Process for determining competing cause event probability and/or system availability during the simultaneous occurrence of multiple events

• US 6,816,813 B2
• Filed: 10/15/2002
• Issued: 11/09/2004
• Est. Priority Date: 10/15/2002
• Status: Expired due to Term

• Current Assignee: The Procter & Gamble Company
• Original Assignee: The Procter & Gamble Company
• Inventors: Rosen, Oscar, Tan, Jonathan Samuel
• Primary Examiner(s): Hoff, Marc S.
• Assistant Examiner(s): Raymond, Edward
• Application Number:
  US10/272,156
• Publication Number:
  US 20040078167A1
• Time in Patent Office: 756 Days
• Field of Search: 702/181, 702/33-35, 702/57-59, 702/81, 702/176, 702/182-184, 702/189, 714/100, 714/1, 714/2, 714/47, 714/48, 714/715, 714/728, 706/56, 703/14-17
• US Class Current: 702/181
• CPC Class Codes: G05B 23/0243 model based detection method, e.g. first-principles knowledge model
• CPC Class Codes: G06F 17/18 for evaluating statistical data , e.g. average values, frequency distributions, probability functions, regression analysis forecasting specially adapted for a specific administrative, business or logistic context G06Q10/04

Abstract

A method for determining the probability of observing an event. The event may occur either alone or in combination with one or more other events. The method may be non-combinatorial in that it does not require a separate calculation for each simultaneously occurring event, thereby significantly reducing computation time for complex systems having multiple events. Further, the method may be numerically reversed to calculate the probability of an event occurring based upon the number of observations. The method is particularly useful for predicting availability, component failure, or the possibility of a false start in production systems.

Claims

1. A method of calculating the probability of an event being observed during the occurrence of one or more simultaneous events in a system, said method comprising the step of calculating said probability according to the equation:

2. A non-combinatorial method according to claim 1, wherein ∫

₀^∞

·

h_i(t)*R_sys(t)dt=0, and comprising the steps of;

calculating the probability of each said event occurring independently of said other events according to the equation;

3. A method according to claim 2 wherein said step of calculating said probability that event will be observed when event i occurs simultaneously with at least one said other event is given by the equation:

4. A method according to claim 2 wherein said step of calculating said probability that event will be observed when event i occurs simultaneously with at least one said other event is given by the equation:

5. A method according to claim 2 further comprising the step of determining the probability of the simultaneous occurrence of more than n events according to the equations:

6. A method according to claim 5 further comprising the step of determining the probability of the simultaneous occurrence of more than n events, by considering progressively larger values of n until said Residual⁽ⁿ⁾ becomes less than a predetermined threshold using the equation:

7. A method according to claim 2, given a probability of observing Pevent0_i, of calculating the probability that event has occurred alone or with at least one other event by iteratively adjusting the value of R_i(0) until said equation is within a predetermined error threshold using the steps of:

(a) selecting a value of R_i(0);

(b) determining a value of Pevent0_i from the equation;

8. A method according to claim 1, wherein Pevent0_i=0, and comprising the step of determining the probability that an event in the system will be observed following a start-up of the system, by calculating said probability according to the equation:

9. A method according to claim 8 further comprising the step of determining the availability of said system having alternating uptimes and downtimes, said method further comprising the steps of:

(a) collecting event data for said uptimes and said downtimes;

(b) organizing said data by failure mode;

(c) selecting a competing mathematical model for uptime and a mathematical model for downtime for each failure mode;

(d) performing a calculation to determine the availability of the system, said calculation comprising the steps of;

(i) calculating the Mean Time Between Failures for the system according to the equation;

10. A method according to claim 9 further comprising the step of considering at least two simultaneously occurring events when determining said availability, each of said events being able to cause a false start event to occur, said at least two events being mutually exclusive.

11. A method according to claim 8 further comprising the step of rank ordering said events according to the effect each said event has on the availability of the system.

12. A method according to claim 8 wherein each said event has at least one uptime mathematical distribution parameter and at least one downtime mathematical distribution parameter, and further comprising the step of recalculating said system availability based upon at least one change in said at least one uptime mathematical distribution parameter and/or said at least one downtime mathematical distribution parameter.

13. A method according to claim 12, comprising the step of combining at least one uptime mathematical distribution parameter and/or at least one downtime mathematical distribution parameter from a plurality of systems, and using said combined at least one uptime and/or at least one downtime mathematical distribution parameter to select said competing mathematical model for uptime and/or said mathematical model for downtime.

14. A method for determining the probability of a plurality of events occurring simultaneously, said method comprising the steps of:

(a) obtaining data specifying the probability of each said event occurring independently of said other events;

(b) organizing said data according to a failure mode associated with said event;

(c) calculating the probability of said events being simultaneously observed using a non-combinatorial equation; and

(d) iteratively calculating the probability of each said event occurring independently of said other events based upon said non-combinatorial equation.

15. A computer readable medium comprising a method of calculating the probability of an event being observed during the occurrence of one or more simultaneous events in the system, wherein the probability is calculated according to the equation:

16. A medium according to claim 15, wherein said medium is selected from the group consisting of a carrier wave, a compact disc, and a network server.

17. A computer program for determining the probability of an event being observed during the occurrence of one or more simultaneous events in the system, wherein the probability is determined by the computer program according to the equation

18. A computer program according to claim 17, wherein ∫

₀^∞

h_i(t)*R_sys(t)dt or Pevent0_i is set equal to 0.