Bayesian Reliability Demonstration Research Articles

Flexible Bayesian reliability demonstration testing

AbstractThe aim is to demonstrate the reliability of a population at consecutive points in time, where a sample at each current point must prove that at least 100% of the devices function until the next point with a probability of at least . To test the reliability of the population, we flexibilise standard lifetime models by allowing the unknown parameter(s) of the corresponding counting process to vary in time. At the same time, we assign a prior distribution that assumes the parameters to be constant within a certain interval. This flexibilisation has several advantages: it can be applied for all parametric lifetimes; its Markov property allows the efficient derivation of the number of defective devices, even for a large number of testing times; and the inference is less certain and hence more realistic and leads to less frequent acceptance of poor quality populations. On the other hand, the inference is stabilised by the informative prior. Based on the flexibilisation of the homogeneous Poisson process (HPP), we derive acceptance sampling plans to test the future reliability of a population. Applying the zero failure sampling plans on simulations of Weibull processes shows their good frequentist properties and their robustness. In the case of utility meters subject to German regulations (Mess‐ und Eichverordnung (MessEV). 2014: 2010–2073.), application of the derived sequential sampling plans when the conditions of these plans are met can lead to an extension of the verification validity period. These sampling plans protect the consumer better than those from an HPP and are still cost efficient.

개발단계의 제품 인증을 위한 베이지언 2단계 신뢰성 실증시험의 통계적 설계

개발단계의 제품 인증을 위한 베이지언 2단계 신뢰성 실증시험의 통계적 설계

Software Reliability Demonstration Testing Plan Based on Bayesian Theory

For highly reliable software, it is expensive, time consuming or even infeasible to perform reliability testing by traditional Bayesian-based software reliability demonstration testing plan. Meanwhile, when determining the prior distribution function, people only consider conjugate prior distribution in order to realize the calculation in mathematics but ignores the characteristics of highly reliable software. To address this problem, by introducing the construction method of multilayer prior distribution function into the software reliability demonstration testing plan, this paper put forward a new Bayesian software reliability demonstration testing plan with zero-failure data, which can be used for highly reliable software reliability demonstration testing. Finally through examples, it illustrated the superiority of the method.

Continuous Bayesian Reliability Demonstration Test Method for Safety Critical Software

Continuous Bayesian Reliability Demonstration Test Method for Safety Critical Software

Bayesian reliability demonstration for systems with redundancy

Zero-failure testing for Bayesian reliability demonstration (BRD) is studied, aiming at minimal expected costs of testing and process failure. For the process after testing, reliability is formulated in terms of failure-free periods, based on the assumption that failure in the process would be catastrophic, causing the process to be discontinued and incurring high costs. BRD is considered for systems with redundancy, which are required to perform multiple independent types of task. Optimal BRD testing is also considered in combination with flexibility in the system redundancy, where more components can be installed to reduce test effort. Attention is restricted to systems with exchangeable components, with testing only at the component level. Generalizations are briefly discussed at the end of this paper.

Bayesian reliability demonstration with multiple independent tasks

Bayesian reliability demonstration with multiple independent tasks

Bayesian reliability demonstration for failure-free periods

We study sample sizes for testing as required for Bayesian reliability demonstration in terms of failure-free periods after testing, under the assumption that tests lead to zero failures. For the process after testing, we consider both deterministic and random numbers of tasks, including tasks arriving as Poisson processes. It turns out that the deterministic case is worst in the sense that it requires most tasks to be tested. We consider such reliability demonstration for a single type of task, as well as for multiple types of tasks to be performed by one system. We also consider the situation, where tests of different types of tasks may have different costs, aiming at minimal expected total costs, assuming that failure in the process would be catastrophic, in the sense that the process would be discontinued. Generally, these inferences are very sensitive to the choice of prior distribution, so one must be very careful with interpretation of non-informativeness of priors.

A BAYESIAN/CLASSICAL APPROACH TO RELIABILITY DEMONSTRATION

[This abstract is based on the author's abstract.] A generalized Bayesian reliability demonstration test planning procedure is proposed. The procedure is based on the exponential failure-time distribution and an inverted gamma prior distribution o..

BAYESIAN SINGLE-LEVEL BINOMIAL AND EXPONENTIAL RELIABILITY DEMONSTRATION TEST PLANS

Bayesian reliability demonstration test plans are developed for binomial and exponential sampling distributions using mixtures of beta and inverse gamma prior distributions, respectively. Both types of plans consider a single specified target reliability and rectify an important drawback of an existing well-known classical single-level test planning procedure. The plans are developed in such a way that they attain a specified probability of passing the test when the target reliability has been met as well as provide desired confidence that the target reliability has been met given that the test has been passed.

Exact computation for some sequential tests

Assume that the probability density function for the lifetime of a newly designed product has the form: , for some known H(·). The Exponential ϵ(θ), Rayleigh, and Pareto Pdf's are special cases. A class of continuous-time sequential tests based on the transformed total time on test and the total number of failures is proposed. The use of Steck's (1971) recursions for rectangle probabilities of uniform order statistics simplifies the exact computation for the operating characteristic, the average sample number, and the average failure number. Applications are given to Epstein and Sobel's (1955) continuous-time sequential probability ratio tests (SPRT), Anderson (1960) type of modification to the SPRT, a Bayesian sequential reliability demonstration test (BSRDT) and a predictive sequentila reliability demonstration test (PSRDT). Jeffreys’ prior appears inappropriate for both BSRDT's and PSRDT's. An ad hoc noninformative prior is used for BSRDT's and PSRDT's. Relationship between BSRDT's and PSRDT's is discussed. Numerical examples are given for illustrating the recursion formulas for the OC and ASN functions.

On the behaviour of some quantities used in Bayesian reliability demonstration tests : J. J. Higgins and C. P. Tsokos. IEEE Trans. Reliab.R-25 (4), 261 (October 1976)

On the behaviour of some quantities used in Bayesian reliability demonstration tests : J. J. Higgins and C. P. Tsokos. IEEE Trans. Reliab.R-25 (4), 261 (October 1976)

On the Behavior of Some Quantities Used in Bayesian Reliability Demonstration Tests

Equipment mean time between failures (MTBF) is assumed to be a frequency random variable. The goodness of fit of the uniform prior as a probability model for the MTBF is compared to the goodness of fit of the inverted gamma prior for actual failure data. These distributions can both be adequately fitted to the same failure data when the method of moments is used to fit the distributions. A comparison of posterior producer and consumer risks in a Bayesian reliability demonstration test is made using the fitted inverted gamma and uniform distributions as the priors. There can be rather large differences in the values of the posterior risks even when the two priors fit the data equally well or equally poorly.

Some approaches to Bayesian reliability demonstration : R. E. Schafer. Proc. Reliability and Maintainability Symp. Washington D.C., p. 253, 28–30 January, 1975

Some approaches to Bayesian reliability demonstration : R. E. Schafer. Proc. Reliability and Maintainability Symp. Washington D.C., p. 253, 28–30 January, 1975

Bayesian Reliability Demonstration

Bayesian Reliability Demonstration