METHODS AND SYSTEMS FOR CONTINOUSLY ESTIMATING PERSISTENT AND INTERMITTENT FAILURE PROBABILITIES FOR PRODUCTION RESOURCES

• US 20100011255A1
• Filed: 06/23/2009
• Published: 01/14/2010
• Est. Priority Date: 07/10/2008
• Status: Active Grant

• Current Assignee: Xerox Corporation (Xerox Holdings Corp.)
• Original Assignee: Palo Alto Research Center, Inc. (Xerox Holdings Corp.)
• Inventors: Liu, Juan, Price, Robert, Do, Minh Binh, Zhou, Rong, Kuhn, Lukas D., de Kleer, Johan
• Granted Patent: US 8,165,705 B2
• Time in Patent Office: Days
• US Class Current: 714/47
• CPC Class Codes: G06Q 10/04 Forecasting or optimisation specially adapted for administrative or management purposes, e.g. linear programming or "cutting stock problem" market predictions or forecasting for commercial activities G06Q30/0202
• CPC Class Codes: G06Q 10/06 Resources, workflows, human or project management; Enterprise or organisation planning; Enterprise or organisation modelling
• CPC Class Codes: Y02P 90/80 Management or planning

Abstract

Production control systems and methods are presented for estimation of production resource failure probabilities in which a set of four count values are maintained and updated for each resource including a first count value m₁₁ indicating a number of plans where the resource m was used and failed, a second count value m₁₀ indicating a number of plans where the resource m was used and succeeded, a third count value m₀₁ indicating a number of plans where the resource m was not used and failed, and a fourth count value m₀₀ indicating a number of plans where the resource m was not used and succeeded, and the current fault probability for each resource is estimated and stored for single or multiple, persistent or intermittent faults based on the corresponding count values.

Claims

1. A method for estimating failure probabilities for resources in a production system, the method comprising:

maintaining a set of four count values for each of a plurality of resources in a production system, the four count values for each individual resource m including;

a first count value m₁, indicating a number of plans where the resource m was used and failed,

a second count value m₁₀ indicating a number of plans where the resource m was used and succeeded,

a third count value m₀₁ indicating a number of plans where the resource m was not used and failed, and

a fourth count value m₀₀ indicating a number of plans where the resource m was not used and succeeded;

for each plan executed in the production system, incrementing a select one of the count values for each of the resources based on a list of resources used in the plan and the success or failure of the plan;

for each resource, estimating a current fault probability value for single or multiple, persistent or intermittent faults based on at least one of the corresponding set of count values; and

storing the current fault probability values for the resources.

2. The method of claim 1, wherein for each resource, estimating the current fault probability value for a single persistent fault includes:

exonerating the resource by setting the current fault probability to zero if the second or third count values m₁₀ or m₀₁ are greater than zero; and

otherwise, setting the current fault probability to 1/X, where X is the number of resources where both the second and third count values m₁ and m₀₁ are zero.

3. The method of claim 1, wherein for each resource, estimating the current fault probability value for a single intermittent fault includes:

exonerating the resource by setting the current fault probability to zero if the third count value m₀₁ is greater than zero; and

otherwise, setting the current fault probability according to the equation α

wp₀(M);

where α

is a value selected so that the posterior fault probabilities for all the resources sum to 1;

where w is determined according to the following equation;

$w={{\left[\frac{m_{10}}{m_{11}+m_{10}}\right]}^{m_{10}}<br><br>\left[\frac{m_{11}}{m_{11}+m_{10}}\right]}^{m_{11}}.;<br><br>$

and

where p₀(M) is the previous fault probability value.

4. The method of claim 1, for multiple persistent faults, further comprising:

establishing a plurality of unique diagnoses d to be evaluated, at least one of the diagnoses including a single one of the resources m, and at least one of the diagnoses including at least two of the resources m, each diagnosis having a unique assignment of either good or faulted to each member resource;

maintaining a set of four diagnosis count values for each diagnosis, the four diagnosis count values for each individual diagnosis including;

a first diagnosis count value d₁₁ indicating a number of failed plans where a bad resource of the diagnosis d was used,

a second diagnosis count value d₁₀ indicating a number of successful plans where a bad resource of the diagnosis d was used,

a third diagnosis count value d₀₁ indicating a number of failed plans where a good resource of the diagnosis d was not used, and

a fourth diagnosis count value d₀₀ indicating a number of successful plans where a good resource of the diagnosis d was not used;

exonerating the resources of a diagnosis by setting the current fault probability for that diagnosis to zero if the second or third diagnosis count values d₁₀ or d₀₁ are greater than zero;

otherwise, setting a current diagnosis fault probability to 1/X, where X is the number of diagnoses where both the second and third diagnosis count values d₁₀ and d₀₁ are zero; and

setting the current fault probability for the evaluated resources according to the following equation;

$p<br><br>\left(m<br><br>o_1,\mathrm{\dots <br><br>}<br><br>,o_t\right)=\underset{d<br><br><br><br>s.t.<br><br>m\in <br><br>d}{\sum <br><br>}<br><br>p<br><br>\left(d<br><br>o_1,\mathrm{\dots <br><br>}<br><br>,o_t\right).,$

where m is the resource, o₁, . . . o_t is a set of observations and d ranges over the remaining set of suspect candidates S (for which the third count value d₀₁ is zero).

5. The method of claim 1, wherein for each resource, estimating the current fault probability value for multiple intermittent faults includes:

establishing a plurality of unique diagnoses d to be evaluated, at least one of the diagnoses including a single one of the resources m, and at least one of the diagnoses including at least two of the resources m, each diagnosis having a unique assignment of either good or faulted to each member resource;

maintaining a set of four diagnosis count values for each diagnosis, the four diagnosis count values for each individual diagnosis including;

a first diagnosis count value d₁, indicating a number of failed plans where a bad resource of the diagnosis d was used,

a second diagnosis count value d₁₀ indicating a number of successful plans where a bad resource of the diagnosis d was used,

a third diagnosis count value d₀₁ indicating a number of failed plans where a good resource of the diagnosis d was not used, and

a fourth diagnosis count value d₀₀ indicating a number of successful plans where a good resource of the diagnosis d was not used;

maintaining a list S of remaining suspect candidate diagnoses for which the third diagnosis count value d₀₁ is zero; and

setting a posterior fault probability for the evaluated resources according to the following equation;

$p<br><br>\left(m<br><br>o_1,\mathrm{\dots <br><br>}<br><br>,o_t\right)=\underset{d<br><br><br><br>s.t.<br><br>m\in <br><br>d}{\sum <br><br>}<br><br>p<br><br>\left(d<br><br>o_1,\mathrm{\dots <br><br>}<br><br>,o_t\right).$

where m is the resource, o₁, . . . o_t is a set of observations, and d ranges over the remaining set of suspect candidates S (for which the third count value d₀₁ is zero

6. The method of claim 1, wherein for each resource, estimating the current fault probability value for multiple intermittent faults includes:

maintaining a counter value i₁₁ associated with each set of modules m utilized in a failing plan i;

computing a failure term for the evaluated resources using the counter value i₁₁ according to the following equation;

Π

_{U fails}[1=Π

<sub>mε

bad(D)∩

U</sub>(1=p_b(m))]=

Π

<sub>iε

I</sub>[1=Π

<sub>mε

bad(D)∩

i</sub>(1=p_b(m))]ⁱ¹¹,

where I is a set of all such sets which have failed at least once, where m is the resource, and where p_b(m) is the probability that a resource m produces an incorrect output when faulted;

computing a success term for the evaluated resources using the counter m₁₀ for each resource according to the following equation;

$\underset{U<br><br><br><br>\mathrm{succeeds}}{\prod <br><br>}<br><br>\underset{m\in <br><br>\mathrm{bad}<br><br>\left(d\right)\bigcap <br><br>U}{\prod <br><br>}<br><br>\left(1-p_b<br><br>\left(m\right)\right)={\left(1-p_b<br><br>\left(m\right)\right)}^{m_{10}}.;<br><br>$

and

setting a posterior fault probability for the evaluated resources according to the following equation;

$p_t<br><br>\left(D<br><br>O,U\right)=\{\begin{array}{c}\underset{U<br><br><br><br>\mathrm{fails}}{\prod <br><br>}<br><br>\left[1-\underset{m\in <br><br>\mathrm{bad}<br><br>\left(D\right)\bigcap <br><br>U}{\prod <br><br>}<br><br>\left(1-p_b<br><br>\left(m\right)\right)\right]\\ \underset{U<br><br><br><br>\mathrm{succeeds}}{\prod <br><br>}<br><br>\underset{m\in <br><br>\mathrm{bad}<br><br>\left(D\right)\bigcap <br><br>U}{\prod <br><br>}<br><br>\left(1-p_b<br><br>\left(m\right)\right),\end{array}$

where O={o₁, . . . o_t} is a set of observations and U is an indication of whether the module was used in the plan associated with the observation o.

7. The method of claim 1, further comprising initializing the current fault probability values for each of the resources to a predetermined value before execution of any plans in the production system.

8. The method of claim 1, further comprising multiplying each count value by a weighting factor after estimating a current fault probability value, the weighting factor being less than 1.

9. A self-diagnosing production control system for controlling operation of a production system to achieve one or more production goals and to diagnose failure status of production resources, the control system comprising:

a planner operatively coupled with the production system to provide plans for execution in the production system;

a plant model operatively coupled with the planner and including a model of a plant of the production system; and

a diagnosis engine operatively coupled with the planner, the production system, and the model, the diagnosis engine comprising;

a belief model including a current fault probability value for single or multiple, persistent or intermittent faults for each of a plurality of resources in the production system, and

a plant condition estimation component comprising a set of four count values for each of a plurality of resources in the production system, the four count values for each individual resource m including a first count value m₁₁ indicating a number of plans where the resource m was used and failed, a second count value m₁₀ indicating a number of plans where the resource m was used and succeeded, a third count value m₀₁ indicating a number of plans where the resource m was not used and failed, and a fourth count value m₀₀ indicating a number of plans where the resource m was not used and succeeded;

the plant condition estimation component being operative to receive a list of resources used in a plan executed in the plant and the success or failure of the plan, and for each plan executed in the production system, to increment a select one of the count values for each of the resources based on a list of resources used in the plan and the success or failure of the plan, and to estimate a current fault probability value for single or multiple, persistent or intermittent faults based on at least one of the corresponding set of count values, and to store the current fault probability values for the resources.

10. The production control system of claim 9, wherein for each resource, the plant condition estimation component estimates the current fault probability value for a single persistent fault by exonerating the resource by setting the current fault probability to zero if the second or third count values m₁₀ or m₀₁ are greater than zero, and otherwise, setting the current fault probability to 1/X, where X is the number of resources where both the second and third count values m₁₀ and m₀₁ are zero.

11. The production control system of claim 9, wherein for each resource, the plant condition estimation component estimates the current fault probability value for a single intermittent fault by exonerating the resource by setting the current fault probability to zero if the third count value m₀₁ is greater than zero, and otherwise, setting the current fault probability according to the equation α

wp₀(M), where α

is a value selected so that the posterior fault probabilities for all the resources sum to 1;

where w is determined according to the following equation;

$w={{\left[\frac{m_{10}}{m_{11}+m_{10}}\right]}^{m_{10}}<br><br>\left[\frac{m_{11}}{m_{11}+m_{10}}\right]}^{m_{11}}.,$

and where p₀(M) is the previous fault probability value.

12. The production control system of claim 9, wherein for each resource, the plant condition estimation component estimates the current fault probability value for multiple persistent faults by:

establishing a plurality of unique diagnoses d to be evaluated, at least one of the diagnoses including a single one of the resources m, and at least one of the diagnoses including at least two of the resources m, each diagnosis having a unique assignment of either good or faulted to each member resource;

maintaining a set of four diagnosis count values for each diagnosis, the four diagnosis count values for each individual diagnosis including;

a first diagnosis count value d₁₁ indicating a number of failed plans where a bad resource of the diagnosis d was used,

a second diagnosis count value d₁₀ indicating a number of successful plans where a bad resource of the diagnosis d was used,

a third diagnosis count value d₀₁ indicating a number of failed plans where a good resource of the diagnosis d was not used, and

a fourth diagnosis count value d₀₀ indicating a number of successful plans where a good resource of the diagnosis d was not used;

exonerating the resources of a diagnosis by setting the current fault probability for that diagnosis to zero if the second or third diagnosis count values d₁₀ or d₀₁ are greater than zero;

otherwise, setting a current diagnosis fault probability to 1/X, where X is the number of diagnoses where both the second and third diagnosis count values d₁₀ and d₀₁ are zero; and

setting the current fault probability for the evaluated resources according to the following equation;

$p<br><br>\left(m<br><br>o_1,\mathrm{\dots <br><br>}<br><br>,o_t\right)=\underset{d<br><br><br><br>s.t.<br><br>m\in <br><br>d}{\sum <br><br>}<br><br>p<br><br>\left(d<br><br>o_1,\mathrm{\dots <br><br>}<br><br>,o_t\right).,$

where m is the resource, o₁, . . . o_t is a set of observations and d ranges over the remaining set of suspect candidates S (for which the third count value d₀₁ is zero).

13. The production control system of claim 9, wherein for each resource, the plant condition estimation component estimates the current fault probability value for multiple persistent faults by:

establishing a plurality of unique diagnoses d to be evaluated, at least one of the diagnoses including a single one of the resources m, and at least one of the diagnoses including at least two of the resources m, each diagnosis having a unique assignment of either good or faulted to each member resource;

maintaining a set of four diagnosis count values for each diagnosis, the four diagnosis count values for each individual diagnosis including;

a first diagnosis count value d₁, indicating a number of failed plans where a bad resource of the diagnosis d was used,

a second diagnosis count value d₁₀ indicating a number of successful plans where a bad resource of the diagnosis d was used,

a third diagnosis count value d₀₁ indicating a number of failed plans where a good resource of the diagnosis d was not used, and

a fourth diagnosis count value d₀₀ indicating a number of successful plans where a good resource of the diagnosis d was not used;

maintaining a list S of remaining suspect candidate diagnoses for which the third diagnosis count value d₀₁ is zero; and

setting a posterior fault probability for the evaluated resources according to the following equation;

$p<br><br>\left(m<br><br>o_1,\mathrm{\dots <br><br>}<br><br>,o_t\right)=\underset{d<br><br><br><br>s.t.<br><br>m\in <br><br>d}{\sum <br><br>}<br><br>p<br><br>\left(d<br><br>o_1,\mathrm{\dots <br><br>}<br><br>,o_t\right).$

where m is the resource, o₁, . . . o_t is a set of observations and d ranges over, the remaining set of suspect candidates S (for which the third count value d₀₁ is zero).

14. The production control system of claim 9, wherein for each resource, the plant condition estimation component estimates the current fault probability value for multiple persistent faults by:

maintaining a counter value i₁₁ associated with each set of modules m utilized in a failing plan i;

computing a failure term for the evaluated resources using the counter value i₁₁ according to the following equation;

Π

_{U fails}[1=Π

<sub>mε

bad(D)∩

U</sub>(1=p_b(m))]=

Π

<sub>iε

I</sub>[1=Π

<sub>mε

bad(D)∩

i</sub>(1=p_b(m))]ⁱ¹¹,

where I is a set of all such sets which have failed at least once, where m is the resource, and where p_b(m) is the probability that a resource m produces an incorrect output when faulted;

computing a success term for the evaluated resources using the counter m₁₀ for each resource according to the following equation;

$\underset{U<br><br><br><br>\mathrm{succeeds}}{\prod <br><br>}<br><br>\underset{m\in <br><br>\mathrm{bad}<br><br>\left(d\right)\bigcap <br><br>U}{\prod <br><br>}<br><br>\left(1-p_b<br><br>\left(m\right)\right)={\left(1-p_b<br><br>\left(m\right)\right)}^{m_{10}}.;<br><br>$

and

setting a posterior fault probability for the evaluated resources according to the following equation;

$p_t<br><br>\left(D<br><br>O,U\right)=\{\begin{array}{c}\underset{U<br><br><br><br>\mathrm{fails}}{\prod <br><br>}<br><br>\left[1-\underset{m\in <br><br>\mathrm{bad}<br><br>\left(D\right)\bigcap <br><br>U}{\prod <br><br>}<br><br>\left(1-p_b<br><br>\left(m\right)\right)\right]\\ \underset{U<br><br><br><br>\mathrm{succeeds}}{\prod <br><br>}<br><br>\underset{m\in <br><br>\mathrm{bad}<br><br>\left(D\right)\bigcap <br><br>U}{\prod <br><br>}<br><br>\left(1-p_b<br><br>\left(m\right)\right),\end{array}$

where O={o₁, . . . o_t} is a set of observations and U is an indication of whether the module was used in the plan associated with the observation o.

15. The production control system of claim 9, wherein the plant condition estimation component initializes the current fault probability values for each of the resources to a predetermined value before execution of any plans in the production system.

16. The production control system of claim 9, wherein the plant condition estimation component multiplies each count value by a weighting factor after estimating the current fault probability value, the weighting factor being less than 1.

17. A computer readable medium having computer executable instructions for performing the steps of:

maintaining a set of four count values for each of a plurality of resources in a production system, the four count values for each individual resource m including;

a first count value m₁₁ indicating a number of plans where the resource m was used and failed,

a second count value m₁₀ indicating a number of plans where the resource m was used and succeeded,

a third count value m₀₁ indicating a number of plans where the resource m was not used and failed, and

a fourth count value m₀₀ indicating a number of plans where the resource m was not used and succeeded;

for each plan executed in the production system, incrementing a select one of the count values for each of the resources based on a list of resources used in the plan and the success or failure of the plan;

for each resource, estimating a current fault probability value for single or multiple, persistent or intermittent faults based on at least one of the corresponding set of count values; and

storing the current fault probability values for the resources.

18. The computer readable medium of claim 17, comprising further computer executable instructions for estimating the current fault probability value for a single persistent fault by exonerating the resource by setting the current fault probability to zero if the second or third count values m₁₀ or m₀₁ are greater than zero, and otherwise, setting the current fault probability to 1/X, where X is the number of resources where both the second and third count values m₁₀ and m₀₁ are zero.

19. The computer readable medium of claim 17, comprising further computer executable instructions for estimating the current fault probability value for a single intermittent fault by exonerating the resource by setting the current fault probability to zero if the third count value m₀₁ is greater than zero, and otherwise, setting the current fault probability according to the equation α

wp₀(M), where α

is a value selected so that the posterior fault probabilities for all the resources sum to 1, where w is determined according to the following equation;

$w={{\left[\frac{m_{10}}{m_{11}+m_{10}}\right]}^{m_{10}}<br><br>\left[\frac{m_{11}}{m_{11}+m_{10}}\right]}^{m_{11}}.,$

and where p₀(M) is the previous fault probability value.

20. The computer readable medium of claim 17, comprising further computer executable instructions for estimating the current fault probability value for multiple persistent faults by:

establishing a plurality of unique diagnoses d to be evaluated, at least one of the diagnoses including a single one of the resources m, and at least one of the diagnoses including at least two of the resources m, each diagnosis having a unique assignment of either good or faulted to each member resource;

maintaining a set of four diagnosis count values for each diagnosis, the four diagnosis count values for each individual diagnosis including;

a first diagnosis count value d₁₁ indicating a number of failed plans where a bad resource of the diagnosis d was used,

a second diagnosis count value d₁₀ indicating a number of successful plans where a bad resource of the diagnosis d was used,

a third diagnosis count value d₀₁ indicating a number of failed plans where a good resource of the diagnosis d was not used, and

a fourth diagnosis count value d₀₀ indicating a number of successful plans where a good resource of the diagnosis d was not used;

exonerating the resources of a diagnosis by setting the current fault probability for that diagnosis to zero if the second or third diagnosis count values d₁₀ or d₀₁ are greater than zero;

otherwise, setting a current diagnosis fault probability to 1/X, where X is the number of diagnoses where both the second and third diagnosis count values d₁₀ and d₀₁ are zero; and

setting the current fault probability for the evaluated resources according to the following equation;

$p<br><br>\left(m<br><br>o_1,\mathrm{\dots <br><br>}<br><br>,o_t\right)=\underset{d<br><br><br><br>s.t.<br><br>m\in <br><br>d}{\sum <br><br>}<br><br>p<br><br>\left(d<br><br>o_1,\mathrm{\dots <br><br>}<br><br>,o_t\right).,$

where m is the resource, o₁, . . . o_t is a set of observations, and d ranges over the remaining set of suspect candidates S(for which the third count value d₀₁ is zero).

21. The computer readable medium of claim 17, comprising further computer executable instructions for estimating the current fault probability value for multiple intermittent faults by:

establishing a plurality of unique diagnoses d to be evaluated, at least one of the diagnoses including a single one of the resources m, and at least one of the diagnoses including at least two of the resources m, each diagnosis having a unique assignment of either good or faulted to each member resource;

maintaining a set of four diagnosis count values for each diagnosis, the four diagnosis count values for each individual diagnosis including;

a first diagnosis count value d₁₁ indicating a number of failed plans where a bad resource of the diagnosis d was used,

a second diagnosis count value d₁₁ indicating a number of successful plans where a bad resource of the diagnosis d was used,

a third diagnosis count value d₀₁ indicating a number of failed plans where a good resource of the diagnosis d was not used, and

a fourth diagnosis count value d₀₀ indicating a number of successful plans where a good resource of the diagnosis d was not used;

maintaining a list S of remaining suspect candidate diagnoses for which the third diagnosis count value d₀₁ is zero; and

setting a posterior fault probability for the evaluated resources according to the following equation;

$p<br><br>\left(m<br><br>o_1,\mathrm{\dots <br><br>}<br><br>,o_t\right)=\underset{d<br><br><br><br>s.t.<br><br>m\in <br><br>d}{\sum <br><br>}<br><br>p<br><br>\left(d<br><br>o_1,\mathrm{\dots <br><br>}<br><br>,o_t\right).$

where m is the resource, o₁, . . . o_t is a set of observations and d ranges over the set of suspect candidates S for which the third count value d₀₁ is zero.

22. The computer readable medium of claim 17, comprising further computer executable instructions for estimating the current fault probability value for multiple persistent faults by:

maintaining a counter value i₁₁ associated with each set of modules m utilized in a failing plan i;

computing a failure term for the evaluated resources using the counter value i₁₁ according to the following equation;

Π

_{U fails}[1=Π

<sub>mε

bad(D)∩

U</sub>(1=p_b(m))]=

Π

<sub>iε

I</sub>[1=Π

<sub>mε

bad(D)∩

i</sub>(1=p_b(m))]ⁱ¹¹,

where I is a set of all such sets which have failed at least once, where m is the resource, and where p_b(m) is the probability that a resource m produces an incorrect output when faulted;

computing a success term for the evaluated resources using the counter m₁₀ for each resource according to the following equation;

$\underset{U<br><br><br><br>\mathrm{succeeds}}{\prod <br><br>}<br><br>\underset{m\in <br><br>\mathrm{bad}<br><br>\left(d\right)\bigcap <br><br>U}{\prod <br><br>}<br><br>\left(1-p_b<br><br>\left(m\right)\right)={\left(1-p_b<br><br>\left(m\right)\right)}^{m_{19}}.;<br><br>$

and

setting a posterior fault probability for the evaluated resources according to the following equation;

$p_t<br><br>\left(D<br><br>O,U\right)=\{\begin{array}{c}\underset{U<br><br><br><br>\mathrm{fails}}{\prod <br><br>}<br><br>\left[1-\underset{m\in <br><br>\mathrm{bad}<br><br>\left(D\right)\bigcap <br><br>U}{\prod <br><br>}<br><br>\left(1-p_b<br><br>\left(m\right)\right)\right]\\ \underset{U<br><br><br><br>\mathrm{succeeds}}{\prod <br><br>}<br><br>\underset{m\in <br><br>\mathrm{bad}<br><br>\left(D\right)\bigcap <br><br>U}{\prod <br><br>}<br><br>\left(1-p_b<br><br>\left(m\right)\right),\end{array}$

where O={o₁, . . . o_t} is a set of observations and U is an indication of whether the module was used in the plan associated with the observation o.