Bayesian approach to variable sampling plans for the Weibull distribution with censoring.

by Jian-Wei Chen.Thesis (M.Phil.)--Chinese University of Hong Kong, 1996.Includes bibliographical references (leaves 84-86).Chapter Chapter 1 --- IntroductionChapter 1.1 --- Introduction --- p.1Chapter 1.2 --- Bayesian approach to single variable sampling plan for the exponential distribution --- p.3Chapter 1.3 --- Outline of the thesis --- p.7Chapter Chapter 2 --- Single Variable Sampling Plan With Type II CensoringChapter 2.1 --- Model --- p.10Chapter 2.2 --- Loss function and finite algorithm --- p.13Chapter 2.3 --- Numerical examples and sensitivity analysis --- p.17Chapter Chapter 3 --- Double Variable Sampling Plan With Type II CensoringChapter 3.1 --- Model --- p.25Chapter 3.2 --- Loss function and Bayes risk --- p.27Chapter 3.3 --- Discretization method and numerical analysis --- p.33Chapter Chapter 4 --- Bayesian Approach to Single Variable Sampling Plans for General Life Distribution with Type I CensoringChapter 4.1 --- Model --- p.42Chapter 4.2 --- The case of the Weibull distribution --- p.47Chapter 4.3 --- The case of the two-parameter exponential distribution --- p.49Chapter 4.4 --- The case of the gamma distribution --- p.52Chapter 4.5 --- Numerical examples and sensitivity analysis --- p.54Chapter Chapter 5 --- DiscussionsChapter 5.1 --- Comparison between Bayesian variable sampling plans and OC curve sampling plans --- p.63Chapter 5.2 --- Comparison between single and double sampling plans --- p.64Chapter 5.3 --- Comparison of both models --- p.66Chapter 5.4 --- Choice of parameters and coefficients --- p.66Appendix --- p.78References --- p.8

Bayesian sampling plans with interval censoring

This paper employs Bayesian approach to establish acceptance sampling plans for life tests with interval censoring. Assume that interval data have a multinomial distribution, and the interval probabilities are random and vary from lot to lot according to a conjugate prior of Dirichlet distribution. A Bayes risk is defined with a suitable loss function and a predictive distribution. Optimal Bayesian sampling plans are determined by minimizing the Bayes risk per lot. An example is used and some optimal Bayesian sampling plans with three equally-spaced intervals are tabulated for illustration. Sensitivity analysis are conducted to evaluate the influence of the parameter of prior distribution, the cost per sampled item and the cost per used unit time on the proposed Bayesian sampling plans

On the Type-I Half-logistic Distribution and Related Contributions: A Review

The half-logistic (HL) distribution is a widely considered statistical model for studying lifetime phenomena arising in science, engineering, finance, and biomedical sciences. One of its weaknesses is that it has a decreasing probability density function and an increasing hazard rate function only. Due to that, researchers have been modifying the HL distribution to have more functional ability. This article provides an extensive overview of the HL distribution and its generalization (or extensions). The recent advancements regarding the HL distribution have led to numerous results in modern theory and statistical computing techniques across science and engineering. This work extended the body of literature in a summarized way to clarify some of the states of knowledge, potentials, and important roles played by the HL distribution and related models in probability theory and statistical studies in various areas and applications. In particular, at least sixty-seven flexible extensions of the HL distribution have been proposed in the past few years. We give a brief introduction to these distributions, emphasizing model parameters, properties derived, and the estimation method. Conclusively, there is no doubt that this summary could create a consensus between various related results in both theory and applications of the HL-related models to develop an interest in future studies

Statistical inferences of Rs;k = Pr(Xk-s+1:k \u3e Y ) for general class of exponentiated inverted exponential distribution with progressively type-II censored samples with uniformly distributed random removal

The problem of statistical inference of the reliability parameter Pr(Xk-s+1:k \u3e Y ) of an s-out-of-k : G system with strength components X1,X2,…,Xk subjected to a common stress Y when X and Y are independent two-parameter general class of exponentiated inverted exponential (GCEIE) progressively type-II right censored data with uniformly random removal random variables, are discussed. We use p-value as a basis for hypothesis testing. There are no exact or approximate inferential procedures for reliability of a multicomponent stress-strength model from the GCEIE based on the progressively type-II right censored data with random or fixed removals available in the literature. Simulation studies and real-world data analyses are given to illustrate the proposed procedures. The size of the test, adjusted and unadjusted power of the test, coverage probability and expected confidence lengths of the confidence interval, and biases of the estimator are also discussed

A data analytics approach to gas turbine prognostics and health management

As a consequence of the recent deregulation in the electrical power production industry, there has been a shift in the traditional ownership of power plants and the way they are operated. To hedge their business risks, the many new private entrepreneurs enter into long-term service agreement (LTSA) with third parties for their operation and maintenance activities. As the major LTSA providers, original equipment manufacturers have invested huge amounts of money to develop preventive maintenance strategies to minimize the occurrence of costly unplanned outages resulting from failures of the equipments covered under LTSA contracts. As a matter of fact, a recent study by the Electric Power Research Institute estimates the cost benefit of preventing a failure of a General Electric 7FA or 9FA technology compressor at $10 to$20 million. Therefore, in this dissertation, a two-phase data analytics approach is proposed to use the existing monitoring gas path and vibration sensors data to first develop a proactive strategy that systematically detects and validates catastrophic failure precursors so as to avoid the failure; and secondly to estimate the residual time to failure of the unhealthy items. For the first part of this work, the time-frequency technique of the wavelet packet transforms is used to de-noise the noisy sensor data. Next, the time-series signal of each sensor is decomposed to perform a multi-resolution analysis to extract its features. After that, the probabilistic principal component analysis is applied as a data fusion technique to reduce the number of the potentially correlated multi-sensors measurement into a few uncorrelated principal components. The last step of the failure precursor detection methodology, the anomaly detection decision, is in itself a multi-stage process. The obtained principal components from the data fusion step are first combined into a one-dimensional reconstructed signal representing the overall health assessment of the monitored systems. Then, two damage indicators of the reconstructed signal are defined and monitored for defect using a statistical process control approach. Finally, the Bayesian evaluation method for hypothesis testing is applied to a computed threshold to test for deviations from the healthy band. To model the residual time to failure, the anomaly severity index and the anomaly duration index are defined as defects characteristics. Two modeling techniques are investigated for the prognostication of the survival time after an anomaly is detected: the deterministic regression approach, and parametric approximation of the non-parametric Kaplan-Meier plot estimator. It is established that the deterministic regression provides poor prediction estimation. The non parametric survival data analysis technique of the Kaplan-Meier estimator provides the empirical survivor function of the data set comprised of both non-censored and right censored data. Though powerful because no a-priori predefined lifetime distribution is made, the Kaplan-Meier result lacks the flexibility to be transplanted to other units of a given fleet. The parametric analysis of survival data is performed with two popular failure analysis distributions: the exponential distribution and the Weibull distribution. The conclusion from the parametric analysis of the Kaplan-Meier plot is that the larger the data set, the more accurate is the prognostication ability of the residual time to failure model.PhDCommittee Chair: Mavris, Dimitri; Committee Member: Jiang, Xiaomo; Committee Member: Kumar, Virendra; Committee Member: Saleh, Joseph; Committee Member: Vittal, Sameer; Committee Member: Volovoi, Vital

On estimating the reliability in a multicomponent system based on progressively-censored data from Chen distribution

This research deals with classical, Bayesian, and generalized estimation of stress-strength reliability parameter, Rs;k = Pr(at least s of (X1;X2; :::;Xk) exceed Y) = Pr(Xks+1:k \u3eY) of an s-out-of-k : G multicomponent system, based on progressively type-II right-censored samples with random removals when stress and strength are two independent Chen random variables. Under squared-error and LINEX loss functions, Bayes estimates are developed by using Lindley’s approximation and Markov Chain Monte Carlo method. Generalized estimates are developed using generalized variable method while classical estimates - the maximum likelihood estimators, their asymptotic distributions, asymptotic confidence intervals, bootstrap-based confidence intervals - are also developed. A simulation study and a real-world data analysis are provided to illustrate the proposed procedures. The size of the test, adjusted and unadjusted power of the test, coverage probability and expected lengths of the confidence intervals, and biases of the estimators are also computed, compared and contrasted

Random Effect Models For Repairable System Reliability

The practical motivation for the work described in this thesis arose from the development of a new Jaguar car engine. Development tests on prototype engines led to multiple failure time data which are modelled as a non-homogeneous Poisson process in its log-linear form. Initial analysis of the data using failure time plots showed considerable differences between prototype engines and suggested the use of models incorporating random effects for the engine effects. These models were fitted using the method of maximum likelihood. Two random effects have been considered: a proportional effect and a time dependent effect. In each case a simulation study showed the method of maximum likelihood to produce good estimates of the parameters and standard errors. There is also shown to be a bias in the estimate of the random effect, especially in smaller samples. The likelihood ratio test has been shown to be valid in assessing the statistical significance of the random effect, and a simulation exercise has demonstrated this in practical terms. Applying this test to the models fitted to the Jaguar data gives the proportional random effect to be significant while the time dependent random effect is not found to be significantly different from zero. This test has also been demonstrated to be of use in distinguishing between the two models and again the proportional random effect model is found to be more suitable for the Jaguar data. Residual analysis is performed to aid model validation Covariates are included, in various forms, in the proportional random effect model and the inclusion of these in the time dependent model is briefly discussed. The use of these models is demonstrated for the Jaguar data by including the type of test an engine performed as a covariate. The covariate models have also been used to compare engine phases. A framework for extending the models for interval censored data is developed. Finally this thesis discusses possible extensions of the work summarised in the previous paragraphs. This includes work on alternative models, Bayesian methods and experimental design.Jaguar Cars Limite