A Comparison of Three Methods for Calculating Lower Confidence Limits on System Reliability Using Binomial Component Data

Martz, Harry F.; Duran, Benjamin S.

doi:10.1109/tr.1985.5221967

Cited by 27 publications

(10 citation statements)

References 24 publications

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“…Binomial confidence limits are then constructed from the numbers of resampled system successes and failures. This method and the simple bootstrap were assessed using simulations by Martz and Duran ( 1985), who found that the former method is excessively conservative, whereas the latter is unreliable, often extremely nonconservative.…”

Section: Upper Confidence Limitsmentioning

confidence: 99%

Estimating Products in Forensic Identification Using DNA Profiles

Balding

1995

Journal of the American Statistical Association

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In many areas, such as reliability and forensic identification, it is of interest to estimate a product of unknown parameters, each of which is estimated from test data. The maximum likelihood estimator usually used in both applications is approximately unbiased but has an asymmetric sampling distribution, particularly when the sample size is not large. Consequently, most estimates understate the parameter value, often substantially, and this may be a serious drawback if "overoptimism" is highly undesirable. Further, widely used methods of interval estimation based on confidence limits suffer from a range of theoretical and computational problems. Alternative methods of estimation are developed and discussed, based on frequentist, Bayesian, and likelihood approaches.

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Section: Upper Confidence Limitsmentioning

confidence: 99%

Estimating Products in Forensic Identification Using DNA Profiles

Balding

1995

Journal of the American Statistical Association

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“…If this information can be considered in the test plan, a more efficient test can be designed. Much research on how to estimate system reliability from component reliabilities has been done [2][3][4][5][6][7][8][9]. These methods can be classified into three categories:…”

Section: Introductionmentioning

confidence: 99%

“…• Approximated analytical method [2][3][4]6] • Simulation method [4][5][6]9] • Bayesian method [7][8][9] The variance decomposition method is one of the most popular analytical methods. Coit [2] and Jin and Coit [3] used the estimated means and the variances of component reliabilities to get the mean and variance of the system reliability first, and then computed the confidence interval for the system reliability by assuming the system reliability is lognormally distributed.…”

Section: Introductionmentioning

confidence: 99%

“…Bayesian theory was also applied in the system reliability estimation in the last two decades [7][8][9]. Although the Bayesian method can handle the non-failure situation, it is cumbersome for practical use and the results are affected by the assumed prior distribution.…”

Section: Introductionmentioning

confidence: 99%

“…In additional to the above analytical solutions, bootstrap estimation is also studied in recent years [5,6,9]. In the use of simulation, for a zero failure subsystem, its reliability is either simulated from an assumed beta prior distribution [5], or using ε − = 1 i r for some small value of ε [9].…”

Section: Introductionmentioning

confidence: 99%

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Reliability estimation for one-shot systems with zero component test failures

Guo¹,

Honecker²,

Mettas³

et al. 2010

2010 Proceedings - Annual Reliability and Maintainability Symposium (RAMS)

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& CONCLUSIONSTests for one-shot systems such as missiles and rockets are very expensive. In order to design an efficient test plan to demonstrate the required reliability in the final system test, system reliability should be studied in advance. Before the final system tests, many subsystem level tests usually have already been conducted by customers and manufacturers. Therefore, the system reliability can be estimated using the information obtained from these tests before the final system test. Due to the highly reliable nature of one-shot systems, it is very unlikely to observe many failures, even at the subsystem level tests. To accurately estimate the system reliability with few failures or even without failures is very challenging. A lot of research has been done on how to estimate the system reliability and its confidence intervals from its subsystem test data. However, most of them require failures at the sub-level tests. When there are no failures, these methods do not work.In this paper, a flexible and practical method is designed to estimate the system reliability and its confidence bounds when there are few or no failures during the subsystem tests. This method can be applied to series, parallel and complex systems. The estimated system reliability information is then used to design an efficient test plan for the final system reliability demonstration test. A case study shows that the proposed method is very efficient and accurate when compared with existing methods and simulation results.

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References

2000

Reliability

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A Comparison of Three Methods for Calculating Lower Confidence Limits on System Reliability Using Binomial Component Data

Cited by 27 publications

References 24 publications

Estimating Products in Forensic Identification Using DNA Profiles

Estimating Products in Forensic Identification Using DNA Profiles

Reliability estimation for one-shot systems with zero component test failures

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