Method and apparatus for predicting multi-part performability

• US 6,934,673 B2
• Filed: 05/25/2001
• Issued: 08/23/2005
• Est. Priority Date: 05/25/2001
• Status: Expired due to Fees

• Current Assignee: Hewlett-Packard Development Company, L.P. (HP Inc.)
• Original Assignee: Hewlett-Packard Development Company, L.P. (HP Inc.)
• Inventors: Alvarez, Guillermo, Uysal, Mustafa, Merchant, Arif A., Wilkes, John, Becker-Szendy, Ralph
• Primary Examiner(s): THOMSON, WILLIAM D
• Application Number:
  US09/865,999
• Publication Number:
  US 20020177989A1
• Time in Patent Office: 1,551 Days
• Field of Search: 703/2, 703/20, 703/21, 703/22, 703/24, 703/25, 703/13, 703/27, 714/44, 714/47, 714/48, 702179-181, 702182-186
• US Class Current: 703/21
• CPC Class Codes: G06F 11/008 Reliability or availability analysis
• CPC Class Codes: G06F 11/3447 Performance evaluation by modeling
• CPC Class Codes: G06F 11/3452 Performance evaluation by statistical analysis

Abstract

A method of and apparatus for determining whether a multi-component target system meets a given multi-part performability requirement is provided. A description of the target system, failure probabilities for components of the target system and a multi-part performability requirement for the target system are obtained. The multi-part performability requirement indicates desired performance levels and corresponding fractions of time. One or more failure-scenarios are successively computed that represent one or more states of the target system having zero or more components failed and a corresponding probability of occurrence of the one or more of the states of the target system. Performance of the target system is modeled under the failure scenarios using a performance predictor module for generating a multi-part performability function. The multi-part performability function is compared with said multi-part performability requirement to determine whether the target system meets the multi-part performability requirement.

Claims

1. A method of determining whether a multi-component target system meets a given multi-part performability requirement, the method comprising:

obtaining a description of the target system and failure probabilities for components of the target system that can fail independently,

obtaining a multi-part performability requirement for the target system, the multi-part performability requirement indicating desired performance levels for the target system and corresponding fractions of time,

producing a first failure-scenario of said target system using a computer-implemented failure scenario generator module that receives as input the target system description and the failure probabilities, the first failure-scenario comprising one or more states of the target system having zero or more components failed and a corresponding probability of occurrence of the one or more of the states of the target system,

modeling performance of the target system under the first failure scenario using a computer-implemented performance predictor module for generating a multi-part performability function of said target system, the performance predictor module receiving as input said first failure-scenario,

comparing said multi-part performability function with said multi-part performability requirement, and

determining from said comparing whether said target system meets said multi-part performability requirement.

2. The method as set forth in claim 1, the step of comparing further comprising:

calculating if said first failure-scenario provides sufficient data for generating a multi-part performability function determinative of target system performance capability when compared to said multi-part performability requirements, and

if so, proceeding with said step of determining, or

if not

repeating said steps of producing, generating, comparing, and calculating for successive next failure-scenarios until sufficient data is obtained for generating a multi-part performability function determinative of said target system performance capability when compared to said multi-part performability requirements.

3. The method as set forth in claim 1, performance predictor module also receiving as input a workload description.

4. The method as set forth in claim 1, the step of producing comprising:

synthesizing a model of the target system based on predetermined individual components of the target system wherein each of said components has a characteristic failure specification.

5. The method as set forth in claim 4, further comprising the steps of:

combining components of the target system as a macro-component;

computing the failure probability of the macro-component as a function of the failure probabilities of its respective components; and

using macro-components in said computing.

6. The method as set forth in claim 1, wherein the step of producing is performed in accordance with the following:

let “

FP(c)”

denote a probability that a system component “

c”

of the target system will fail;

then,

(1) Let “

D”

represent a failure-free system;

(2) Let “

c₁, c₂ . . . c_mf be components that can fail independently in D;

(3) Let “

sf”

be the number of concurrent failures being considered in the last invocation (initially

     0);

(4) Let “

s”

be the ordinal number, among the scenarios with exactly “

sf”

failures, of the scenario returned in the last invocation (initially

     0);

(5) If there exist exactly “

s”

scenarios with “

sf”

concurrent failures, then sf=sf+1;

s=0;

(6) If sf≦

mf, then s=s+1, otherwise exit;

(7) choose a₁, a₂ . . . a_sf (where a_i, i=1, . . . sf are different integers between 1 and mf) such that there are exactly “

s−

1”

scenarios with “

sf”

concurrent failures more likely to occur than c_a1, c_a2 . . . c_asf,

(8) set sc=D with components c_a1, c_a2 . . . c_asf marked as failed;

(9) set p=FP(c_a1), x FP(c_a2) x . . . x FP(c_a(sf)) x (1−

FP(c_b1)), x . . . x (1−

FB(c_b(mf-sf))), where c_b1, . . . C_b(mf-sf) are all the components that did not fail in “

sc”

; and

(10) return (sc,p).

7. The method as set forth in claim 2, further comprising:

grouping states together wherein said target system is non-functional, and

representing the grouped states in the multi-part performability function.

8. The method as set forth in claim 2, further comprising:

grouping states together wherein the target system is fully functional; and

representing the grouped states in the multi-part performability function.

9. The method as set forth in claim 2,

wherein the failure-scenarios are computed according to an order of likelihood of occurrence.

10. The method as set forth in claim 9, comprising:

if a multiplicity of like components having like failure probability and effect are employed within said target system, treating said multiplicity of like components as a single component of said target system.

11. The method as set forth in claim 2, wherein repeating the steps of producing, generating, comparing, and calculating for successive next failure-scenarios is performed in accordance with the following:

(1) set i=1;

(2) generate the next state S_i and its occurrence probability OP(S_i);

(3) compute the performance U(S_i) using the performance predictor module; and

(4) if, $\underset{k=1}{\overset{i}{\sum <br><br>}}<br><br>O<br><br>\text{\hspace{1em}<br><br>}<br><br>P<br><br>\left(S_k\right)<br><br>1<br><br>\left(U<br><br>\left(S_k\right)\ge <br><br>r_j\right)\ge <br><br>f_j,\text{\hspace{1em}<br><br>}<br><br>\mathrm{for}<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{all}<br><br>\text{\hspace{1em}<br><br>}<br><br>j=1,2,\mathrm{\dots <br><br>}<br><br>\text{\hspace{1em}<br><br>}<br><br>n,$

then the target system is capable of fulfilling the multi-part performability requirements, exit and report;

or

(5) if, $\underset{k=1}{\overset{i}{\sum <br><br>}}<br><br>O<br><br>\text{\hspace{1em}<br><br>}<br><br>P<br><br>\left(S_k\right)<br><br>1<br><br>\left(U<br><br>\left(S_k\right)<<br><br>r_j\right)\ge <br><br>1-f_j,\text{\hspace{1em}<br><br>}<br><br>\mathrm{for}<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{any}<br><br>\text{\hspace{1em}<br><br>}<br><br>\text{\hspace{1em}<br><br>}<br><br>j=1,2,\mathrm{\dots <br><br>}<br><br>\text{\hspace{1em}<br><br>}<br><br>n,$

then the target system fails the multi-part performability requirements, exit and report; and

otherwise,

(6) set i=i+1 and go to step (2).

12. A computer readable media comprising computer code for implementing a method of determining whether a multi-component target system meets a given multi-part performability requirement, the method comprising the steps of:

producing a first failure-scenario of said target system, the first failure-scenario comprising one or more states of the target system having zero or more components failed and a corresponding probability of occurrence of the one or more of the states of the target system;

modeling performance of the target system under the first failure scenario for generating a multi-part performability function;

comparing said multi-part performability function with said multipart performability requirements; and

determining from said comparing whether said target system has a capability of performing said multi-part performability requirements.

13. The media as set forth in claim 12, further comprising computer code for:

calculating if said first failure-scenario provides sufficient data for generating a multi-part performability first function determinative of predicting multi-part performability when compared to said multi-part performability requirements, and

if so, proceeding with said step of determining;

or

if not,

repeating the steps of producing, generating, comparing, and calculating for successive next failure-scenarios until sufficient data is obtained for generating a multi-part performability function determinative of the target system performance capability when compared to the multi-part performability requirements.

14. The media as set forth in claim 13, further comprising computer code for:

grouping states together wherein said target system is non-functional; and

grouping states together wherein said target system is fully functional in accordance with said performance requirements.

15. The media as set forth in claim 14,

wherein failure-scenarios are computed according to an order of likelihood of occurrence.

16. A computer system for determining whether a multi-component target system meets a given multi-part performability requirement, comprising:

a failure scenario generator module for producing a first failure-scenario of the target system from a description of the target system and failure probabilities for components of the target system that can fail independently, the first failure-scenario comprising one or more states of the target system having zero or more components failed and a corresponding probability of occurrence of the one or more of the states of the target system,

a performance predictor module for modeling performance of the target system under the first failure scenario wherein a multi-part performability function of the target system is generated from the performance predicted for the target system, the performance predictor module receiving as input the first failure-scenario, and

a performability evaluator module for comparing the multi-part performability function with a multi-part performability requirement for the target system, the multi-part performability requirement indicating desired performance levels for the target system and corresponding fractions of time, and for determining from the comparison whether the target system meets the multi-part performability requirement.

17. The computer system as set forth in claim 16, wherein the performability evaluator module determines whether the first failure-scenario provides sufficient data for generation of a multi-part performability function determinative of target system performance capability when compared to the multi-part performability requirements, and

if so, the performability evaluator module proceeds with determining from the comparison whether the target system meets the multi-part performability requirement, or

if not, successive next failure-scenarios are evaluated until sufficient data is obtained for generating a multi-pan performability function determinative of the target system performance capability when compared to the multi-part performability requirements.

18. The computer system as set forth in claim 16, wherein the performance predictor module also receives as input a workload description.

19. The computer system as set forth in claim 16, wherein the performance predictor synthesizes a model of the target system based on predetermined individual components of the target system wherein each of said components has a characteristic failure specification.

20. The computer system as set forth in claim 16, wherein components of the target system are combined as a macro-component and the failure probability of the macro-component is computed as a function of the failure probabilities of its respective components.

21. The computer system as set forth in claim 16, wherein the failure scenario generator operates in accordance with the following:

let “

FP(c)”

denote a probability that a system component “

c”

of the target system will fail;

then,

(1) Let “

D”

represent a failure-free system;

(2) Let “

c₁, C₂ . . . c_mf be components that can fail independently in D;

(3) Let “

sf”

be the number of concurrent failures being considered in the last invocation (initially

     0);

(4) Let “

s”

be the ordinal number, among the scenarios with exactly “

sf”

failures, of the scenario returned in the last invocation (initially

     0);

(5) If there exist exactly “

s”

scenarios with “

sf”

concurrent failures, then sf=sf+1;

s=0;

(6) If sf≦

mf, then s=s+1, otherwise exit;

(7) choose a₁, a₂ . . . a_sf (where a_i, i=1, . . . sf are different integers between 1 and mf) such that there are exactly “

s−

1”

scenarios with “

sf”

concurrent failures more likely to occur than c_a1, C_a2 . . . c_asf;

(8) set sc=D with components c_a1, c_a2 . . . c_asf marked as failed;

(9) set p=FP(c_a1) x FP(c_a2) x . . . x FP(c_a(sf)) x (1−

FP(c_b1)) x . . . x (1−

FB(c_b(mf-sf))), where c_b1, . . . C_b(mf-sf) are all the components that did not fail in “

sc”

; and

(10) return (sc,p).

22. The computer system as set forth in claim 16, wherein states are grouped together in which the target system is non-functional, and the grouped states are represented in the multi-part performability function.

23. The computer system as set forth in claim 16, wherein states are grouped together in which the target system is fully functional, and the grouped states are represented in the multi-part performability function.

24. The computer system as set forth in claim 16, wherein the failure-scenarios are computed according to an order of likelihood of occurrence.

25. The computer system as set forth in claim 24, wherein if a multiplicity of like components having like failure probability and effect are employed within the target system, the multiplicity of like components are treated as a single component of the target system.

26. The computer system as set forth in claim 16, wherein the computer system operates in accordance with the following:

(1) set i=1;

(2) generate the next state S_i and its occurrence probability OP(S_i);

(3) compute the performance U(S_i) using the performance predictor module; and

(4) if, $\underset{k=1}{\overset{i}{\sum <br><br>}}<br><br>O<br><br>\text{\hspace{1em}<br><br>}<br><br>P<br><br>\left(S_k\right)<br><br>1<br><br>\left(U<br><br>\left(S_k\right)\ge <br><br>r_j\right)\ge <br><br>f_j,\text{\hspace{1em}<br><br>}<br><br>\mathrm{for}<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{all}<br><br>\text{\hspace{1em}<br><br>}<br><br>j=1,2,\mathrm{\dots <br><br>}<br><br>\text{\hspace{1em}<br><br>}<br><br>n,$

then the target system is capable of fulfilling the multi-part performability requirements, exit and report;

or

(5) if, $\underset{k=1}{\overset{i}{\sum <br><br>}}<br><br>O<br><br>\text{\hspace{1em}<br><br>}<br><br>P<br><br>\left(S_k\right)<br><br>1<br><br>\left(U<br><br>\left(S_k\right)<<br><br>r_j\right)\ge <br><br>1-f_j,\text{\hspace{1em}<br><br>}<br><br>\mathrm{for}<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{any}<br><br>\text{\hspace{1em}<br><br>}<br><br>\text{\hspace{1em}<br><br>}<br><br>j=1,2,\mathrm{\dots <br><br>}<br><br>\text{\hspace{1em}<br><br>}<br><br>n,$

then the target system fails the multi-part performability requirements, exit and report; and

otherwise,

(6) set i=i+1 and go to step (2).