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Classical statistical inference is nonmonotonic in nature. We show how it can be formalized in the default logic framework. The structure of statistical inference is the same as that represented by default rules. In particular, the prerequisite corresponds to the sample statistics, the justifications require that we do not have any reason to believe that the sample is misleading, and the consequence corresponds to the conclusion sanctioned by the statistical test.

Psychologically, music can affect human mood and influence human behavior. In this paper, a novel method for music mood classification is introduced. In the experiment, music mood classification was performed using feature extraction based on MPEG-7 features from the ISO/IEC 15938 standard for describing multimedia content. The result of this feature extraction are 17 low-level descriptors. Here, we used the Audio Power, Audio Harmonicity, and Audio Spectrum Projection features. Moreover, the discrete wavelet transform (DWT) was utilized for audio signal reconstruction. The reconstructed audio signals were classified by the new method, which uses a support vector machine with a confidence interval (SVM-CI). According to the experimental results, the success rate of the proposed method was satisfactory and SVM-CI outperformed the ordinary SVM.

Uncertainty and its imposed risk have significant impacts on decision-making. However, both are disregarded in many trust-based applications. In this paper, we propose a risk-aware approach to explicitly take uncertainty of trust and its effects into account. Our approach consists of a trust, a confidence, and a risk model. We do not prescribe a specific trust model, and any probabilistic trust model can be empowered by our approach. The confidence model calculates the uncertainty of the trust model in the form of a confidence interval, and is independent of the inner-workings of the trust model. This interval is used by the utility-based risk model which assesses the effects of uncertainty on trust-based decisions. We evaluated our approach by a four-state HMM-based simulated trustee, and employed the Beta, HMM and evidence-based trust models. We proposed and compared different methods for calculating confidence intervals, as well as methods for determining the risk and opportunity of a trust-based interaction. The results demonstrate how our approach should be used to improve the correctness of decision-making in trust-based applications. According to the statistical analysis of the simulation results, confidence intervals can properly represent the trust value and its uncertainty, and strongly improve trust-based decisions.

The Weibull distribution is widely adopted as a lifetime distribution. One of the characteristics the Weibull distribution possesses is that its cumulative distribution function can be expressed by closed form. Parameter estimation for the Weibull distribution has been discussed by many authors. Various methods have been proposed for constructing confidence intervals and joint confidence regions for the parameters of the Weibull distribution based on censored data. This paper discusses those methods that deal with exact confidence intervals or exact joint confidence regions for the parameters. One of the applications of the joint confidence regions of the parameters is to find confidence bounds for the functions of the parameters. In this paper, confidence bounds for the mean lifetime and reliability function for the Weibull distributions are discussed. Some unresolved problems for the exact confidences and joint confidence regions are mentioned in the discussion section.

With today's high technology, some life tests result in no or very few failures by the end of test. In such cases, an approach is to do life test at higher-than-usual stress conditions in order to obtain failures quickly. This study discusses the point and interval estimations of parameters on the simple step-stress model in accelerated life testing with progressive type II censoring. An exponential failure time distribution with mean life that is a log-linear function of stress and a cumulative exposure model are considered. We derive the maximum likelihood estimators of the model parameters. Confidence intervals for the model parameters are established by using pivotal quantity and can be applied to any sample size. A numerical example is investigated to illustrate the proposed methods.

Availability is an important measure of performance of repairable system. The steady state system availability has special importance since it demonstrates the performance of a system after it has been operated for long. The statistical inference about the steady state availability are particularly useful for practitioners. Much work has been done in this regard. Most of these researches proposed certain pivotal quantities for constructing confidence intervals of the steady state availability. Assuming both the lifetime and repair time follow gamma distribution with known shape parameters and unknown scale parameters, we propose a pivotal quantity for making inferences, and further derive the likelihood ratio tests. Tables of critical values are given for the convenience of applying the two-sided likelihood ratio test. Confidence intervals are also obtained by converting the acceptance regions.

In this paper, we consider an interval estimation of the age replacement problem, where the underlying failure time probability is given by the two-parameter Weibull distribution. The parametric bootstrap is used to obtain the probability distribution of an estimator for the optimal age replacement time minimizing the expected cost per unit time in the steady state. We focus on both cases with complete and incomplete samples of failure time data, and calculate not only the higher moments of an estimator for the optimal age replacement time but also the confidence interval.

This paper studies the frequentist inference about the shape and scale parameters of the two-parameter Weibull distribution using upper record values. The exact sampling distribution of the MLE of the shape parameter is derived. The asymptotic normality of the MLEs of both parameters are obtained. Based on these results this paper proposes various confidence intervals of the two parameters. Assuming one parameter is known certain testing procedures are proposed. Furthermore, approximate prediction interval for the immediately consequent record value is derived too. Conclusions are made based on intensive simulations.

In the face of fierce global competition, firms are outsourcing important but nonessential tasks to external professional companies. Corporations are also turning from competitive business models to cooperative strategic partnerships in hopes of swiftly responding to consumer needs and enhancing overall efficiency and industry competitiveness. This research developed an outsourcing partner selection model in hopes of helping firms select better outsourcing partners for long-term collaborations. Process quality and manufacturing time are vital when evaluating outsourcing partner. We therefore used process capability index $C_{pm}$ and manufacturing time performance index $I_h$ in the proposed model. Sample data from random samples are needed to calculate the point estimates of indices, however, it is impossible to obtain a sample with a structure completely identical to that of the population, which means that sampling generates unavoidable sampling errors. The reliability of point estimates are also uncertain, which inevitably leads to misjudgment in some cases. Thus, to reduce estimate errors and increase assessment reliability, we calculated the $100(1-\alpha )$% confidence intervals of the indices $C_{pm}$ and $I_h$, then constructed the joint confidence region of $C_{pm}$ and $I_h$ to develop an outsourcing partner selection model that will help firms select better outsourcing partners for long-term collaborations. We also provide a case as an illustration of how the proposed selection model is implemented.

Supplier selection is a practical problem in supply chain management and quality is the most important criterion in supplier selection. In this study, we developed a supplier selection model based on process quality, in which the Six Sigma quality index $Q_{pk}$ is used as a tool to assess the process quality provided by suppliers. Note that index estimation based on sample data is prone to uncertainty in the assessment of process quality. Therefore, we derived the confidence interval of $Q_{pk}$ via mathematical programming to reduce the likelihood of assessment miscalculations, and then used this interval to perform a pairwise comparison of suppliers. Our goal was to identify criteria that can be used to select the optimal suppliers for long-term collaborations and sustainable partnerships. A case study is also presented to demonstrate the practical implementation of the proposed method.

The design allowables are derived statistically from measured material properties, and the Weibull distribution is one of the most commonly used distributions for statistical modeling. A- and B-basis design allowables are frequently used; they correspond to the confidence lower bounds for the 1st and 10th percentiles, respectively, with a confidence level of 95%. The maximum likelihood method is generally recommended and commonly used for parameter and confidence lower bound estimation. On the other hand, designers are also interested in confidence lower bounds for other percentiles, and in general, confidence intervals to specify uncertainty in percentile estimates. Monte-Carlo simulation methods have been proposed for this purpose; however, they are not easy to code and take a long time to run to obtain reliable results. As an easy-to-use alternative, this study proposes approximate polynomial functions of sample size for various percentiles and confidence levels. The coefficients of the functions are presented in tabular form for each combination of percentiles and confidence levels. They eliminate the need for simulations and provide precise confidence intervals and lower bounds for a large set of Weibull percentiles.

With the gradual maturity of the Internet of Things environment, the collection and analysis technology of production data is continuously improved, and the improvement of product process quality and safety performance can not only increase product value but also prolong product life, in order to achieve the goal of energy-saving and waste-reducing green production. Therefore, this study used process capability indicators of important quality characteristics as evaluation tools for the manual wheelchair products and proposed a smart quality decision-making model for production data. First, we constructed an evaluation index for the important quality characteristics of the carbon fiber wheel rims to verify that each important quality characteristic can meet the required quality level. Next, based on the upper confidence limit of the evaluation index, the fuzzy decision index and fuzzy testing rules were established. In addition, the decision-making index was converted into the index observation value, and an intuitive fuzzy evaluation rule more convenient for practical application was established. Finally, we employed an easy-to-use radar evaluation chart to assess whether the index fell into the improvement range and decide whether to improve. In conclusion, this study considers the need of businesses for quick their responses to decision-making. The fuzzy testing design built on upper confidence limits can incorporate past data experience. It can still maintain the testing accuracy for small-sized samples. At the same time, it can also help enterprises pursue smart manufacturing and management and realize the business philosophy of sustainable development.

Critical time is the point at which the failure rate attains its maximum and then decreases. For the inverse Gaussian distribution, the critical time always exists and can be used as a guide for conducting burn-in. In this paper, we use two different reparametrization schemes to establish monotonicity property of critical time. This property is then used to obtain exact confidence intervals for the critical time when either one of the parameters of the inverse Gaussian distribution is known. When both parameters are unknown we construct an analytically exact confidence interval for the critical time that guarentees the desired coverage probability. An approximate confidence interval, motivated by conservative nature of the above bound, is also proposed. Monte-Carlo simulation is conducted to investigate the performance of the two confidence intervals in terms of the their coverage probability and average width. Finally, a numerical example on repair time data is provided to illustrate the procedure.

We present the quantitative analysis of the photoluminescence (PL) obtained for semiconductor TOPO-capped CdSe/ZnS QDs in solutions at 77–293K. The PL bands are approximated more accurately when assuming the superposition of at least two Gaussian components differing considerably in the linewidth (FWHM) and having different nature.

The bootstrap is a computer-based resampling method that can provide good approximations to the distribution of a given statistic. We review some common forms of bootstrap-based confidence intervals, with emphasis on some recent work on the estimating function bootstrap and Markov chain marginal bootstrap.

The number of online textual reviews on each hotel aspect can reflect the tourist preference difference on distinct aspects. Therefore, not only online textual reviews but their numbers have a significant impact on tourists’ hotel selection decisions. Motivated by this observation, this study proposes a hotel ranking model for hotel selection based on the sentiment analysis of online textual reviews by considering the differences in the number of reviews on different aspects. We explicitly model the differences in the number of reviews on aspects through the confidence interval estimation. In addition, the AS-Capsules model, which can jointly perform aspect detection and aspect-level sentiment classification with high accuracy, is employed for sentiment analysis. We conducted a case study on TripAdvisor.com, the experimental results show that our proposed model is able to effectively assist the tourists in making the desirable decision on hotel selection.

Bootstrap is becoming a useful and very popular tool for obtaining estimations and confidence intervals for coefficients in many researches in different scientific fields without making assumptions about the population. Our goal is to apply bootstrap technique in parameter estimation and confidence intervals for the coefficients in Multiple Logistic Regression model in a study using medical records. We will use R programming language and SPSS software to obtain the coefficients of the model and the estimations using non-parametric bootstrap and we will also make a comparison of the results emphasizing the importance of using resampling methods even in a study with real data.

In the simulation output analysis, there are some measures that should be calculated by time average concept such as the mean queue length. Especially, the confidence interval of those measures might be required for statistical analysis. In this situation, the traditional method that utilizes the central limit theorem (CLT) is inapplicable if the output data set has autocorrelation structure. The bootstrap is one of the most suitable methods which can reflect the autocorrelated phenomena in statistical analysis. Therefore, the confidence interval for a time averaged measure having autocorrelation structure can also be calculated by the bootstrap methods. This study introduces the method that constructs these confidence intervals applying the bootstraps. The bootstraps proposed are the threshold bootstrap (TB), the moving block bootstrap (MBB) and stationary bootstrap (SB). Finally, some numerical examples will be provided for verification.

This paper examines the performance of a new probability model developed in terms of the surface area and velocity of an aero-structure, and presents some relevant statistical inferences. Several examples will compare the robustness of three kinds of point estimators developed for the lift coefficient. Four different types of confidence intervals for the lift coefficient are also developed, and it is shown that the shortest length confidence interval is an UMA confidence interval. Using the probability model, the correlation coefficient between lift and velocity, and the relevant regression slope are computed. The inferences and the results of this paper can be used particularly in the designing process of an aero-structure, especially when there is some uncertainty about its surface area; this provides some flexibilities for aerodynamicists in determining some of the unknown design characteristics.

Usually confidence interval is defined as an interval with preassigned confidence level 1 - α for all the value of parameters. More generally, however we may consider interval estimation procedures with confidence coefficient varying according to the value of the unknown parameter, and associated procedure to estimate the actual level. Such a consideration leads to more general procedures including conditional procedures given the ancillary.