Reliability analysis: assessment of hardware and human reliability
- Authors: Mafu, Masakheke
- Date: 2017
- Subjects: Bayesian statistical decision theory , Reliability (Engineering) , Human machine systems , Probabilities , Markov processes
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: http://hdl.handle.net/10962/6280 , vital:21077
- Description: Most reliability analyses involve the analysis of binary data. Practitioners in the field of reliability place great emphasis on analysing the time periods over which items or systems function (failure time analyses), which make use of different statistical models. This study intends to introduce, review and investigate four statistical models for modeling failure times of non-repairable items, and to utilise a Bayesian methodology to achieve this. The exponential, Rayleigh, gamma and Weibull distributions will be considered. The performance of the two non-informative priors will be investigated. An application of two failure time distributions will be carried out. To meet these objectives, the failure rate and the reliability functions of failure time distributions are calculated. Two non-informative priors, the Jeffreys prior and the general divergence prior, and the corresponding posteriors are derived for each distribution. Simulation studies for each distribution are carried out, where the coverage rates and credible intervals lengths are calculated and the results of these are discussed. The gamma distribution and the Weibull distribution are applied to failure time data.The Jeffreys prior is found to have better coverage rate than the general divergence prior. The general divergence shows undercoverage when used with the Rayleigh distribution. The Jeffreys prior produces coverage rates that are conservative when used with the exponential distribution. These priors give, on average, the same average interval lengths and increase as the value of the parameter increases. Both priors perform similar when used with the gamma distribution and the Weibull distribution. A thorough discussion and review of human reliability analysis (HRA) techniques will be considered. Twenty human reliability analysis (HRA) techniques are discussed; providing a background, description and advantages and disadvantages for each. Case studies in the nuclear industry, railway industry, and aviation industry are presented to show the importance and applications of HRA. Human error has been shown to be the major contributor to system failure.
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Bayesian accelerated life tests: exponential and Weibull models
- Authors: Izally, Sharkay Ruwade
- Date: 2016
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: http://hdl.handle.net/10962/3003 , vital:20351
- Description: Reliability life testing is used for life data analysis in which samples are tested under normal conditions to obtain failure time data for reliability assessment. It can be costly and time consuming to obtain failure time data under normal operating conditions if the mean time to failure of a product is long. An alternative is to use failure time data from an accelerated life test (ALT) to extrapolate the reliability under normal conditions. In accelerated life testing, the units are placed under a higher than normal stress condition such as voltage, current, pressure, temperature, to make the items fail in a shorter period of time. The failure information is then transformed through an accelerated model commonly known as the time transformation function, to predict the reliability under normal operating conditions. The power law will be used as the time transformation function in this thesis. We will first consider a Bayesian inference model under the assumption that the underlying life distribution in the accelerated life test is exponentially distributed. The maximal data information (MDI) prior, the Ghosh Mergel and Liu (GML) prior and the Jeffreys prior will be derived for the exponential distribution. The propriety of the posterior distributions will be investigated. Results will be compared when using these non-informative priors in a simulation study by looking at the posterior variances. The Weibull distribution as the underlying life distribution in the accelerated life test will also be investigated. The maximal data information prior will be derived for the Weibull distribution using the power law. The uniform prior and a mixture of Gamma and uniform priors will be considered. The propriety of these posteriors will also be investigated. The predictive reliability at the use-stress will be computed for these models. The deviance information criterion will be used to compare these priors. As a result of using a time transformation function, Bayesian inference becomes analytically intractable and Markov Chain Monte Carlo (MCMC) methods will be used to alleviate this problem. The Metropolis-Hastings algorithm will be used to sample from the posteriors for the exponential model in the accelerated life test. The adaptive rejection sampling method will be used to sample from the posterior distributions when the Weibull model is considered.
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