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Systems Engineering Program. Department of Engineering Management, Information and Systems. EMIS 7305/5305 Systems Reliability, Supportability and Availability Analysis. Systems Reliability Growth Modeling and Analysis. Dr. Jerrell T. Stracener, SAE Fellow. Leadership in Engineering.

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Systems Engineering Program

Department of Engineering Management, Information and Systems

EMIS 7305/5305

Systems Reliability, Supportability and Availability Analysis

Systems Reliability Growth Modeling and Analysis

Dr. Jerrell T. Stracener, SAE Fellow

Leadership in Engineering


  • R&M 2000 Building Blocks

  • Growth Curves

  • Reliability growth is the positive improvement

  • of system reliability through the systematic and

  • permanent removal of the reasons for failure

  • Growth curves are management tools; they

  • show the manager where the system reliability

  • is now and where is must go

  • Air Force Regulation 800-18, Air Force reliability

  • and maintainability program, requires the use of

  • reliability growth curves to track improvements

  • to achieve reliability requirements


  • R&M 2000 Building Blocks

  • Growth Curves

  • Decision makers can use these growth curves

  • to assess the need to reallocate resources or

  • change schedules to achieve R&M requirements

  • Reliability improvements can be achieved

  • through testing to identify deficiencies and/or

  • weaknesses, followed by positive actions to

  • correct them. Test, analyze, and fix (TAAF) is

  • one process for achieving reliability growth.


Reliability Growth Model Types

Engineering Statistical

models models

Deterministic Models Poisson Process Time Series

models

Endless-Burn-In AMSAA/Duane ARIMA

Cox-Lewis

Modified Duane



  • The Duane Model

  • In 1964 J.T Duane, with General Electric Company, published a paper in the IEEE Transactions on Aerospace (Vol. 2, No. 2, April 1964) titled “Learning Curve Approach to Reliability Monitoring.”

  • Duane formulated a mathematical relationship for forecasting and monitoring reliability improvement as a function of cumulative time.

  • The model was based on concluding, from analysis of data, that a straight line provided a reasonably good fit to cumulative MTBF vs. cumulative time when plotted on a log-log scale.


  • Reliability Growth Analysis

  • To meet reliability goals, a technique must be

  • used to track reliability and signal when corrective

  • action should be taken

  • J.T. Duane

  • (1964) noticed

  • that in many

  • cases this

  • relationship

  • followed a

  • straight

  • line on a

  • log-log plot


  • The Duane Model

  • The Duane Model can be formulated in two different,

  • but mathematically equivalent, ways: MTBF as a

  • Function of time and failure rate as a function of time.

  • In terms of MTBF, the Duane Model is:

  • where MTBFc(t) is the cumulative MTBF at cumulative

  • time t, t is cumulative time, and  and  are

  • parameters of the model.


The Duane Model

The parameter  is the reliability improvement, or

growth, rate and  is cumulative MTBF at t=1 hour.

Notice that the graph of the Duane Model on log-log

scale is a straight line since

log MTBF(t) = log k +  log t

which is of the form

y = a + bx


The Duane Model

Since

where rc=the cumulative number of failures in time t,


The Duane Model

Then

But since


  • The Duane Model

  • The instantaneous MTBF as a function of

  • cumulative test time is obtained mathematically

  • from MTBFC(t) and is given by

  • where MTBF(t) is the instantaneous MTBF at time

  • t and is interpreted as the equipment MTBF if

  • reliability development testing was terminated after

  • a cumulative amount of testing time, t.


1000

Instantaneous

MTBF

100

Cumulative

10

1000

10

100

10000

Cumulative Test Hours

MTBF Growth Curves


  • The Duane Model

  • The Duane Model may also be formulated in

  • terms of equipment failure rate as a function of

  • cumulative test time as follows:

  • and

  • where

  • C(t) is the cumulative failure rate after test time t

  • k* is the initial failure rate and k*=1/k,

  • B is the failure rate growth (decrease rate)

  • i(t) is the instantaneous failure rate at time t


The Duane Model

The initial MTBF or failure rate at the beginning of

RDT depends on a number of other factors including

type of equipment (electronics, structure, etc.)

complexity of the design and equipment operation,

technology, in terms of MTBF of failure rate,

depends on the same factors as does the starting

value, and this in addition depends on management

FRACAS and TAAF implementation.







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