PROCESS FOR DETERMINING COMPETING CAUSE EVENT PROBABILITY AND/OR SYSTEM AVAILABILITY DURING THE SIMULTANEOUS OCCURRENCE OF MULTIPLE EVENTS

• US 20040078167A1
• Filed: 10/15/2002
• Published: 04/22/2004
• Est. Priority Date: 10/15/2002
• Status: Active Grant

• Current Assignee: The Procter & Gamble Company
• Original Assignee: The Procter & Gamble Company
• Inventors: Rosen, Oscar, Tan, Jonathan Samuel
• Granted Patent: US 6,816,813 B2
• Time in Patent Office: Days
• 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:

Pevent_i=∫

₀^∞

h_i(t)*R_sys(t)dt+Pevent0_i,

wherein Pevent_i is the probability that a particular event will be observed;

h_i(t) is the instantaneous rate of occurrence of event i;

R_sys(t) is the reliability function of the system in which said events may occur; and

Pevent0_i is the probability that an event will be observed when said event occurs simultaneously with other events; and

i represents a particular event.

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;

Pevent0_i=Σ

_n=1^Ny_i⁽ⁿ⁾

wherein y_i⁽ⁿ⁾ is the probability the event of interest will be observed when said event occurs simultaneously with n−

1 other events; and

wherein N is the total number of possible events;

determining the probability that event i will be observed alone according to the equation;

y_i⁽1)=[(1−

R_i(0))/R_i(0)]*Π

_j=1^NR_j(0)

wherein R_j(0) is the probability the event j will not occur; and

calculating the probability that event i will be observed when said event i occurs simultaneously with at least one other event.

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:

y_i⁽ⁿ⁺¹⁾=[(1−

R_i(0))/(R_i(0)*(n+1))]*Σ

_j=1^Ny_j⁽ⁿ⁾−

n*y_i⁽ⁿ⁾]

wherein n+1 indicates the addition of another simultaneously occurring event to consideration;

y_i⁽ⁿ⁾ is the probability of the event of interest being observed as it occurs with n−

1 other events, when said event is randomly selected from all of said simultaneously occurring events; and

n is the number of simultaneously occurring events under consideration.

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:

y_i⁽ⁿ⁺¹⁾=[(1−

R_i(0))/(R_i(0)]*Σ

_j=i+1^Ny_j⁽ⁿ⁾

wherein n+1 indicates the addition of another simultaneously occurring event to consideration; and

y_i⁽ⁿ⁾ is the probability of the event of interest being observed as it occurs with n−

1 other events and event k will always be observed over event p for all p>

k, wherein p and k are factors which designate the dominance of event k over event p.

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:

Residual⁽⁰⁾=1−

Π

_j=1^NR_j(0) Residual⁽ⁿ⁾=Residual<sup>(n−

1)</sup>−

Σ

_j=1^Ny_j⁽ⁿ⁾

wherein Residual⁽0) is the probability of any event occurring,

Residual⁽ⁿ⁾ is the probability of any event occurring when more than n events are simultaneously occurring, and said event is one of said events which are simultaneously occurring;

Residual<sup>(n−

1)</sup> is the probability of any event occurring when more than n−

1 events are simultaneously occurring; and

N is the total number of events.

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:

Pevent0_i=Σ

^S_n=1y⁽ⁿ⁾

wherein S≦

N.

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;

Pevent_determined0_i=Σ

_n=1^Ny_i⁽ⁿ⁾;

(c) if the determined value of Pevent0_i is within a predetermined tolerance from the known value of Pevent0_i then stop; and

(d) converging the value of Pevent_determined0_i−

Pevent_actual0_i for all values of i=1, 2, 3 . . . N until a predetermined tolerance is reached.

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:

Pevent_i=∫

₀^∞

h_i(t)*R_sys(t) dt.

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;

MTBF_sys=∫

₀^∞

R_sys(t)d(t)

 

wherein MTBF_sys is the mean time between failures for all failure modes in the system;

 

and R_sys(t) is the reliability function of the system;

(ii) calculating for each failure mode the probability that said failure mode will cause said system to fail according to the equation;

Pevent_i=∫

₀^∞

h_i(t)*R_sys(t)dt

 

wherein Pevent_i is the probability that a particular failure mode will cause the system to stop during an uptime of the system;

 

h_i(t) is the instantaneous rate of failure of failure mode i; and

 

R_sys(t) is the reliability function of the system, said reliability function being based upon said mathematical model for uptime;

(iii) calculating the Mean Time to Repair the system according to the equation;

MTTR_sys=Σ

(Pevent_i*MTTR_i)

 

wherein MTTR_sys is the mean time to repair the system upon a failure mode occurring and MTTR_i is the mean time to repair failure mode i when that failure mode occurs; and

(iv) calculating the availability of the system according to the equation;

Availability=MTBF_sys/(MTBF_sys+MTTR_sys).

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:

Pevent_i=∫

₀^∞

h_i(t)*R_sys(t)dt+Pevent0_i,

wherein Pevent_i is the probability that a particular event will be observed;

h_i(t) is the instantaneous rate of occurrence of event i.

R_sys(t) is the reliability function of the system in which said events may occur; and

Pevent0_i is the probability that one or more events will simultaneously be observed when said event occurs simultaneously with other events; and

i represents a particular event.

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

Pevent_i=∫

₀^∞

h_i(t)*R_sys(t)dt+Pevent0_i,

wherein Pevent_i is the probability that a particular event will be observed;

h_i(t) is the instantaneous rate of occurrence of event i; and

R_sys(t) is the reliability function of the system in which said events may occur;

and Pevent0_i is the probability that one or more events will simultaneously be observed when said event occurs simultaneously with other events; and

i represents a particular event.

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.