A Bayes Reliability Growth Model for A Development Testing Program

Fard, Nasser; Dietrich, D.L.

doi:10.1109/tr.1987.5222474

Cited by 25 publications

(14 citation statements)

References 6 publications

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“…3 can be useful for indicating any differences between the observed data and the model assumptions. The results in (27) and (28) use both the prior and the likelihood, so reasonable agreement between the distribution and the observed data should indicate that the model assumptions are reasonable.…”

Section: A Prior Predicted Cumulative Number Of Failure Modesmentioning

confidence: 89%

“…By considering the prior distribution in place of the posterior, the -expected value for a single failure mode in (19) is modified slightly to be (27) Note that in this context is any time in the interval . Summing over all failure modes, and taking the limit as becomes large, yields The distributional results from Section II.G will also apply in this case, and the distribution on the prior number of failure modes will be Poisson with the -mean given by (28). An example plot showing the cumulative observed number of failure modes and the prior predicted distribution as a function of time is shown in Fig.…”

Section: A Prior Predicted Cumulative Number Of Failure Modesmentioning

confidence: 99%

“…The result in (20) is then updated as (37) For the prior number of failure modes used in the visual goodness of fit in Section IV, the likelihood of observing a failure mode on at least one of the systems by time is updated as (38) The expression in (28) is then modified to be (39) When comparing the observed failure modes to the prior prediction, note that the time of first occurrence for a failure mode should be the minimum of the occurrence times observed over all of the systems under test. Modifications to the chi-square test in Section IV.B are not necessary for multiple systems, as (33) and (34) can be used directly in place of (9) and (10).…”

Section: A Multiple Systems Under Testmentioning

confidence: 99%

“…The time variance of the parameter in this case implicitly models the reduction in mode failure intensity due to corrective action. Smith developed a Bayesian reliability growth model for developmental test programs [27], with corrections given by Fard and Dietrich [28]. The model assumes ordered reliability improvement at each stage along with uniform prior distributions.…”

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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: A Prior Predicted Cumulative Number Of Failure Modesmentioning

confidence: 89%

Section: A Prior Predicted Cumulative Number Of Failure Modesmentioning

confidence: 99%

Section: A Multiple Systems Under Testmentioning

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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“…He assumed a uniform prior on the parameter space. Fard and Dietrich (1987) made a comment on Smith's derivation of the proportionality constant of the joint posterior density. This prior is totally determined by the number, m, of the stages in RGT, and has no parameter that needs to be adjusted to an actual situation.…”

Section: Introductionmentioning

confidence: 99%

On Bayesian Analysis of Binomial Reliability Growth

Zhao

2002

JJSS

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This paper introduces a new class of prior distributions for reliability growth tests with binomial data under the monotone model. The proposed prior has a conditional form, which accords well with various actual situations in reliability growth tests. The expressions of the corresponding means and variances for all stages with and without conditioning are obtained, and the relationship between the shape of the prior distributions and their parameters are discussed. These results are helpful in order to incorporate expert opinions. The posterior density and the Bayesian lower bound of the relibility at the end of the test, and a computation method for them are given. The new family of prior distributions includes the uniform prior used by Smith (1977) and the ordered Dirichlet priors presented by Soyer (1992, 1993) as special cases. Comparisons are made by two examples, which show the limitations of the later two.

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Development programs for one‐shot systems using multiple‐state design reliability models

Shevasuthisilp

Vardeman

2004

Naval Research Logistics

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Design reliability at the beginning of a product development program is typically low, and development costs can account for a large proportion of total product cost. We consider how to conduct development programs (series of tests and redesigns) for one-shot systems (which are destroyed at first use or during testing). In rough terms, our aim is to both achieve high final design reliability and spend as little of a fixed budget as possible on development. We employ multiple-state reliability models. Dynamic programming is used to identify a best test-and-redesign strategy and is shown to be presently computationally feasible for at least 5-state models. Our analysis is flexible enough to allow for the accelerated stress testing needed in the case of ultra-high reliability requirements, where testing otherwise provides little information on design reliability change.

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A Bayes Reliability Growth Model for A Development Testing Program

Cited by 25 publications

References 6 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

On Bayesian Analysis of Binomial Reliability Growth

Development programs for one‐shot systems using multiple‐state design reliability models

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