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Weibull Renewal Analysis
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English
Abstract
Renewal theory concerns itself with the replacement of randomly failing parts. In the simplest case we have a one component system which is kept running continuously by replacing a failed component at the instant of failure with an identical “new” component. The random variable N(t) = the number of failures (or replacements) to time t is then of interest in many types of reliability analysis. In this paper the distribution of N(t) is considered when the underlying failure law is a Weibull distribution. Tables of the mean and standard deviation of N(t) for various values of the Weibull slope parameter are presented. Applications to warranty and spare parts analyses are also noted.
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Citation
White, J., "Weibull Renewal Analysis," SAE Technical Paper 640624, 1964, https://doi.org/10.4271/640624.Also In
References
- Barlow, R. E. Hunter L. C. Proschan, F. “Probabilistic Models in Reliability Theory.” New York, N.Y. John Wiley and Sons, Inc.
- Cox, D. R. “Renewal Theory.” New York, N.Y. John Wiley and Sons, Inc. 1962
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- Smith, W. L. “On the Cumulants of Renewal Processes.” Biometrika Vol. 46 1959
- Smith, W. L. “Renewal Theory and its Ramifications.” Journal of the Royal Statistical Society, B Vol. 20 1958
- Smith, W. L. “Asymptotic Renewal Theorems. ” Proceedings of the Royal Society of Edinburgh, A Vol. 64 1954
- Weibull, W. “A Statistical Distribution Function of Wide Applicability.” Journal of Applied Mechanics Vol. 18 1951
- White, J. S. “Estimation for the Weibull Distribution.” Transactions of the seventeenth annual convention of the American Society for Quality Control Cincinnati 1963