the operation data and the first and second conjugate priors for the first distribution probability density function, a Maximum A Posteriori (MAP) estimation to determine distribution parameters for the first distribution probability density function, wherein the data are samples of the key performance indicator” in view of STANFORD with the motivation to improve the estimation accuracy (see UBC Slide 17: “With good hyperparameters, MAP usually outperforms MLE) and to make the estimation computationally efficient (see STANFORD Slide 22: “If we choose a conjugate prior, we avoid calculus with MAP.”) (see MPEP 2143 G ; also MPEP 2143B - simple substitution of one known technique for another).
Regarding claim 12, the combination of BLACK and STANFORD teaches the elements of the parent claim(s). BLACK further teaches the following limitations of the claim:
The computing device of claim 11, wherein the first distribution probability density function is defined within a generalized-gamma distribution family ([0038] “Then X1, X2,..., Xn, form a random sample of size n from the gamma distribution with parameters 𝜃 and k.” Equation (20) indicates that the parameters k and 𝜃 are the gamma shape parameter and the reciprocal of the gamma rate parameter.);
BLACK fails to teach, STANFORD, however, does teach the following element of the claim:
and applying a Bayesian interference to the first distribution probability density function when a gamma shape distribution parameter is unknown.( Slides 3-5 teach the use of Bayesian inference for MAP estimation.);
Since BLACK and STANFORD are both analogous art as they relate to parameter estimation of distribution functions; therefore, before the effective filing date of the claimed invention, it would have been obvious to a person having ordinary skill in the art to have modified BLACK’s teaching on predictive maintenance, as discussed above, to further include “and applying a Bayesian interference to the first distribution probability density function when a gamma shape distribution parameter is unknown” } in view of STANFORD with the motivation to improve the estimation accuracy (see UBC Slide 17: “With good hyperparameters, MAP usually outperforms MLE” and MAP involves Bayesian inference) (see MPEP 2143 G).
Regarding claim 14, the combination of BLACK and STANFORD teach the elements of the parent claim(s). BLACK further teaches the following limitations of the claim:
The computing device of claim 11, wherein the first distribution probability density function is defined within a generalized-gamma distribution family ([0038] “Then X1, X2,..., Xn, form a random sample of size n from the gamma distribution with parameters 𝜃 and k.” Equation (20) indicates that the parameters k and 𝜃 are the gamma shape parameter and the reciprocal of the gamma rate parameter.);
BLACK fails to teach, STANFORD, however, does teach the following element of the claim:
and applying a Bayesian interference to the first distribution probability density function when a gamma shape distribution parameter is unknown and a gamma rate distribution parameter is unknown.( Slides 3-5 teach the use of Bayesian inference for MAP estimation.);
Since BLACK and STANFORD are both analogous art as they relate to parameter estimation of distribution functions; therefore, before the effective filing date of the claimed invention, it would have been obvious to a person having ordinary skill in the art to have modified BLACK’s teaching on predictive maintenance, as discussed above, to further include “and applying a Bayesian interference to the first distribution probability density function when a gamma shape distribution parameter is unknown and a gamma rate distribution parameter is unknown.” in view of STANFORD with the motivation to improve the estimation accuracy (see UBC Slide 17: “With good hyperparameters, MAP usually outperforms MLE and MAP involves Bayesian inference) (see MPEP 2143 G).
Regarding claim 16, the combination of BLACK and STANFORD teach the elements of the parent claim(s). BLACK further teaches the following limitations of the claim:
The computing device of claim 11, wherein the operation data is collected in real-time during a commercial aircraft flight operation, a military aircraft maintenance procedure, a military aircraft flight operation, or during a commercial aircraft maintenance procedure ([0024]: “In addition, the maintenance management system will monitor maintenance activity and update the maintenance records associated with the aircraft as various maintenance operations are performed and completed. Based upon the data maintained by the maintenance management system, the method and system 10 of the present invention can therefore determine the aircraft that will be operational on the projected date of a mission.;
Regarding claim 17, the combination of BLACK and STANFORD teaches the elements of the parent claim(s). BLACK further teaches the following limitations of the claim:
The computing device of claim 11, wherein the first distribution probability density function is a generalized-gamma distribution function including but not limited to gamma, inverse-gamma, or Nakagami distribution function ([0027]: “… the process that describes the probability of failure of an aircraft is actually a more specific form of the modulated power law process, such as a gamma renewal process, a homogenous Poisson process or a power law process, …”)
Regarding claim 20, BLACK teaches on the following limitations of the claim:
A non-transitory computer-readable medium storing a computer program product, the computer program product comprising software instructions that, when run on a computing device, cause the computing device to ([0048]: “The computer program product for performing the contingent claim valuation includes a computer-readable storage medium, such as the non-volatile storage medium, and computer-readable program code portions, such as a series of computer instructions, embodied in the computer readable storage medium.”):
receive operation data about a collection of machines wherein the operation data characterizes one or more aspects of operation of at least one machine of the collection of machines (FIG. 1 , reference numbers 12 and 18, and [0023]: “… as well as information relating to the aircraft, such as the age, the flight time and prior maintenance activities performed upon the aircraft”);
responsive to performing the MAP estimation, predict, based on the distribution parameters, a probability the key performance indicator will take a value for a number of the machines ([0043]: “… a measure of the relative state of readiness of an aircraft or other repairable system is generated based upon an analysis of the complete intensity function of a modulated power law process. … Since the solution … defines the probability of failure of the repairable system, ….”);
and responsive to the prediction, scheduling maintenance for the machines based on the probability (Figure 3, element 66. [0013]: “… the relative states of readiness of the reparable systems are then determined based upon the respective probabilities of failure of the repairable systems.”).
BLACK fails to teach, STANFORD, however, does teach the following limitations of claim 20:
establish a first conjugate prior or a second conjugate prior for a first distribution probability density function (Slide 11: “Observe data, Choose model, Choose prior on 𝜃 . Slide 15: “Beta is a conjugate distribution for Bernoulli.” Slide 21: “MAP for Bernoulli, conjugate prior: …, choose a prior on 𝜃”);
perform, based on the operation data and the first and second conjugate priors for the first distribution probability density function, a Maximum A Posteriori (MAP) estimation to determine distribution parameters for the first distribution probability density function, wherein the operation data are samples of the key performance indicator (Slide 22: This slide shows how to determine the MAP estimation of the distribution parameter 𝜃MAP based on the observed data (flip a coin n + m times);
Since BLACK and STANFORD are both analogous art as they relate to parameter estimation of distribution functions, therefore, before the effective filing date of the claimed invention, it would have been obvious to a person having ordinary skill in the art to have modified BLACK’s teaching on predictive maintenance using a Maximum Likelihood Estimate (e.g. Black [0027]-[0028]), as discussed above, to include “establishing a first conjugate prior or a second conjugate prior for a first distribution probability density function” and “performing, based on the operation data and the first and second conjugate priors for the first distribution probability density function, a Maximum A Posteriori (MAP) estimation to determine distribution parameters for the first distribution probability density function, wherein the data are samples of the key performance indicator” in view of STANFORD with the motivation to improve the estimation accuracy (see UBC Slide 17: “With good hyperparameters, MAP usually outperforms MLE”) and to make the estimation computationally efficient (see STANFORD Slide 22: “If we choose a conjugate prior, we avoid calculus with MAP.”) by substituting the MLE estimation of Black with the better performing MAP approach known in the art (see MPEP 2143 G; also MPEP 2143B - simple substitution of one known technique for another).
Claims 8 and 18 are rejected under 35 U.S.C 103 as being unpatentable over BLACK (US20090299789A1, (IDS filed on 02/13/2024, Cite No. 1)) in view of STANFORD (Stanford CS109 Maximum a Posteriori, winter 2021, Available at https://web.stanford.edu/class/archive/cs/cs109/cs109.1214/lectures/22-MaximumAPosteriori/22-MaximumAPosteriori.pdf, accessed on Aug. 15, 2026), in further view of UBC (The University of British Columbia website, CPSC 440/450 Winter 2023. https://www.cs.ubc.ca/~dsuth/440/22w2/slides/7-bayesian.pdf accessed on Aug. 17, 2026), and further in view of HARRIS (US20030158772A1).
Regarding claim 8, the combination of BLACK, STANFORD and UBC teaches the elements of the parent claim(s).
The combination of BLACK, STANFORD and UBC fails to teach, HARRIS, however, does teach the following element of the claim:
The method of claim 1, wherein the first distribution probability density function is an Erlang distribution function. ([0082]: “Step 5: using the model of the counting process determined in Step 4, determine the model that represents the distribution of the time until the “n" event; i.e., the “total waiting time until” the “n" removal. For example, the Erlang distribution is the model that represents this distribution.“);
Since HARRIS is analogous art as it relates to parameter estimation of distribution functions; therefore, before the effective filing date of the claimed invention, it would have been obvious to a person having ordinary skill in the art to have modified BLACK’s teaching on predictive maintenance, as discussed above, to clearly include “The method of claim 1, wherein the first distribution probability density function is an Erlang distribution function” in view of HARRIS with the motivation to model the distribution of the time until the nth failure ([0082]: “…Step 4, determine the model that represents the distribution of the time until the “n" event”) (see MPEP 2143 G).
Regarding claim 18, the combination of BLACK, STANFORD and UBC teaches the elements of the parent claim(s).
The combination of BLACK, STANFORD and UBC fails to teach, HARRIS, however, does teach the following element of the claim:
The computing device of claim 11, wherein the first distribution probability density function is an Erlang distribution function. ([0082]: “Step 5: using the model of the counting process determined in Step 4, determine the model that represents the distribution of the time until the “n" event; i.e., the “total waiting time until” the “n" removal. For example, the Erlang distribution is the model that represents this distribution.“);
Since HARRIS is analogous art as it relates to parameter estimation of distribution functions; therefore, before the effective filing date of the claimed invention, it would have been obvious to a person having ordinary skill in the art to have modified BLACK’s teaching on predictive maintenance, as discussed above, to clearly include “The computing device of claim 11, wherein the first distribution probability density function is an Erlang distribution function” in view of HARRIS with the motivation to model the distribution of the time until the nth failure ([0082]: “…Step 4, determine the model that represents the distribution of the time until the “n" event”) (see MPEP 2143 G).
Claims 9 and 19 are rejected under 35 U.S.C 103 as being unpatentable over BLACK (US20090299789A1, (IDS filed on 02/13/2024, Cite No. 1)) in view of STANFORD (Stanford CS109 Maximum a Posteriori, winter 2021, Available at https://web.stanford.edu/class/archive/cs/cs109/cs109.1214/lectures/22-MaximumAPosteriori/22-MaximumAPosteriori.pdf, accessed on Aug. 15, 2026), ), in further view of UBC (The University of British Columbia website, CPSC 440/450 Winter 2023. https://www.cs.ubc.ca/~dsuth/440/22w2/slides/7-bayesian.pdf accessed on Aug. 17, 2026), and further in view of WU (US6148268A).
Regarding claim 9, the combination of BLACK, STANFORD and UBC teaches the elements of the parent claim(s).
The combination of BLACK, STANFORD and UBC fails to teach, WU, however, does teach the following element of the claim:
The method of claim 1, wherein the first distribution probability density function is selected from the group consisting of a chi or chi-squared distribution function. (See Fig. 1a . and col. 1 lines 60-65: “The data collected from the repeated measurements of the product characteristic are then plotted in a histogram and the curvature is modeled to a Chi-square function.“);
Since BLACK and WU are in the closely related technical fields, i.e., predictive maintenance and product quality control and WU relates to predicting product quality control using estimations of probability distributions; therefore, before the effective filing date of the claimed invention, it would have been obvious to a person having ordinary skill in the art to have modified BLACK’s system and method on predictive maintenance, as discussed above, to further include “The method of claim 1, wherein the first distribution probability density function is selected from the group consisting of a chi or chi-squared distribution function” in view of WU with the motivation to model the distribution when the fleet is operating at near optimum conditions (Col. 1 lines 33-35: “In the conditions where the process is operating at near optimum conditions a Chi-square analysis is appropriate.”). (see MPEP 2143 G).
Regarding claim 19, the combination of BLACK, STANFORD and UBC teaches the elements of the parent claim(s).
The combination of BLACK, STANFORD and UBC fails to teach, WU, however, does teach the following element of the claim:
The computing device of claim 11, wherein the first distribution probability density function is selected from the group consisting of a chi or chi-squared distribution function. (See Fig. 1a . and col. 1 lines 60-65: “The data collected from the repeated measurements of the product characteristic are then plotted in a histogram and the curvature is modeled to a Chi-square function.“);
Since BLACK and WU are in the closely related technical fields, i.e., predictive maintenance and product quality control and WU relates to predicting product quality control using estimations of probability distributions; therefore, before the effective filing date of the claimed invention, it would have been obvious to a person having ordinary skill in the art to have modified BLACK’s system and method on predictive maintenance, as discussed above, to further include “The computing device of claim 11, wherein the first distribution probability density function is selected from the group consisting of a chi or chi-squared distribution function” in view of WU with the motivation to model the distribution when the fleet is operating at near optimum conditions (Col. 1 lines 33-35: “In the conditions where the process is operating at near optimum conditions a Chi-square analysis is appropriate.”). (see MPEP 2143 G).
Claims 3, 5, 13, and 15 are rejected under 35 U.S.C 103 as being unpatentable over BLACK (US20090299789A1, (IDS filed on 02/13/2024, Cite No. 1)) in view of STANFORD (Stanford CS109 Maximum a Posteriori, winter 2021, Available at https://web.stanford.edu/class/archive/cs/cs109/cs109.1214/lectures/22-MaximumAPosteriori/22-MaximumAPosteriori.pdf, accessed on Aug. 15, 2026), in further view of UBC (The University of British Columbia website, CPSC 440/450 Winter 2023. https://www.cs.ubc.ca/~dsuth/440/22w2/slides/7-bayesian.pdf accessed on Aug. 17, 2026), and further in view of RIFFI (Riffi, M.I. and El-Masri, H.S., 2020. Bayesian inference on the generalized gamma distribution using conjugate priors. IUG Journal of Natural Studies, 28(2), pp.1-18).
Regarding claim 3, the combination of BLACK, STANFORD and UBC teaches the elements of the parent claim(s).
The combination of BLACK, STANFORD and UBC fails to teach, RIFFI, however, does teach the following element of the claim:
…, wherein the first conjugate prior satisfies the following relation with (µ, δ) hyperparameters:
p
(
α
|
δ
,
μ
,
β
)
∝
β
μ
δ
α
Γ
(
α
)
δ
(Page 5, equation 3.5. The recited conjugate prior is a special case of RIFFI’s equation. The analysis is set forth below.
The Generalized Gamma distribution given in the specification is
p
x
α
,
β
,
γ
=
|
γ
|
β
α
x
γ
α
-
1
Γ
(
α
)
e
-
β
x
γ
(1.1)
while the Generalized Gamma distribution given in RIFFI (page 2, (1.1)) is
f
(
x
,
a
,
γ
,
δ
)
=
δ
a
γ
+
1
δ
Γ
(
γ
+
1
δ
)
x
γ
e
-
a
x
δ
x
>
0
,
δ
>
0
,
a
>
0
,
γ
>
-
1
(1.2)
Clearly, different parameterizations are used.
To facilitate the analysis, in view of (1.1), Riffi’s distribution is re-written as
f
x
A
,
B
,
C
=
C
A
B
+
1
C
Γ
(
B
+
1
C
)
x
B
e
-
A
x
C
, x>0, A>0, B>-1, C >0 (2)
Comparing (1.1) and (2), we have
α
=
B
+
1
C
,
β
=
A
,
γ
=
C
(3.1)
Or equivalently,
A
=
β
,
B
=
α
γ
-
1
,
C
=
γ
(3.2)
The closest equation from Riffi is equation (3.5); when B is unknown. In this case, the conjugate prior
π
B
is given by:
π
B
∝
A
s
(
B
+
1
C
)
Γ
b
(
B
+
1
C
)
t
B
(4.1), s>0, b>0 and t>0 are hyperparameters.
In view of (3.1) with change of variable, we obtain
p
α
=
|
γ
|
π
(
α
γ
-
1
)
∝
β
s
α
Γ
b
(
α
)
t
α
=
(
t
β
s
)
α
Γ
b
(
α
)
=
(
β
t
1
s
)
s
α
Γ
b
(
α
)
(4.2)
By setting b = s =
δ
and
t
1
s
=
μ
, (4.2) becomes
p
α
∝
(
β
μ
)
δ
α
Γ
δ
(
α
)
which is exactly the recited conjugate prior.)
RIFFI is analogous art as it relates to parameter estimation of probability density functions. Therefore, before the effective filing date of the claimed invention, it would have been obvious to a person having ordinary skill in the art to have modified the combination of BLACK and STANFORD in view of RIFFI to include “wherein the first conjugate prior satisfies the following relation with (µ, δ) hyperparameters:
p
(
α
|
δ
,
μ
,
β
)
∝
β
μ
δ
α
Γ
(
α
)
δ
“ with the motivation to improve the parameter estimation accuracy (see RIFFI, Abstract) (see MPEP 2143 G).
Claim 13 is rejected under the same rationale.
Regarding claim 5, the combination of BLACK, STANFORD and UBC teaches the elements of the parent claim(s).
The combination of BLACK, STANFORD and UBC fails to teach, RIFFI, however, does teach the following element of the claim:
…, wherein the second conjugate prior satisfies the following relation with (δ, η, µ) hyperparameters:
p
(
α
,
β
|
δ
,
η
,
μ
)
∝
(
β
μ
)
δ
α
e
δ
η
β
Γ
(
α
)
δ
(Page 6, equation 3.11. The recited conjugate prior is a special case of RIFFI’s equation. The analysis is set forth below.
Similar to the analysis for claim 3, in order to facilitate the analysis, RIFFI’s equation (3.11) is rewritten as
π
(
A
,
B
)
∝
A
s
(
B
+
1
C
)
Γ
b
(
B
+
1
C
)
t
B
e
-
A
m
C
(5.1)
In view of (3.1), we make the following change of variables:
α
=
B
+
1
γ
and
β
=
A
.
Then, we have
p
β
,
α
=
γ
π
(
β
,
α
γ
-
1
)
∝
π
(
β
,
α
γ
-
1
)
∝
β
s
α
e
β
m
γ
Γ
b
(
α
)
t
α
γ
(5.2)
By setting t =
μ
,
b = s =
δ
=
γ
, and m =
(
δ
η
)
1
/
δ
, we arrive at the claimed conjugate prior
(
β
μ
)
δ
α
e
δ
η
β
Γ
(
α
)
δ
) when
α
and
β
are unknown.
RIFFI is analogous art as it relates to parameter estimation of probability density functions. Therefore, before the effective filing date of the claimed invention, it would have been obvious to a person having ordinary skill in the art to have modified the combination of BLACK and STANFORD in view of RIFFI to include “wherein the second conjugate prior satisfies the following relation with (δ, η, µ) hyperparameters:
p
(
α
,
β
|
δ
,
η
,
μ
)
∝
(
β
μ
)
δ
α
e
δ
η
β
Γ
(
α
)
δ
“ with the motivation to improve the parameter estimation accuracy (see RIFFI, Abstract) (see MPEP 2143 G).
Claim 15 is rejected under the same rationale.
Pertinent Prior Art
The prior art made of record and not relied upon is considered pertinent to applicant's disclosure:
MOAVENI (U.S PG-Pub. No. 2024/0411279 A1) teaches the use of conjugate prior of non-stationary Gaussian process for parameter estimation.
AGARWAL (Agarwal, A. and Daumé III, H., 2010. A geometric view of conjugate priors. Machine learning, 81(1), pp.99-113.) teaches the geometric interpretation of conjugate priors to derive the hyperparameters and expression of the priors.
Conclusion
Any inquiry concerning this communication or earlier communications from the examiner should be directed to HUA MEI H CHEN whose telephone number is (571)270-0493. The examiner can normally be reached Monday-Friday 8am-5pm.
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/HUA MEI HARRY CHEN/ Examiner, Art Unit 2857
/SHELBY A TURNER/ Supervisory Patent Examiner, Art Unit 2857
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