AMSAA maturity projection model based on stein estimation

Ellner, Paul M.; Hall, JW

doi:10.1109/rams.2005.1408374

Cited by 9 publications

(10 citation statements)

References 3 publications

(10 reference statements)

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“…The failure intensities for the collection of failure modes found in a complex system are shown to be adequately modeled as a random realization from a gamma distribution in both [17] and [18]. Using a gamma distribution in this way also recognizes what may be referred to as the vital few, trivial many property among mode failure intensities.…”

Section: Failure Mode Posterior Distributionmentioning

confidence: 99%

“…The posterior expected number of failure modes is found by first defining the indicator function for the unobserved failure mode as mode occurs by time otherwise (17) The posterior predicted mean of is found by examining the posterior probability that the unobserved failure mode is observed by some time . The likelihood of observing a failure mode by time is given from Assumption 3 in Section II.A as (18) Using the posterior distribution on the mode failure intensity in (4) with the , , and set to 0 for an unobserved failure mode, the unconditional marginal distribution for can be found by calculating the joint distribution of (4) and (18), and then marginalizing with respect to . The unconditional -expected value is given by (19) Summing over all unobserved modes in the system yields (20) and taking the limit as becomes large results in (21) Because is a Bernoulli random variable, summing over the unobserved modes yields a Binomial random variable.…”

Section: G Failure Modes Observed During Follow-on Testingmentioning

confidence: 99%

“…Ellner and Wald [17] provided the first projection model that allowed for arbitrary corrective action strategies by only using the first observed time of occurrence for the failure modes seen in testing. Ellner and Hall [18] extended this approach using a shrinkage estimation technique, with the limitation being that corrective actions must be delayed until the end of the test event. Crow also combined techniques from [12] and [16] in the popular Crow-Extended Model [19] to allow for arbitrary corrective actions.…”

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confidence: 99%

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A Bayesian Model for Complex System Reliability Growth Under Arbitrary Corrective Actions

Wayne

Modarres²

2015

IEEE Trans. Rel.

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This paper presents a new method for projecting the reliability growth of a complex continuously operating system. The model allows for arbitrary corrective action strategies, and it differs from other models of this type by using all available data rather than failure mode first occurrence times only. It also differs from other reliability growth projection models in that it provides a complete inference framework via the posterior distribution on the system failure intensity. A unique feature of this approach relative to other Bayesian techniques is the analytic expression for the failure intensity contribution from unobserved failure modes. Expressions for estimating the initial failure intensity, growth potential failure intensity, and the cumulative number of failure modes expected in future testing are also developed. Extensions to the basic framework are also developed. The first accounts for multiple systems under test, and the second develops the posterior distribution while allowing for uncertainty on the Fix Effectiveness Factor values that are assessed. Two separate goodness-of-fit procedures are presented for assessing the appropriateness of the underlying model assumptions.Index Terms-Bayesian reliability, fix effectiveness, reliability growth, reliability growth projection.

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Section: Failure Mode Posterior Distributionmentioning

confidence: 99%

Section: G Failure Modes Observed During Follow-on Testingmentioning

confidence: 99%

mentioning

confidence: 99%

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A Bayesian Model for Complex System Reliability Growth Under Arbitrary Corrective Actions

Wayne

Modarres²

2015

IEEE Trans. Rel.

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“…Denoting this failure intensity by r(T), where T denotes the duration of Phase I, the ACPM assessment of r(T)is based on: (1) the A and B-mode failure data generated during Phase I test duration, T; and (2) assessments of the FEFs for the B-modes surfaced during Phase I. Since the assessments of the FEFs are often largely based on engineering judgment, the resulting assessment, r (T) , of the system failure intensity after corrective action implementations is called a reliability projection (as opposed to a demonstrated assessment, which would be based solely on test data) [7]. The ACPM and estimation procedure was motivated by the desire to replace the widely used "adjustment procedure".…”

Section: Amsaa-crow Projection Model (Acpm)mentioning

confidence: 99%

MathematicalModel For Finding ACPM Of MTBF Projection In Plasma Vasopressin And Response To Treatment In Primary Nocturnal Enuresis

Lakshmi¹,

Senbagavalli²

2014

IOSRJEN

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-In this paper, we apply the results on both the model AMSAA Crow projection model and Reliability growth potential effects of vasopressin to examine the relation between nocturnal vasopressin release and response to treatment with the vasopressin analogue 1-desamino-8-D-Arginine Vasopressin (DDAVP) in children with primary mono symptomatic nocturnal enuresis. In this application the ability to respond to DDAVP is related to endogenous AVP production and is influenced by neuronal patterning in early infancy. The result concludes that ACPM of MTBF projection is estimated of the system failure intensity.ρ GP is the growth potential of Mean time between failure of AVP release according to the result in the estimated growth potential failure intensity , the estimate of the system MTBF growth potential. Thus the ACPM Projection for the system failure intensity, based onβ , the corresponding MTBF Projection value is nearly equal to the Projected system failure intensity based onβ m , the corresponding MTBF Projection values.

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“…This equation arises from considering the problem of estimating the system MTBF at the start of a new test phase after implementing corrective actions to failure modes surfaced in a proceeding test phase. This MTBF projection has been documented in [4] and is described in Section 4. Section 5 contains simulation results.…”

Section: Introductionmentioning

confidence: 99%

An approach to reliability growth planning based on failure mode discovery and correction using AMSAA projection methodology

Ellner¹,

Hall²

RAMS '06. Annual Reliability and Maintainability Symposium, 2006.

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Exact expressions for the expected number of surfaced failure modes and system failure intensity as functions of test time are presented under the assumption that the surfaced modes are mitigated through corrective actions. These exact expressions depend on a large number of parameters. Functional forms are derived to approximate these quantities that depend on only a few parameters. Such parsimonious approximations are suitable for developing reliability growth plans and portraying the associated planned growth path. Simulation results indicate that the functional form of the derived parsimonious approximations can adequately represent the expected reliability growth associated with a variety of patterns for the failure mode initial rates of occurrence. A sequence of increasing MTBF target values can be constructed from the parsimonious MTBF projection approximation based on the following:(1) planning parameters that determine the parsimonious approximation; (2) corrective action mean lag time with respect to implementation and; (3) test schedule that gives the number of planned Reliability, Availability, and Maintainability (RAM) test hours per month and specifies corrective action implementation periods.

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AMSAA maturity projection model based on stein estimation

Cited by 9 publications

References 3 publications

A Bayesian Model for Complex System Reliability Growth Under Arbitrary Corrective Actions

A Bayesian Model for Complex System Reliability Growth Under Arbitrary Corrective Actions

MathematicalModel For Finding ACPM Of MTBF Projection In Plasma Vasopressin And Response To Treatment In Primary Nocturnal Enuresis

An approach to reliability growth planning based on failure mode discovery and correction using AMSAA projection methodology

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