Design of single and double acceptance sampling plans based on interval type-2 fuzzy sets

Defectiveness of items is generally considered as a certain value in acceptance sampling plans (ASPs). It is clear that, it may not be certainly known in some real-case problems. Uncertainties of the inspection process such as measurement errors, inspectors’ hesitancies or vagueness of the process etc. should be taken into account to obtain more reliable results. The fuzzy set theory (FST) is one of the best methods to overcome these problems. There are some studies in the literature formulating the ASPs with the help of FST. Deciding the right membership functions of the fuzzy sets (FSs) has a vital importance on the quality of the uncertainty modeling. Additionally, the fuzzy set extensions have been offered to model more complicated uncertainties to achieve better modeling. As one of these extensions, type-2 fuzzy sets (T2FSs) gives an ability to model uncertainty in situations where it is not possible to determine exact membership function parameters. In this study, single and double ASPs based on interval T2FSs (IT2FSs) have been designed for binomial and Poisson distributions. Thus, it becomes possible to make more flexible, sensitive and descriptive sensitivity analyzes. The main characteristic functions of ASPs have been derived and the suggested formulations have been illustrated on a comparative application from manufacturing process. Results allowing for more comprehensive analysis as against to the traditional and T1FSs based plans have been obtained.

Introduction to the Theory of Imprecise Probability

The theory of imprecise probability is a generalization of classical ‘precise’ probability theory that allows modeling imprecision and indecision. This is a practical advantage in situations where a unique precise uncertainty model cannot be justified. This arises, for example, when there is a relatively small amount of data available to learn the uncertainty model or when the model’s structure cannot be defined uniquely. The tools the theory provides make it possible to draw conclusions and make decisions that correctly reflect the limited information or knowledge available for the uncertainty modeling task. This extra expressivity however often implies a higher computational burden. The goal of this chapter is to primarily give you the necessary knowledge to be able to read literature that makes use of the theory of imprecise probability. A secondary goal is to provide the insight needed to use imprecise probabilities in your own research. To achieve the goals, we present the essential concepts and techniques from the theory, as well as give a less in-depth overview of the various specific uncertainty models used. Throughout, examples are used to make things concrete. We build on the assumed basic knowledge of classical probability theory.

Subsurface-to-Economics Closing the Loop on Uncertainty Analysis

We are all aware that our future is uncertain. Although some aspects can be predicted with more certainty and others with less, essentially everything is uncertain. Uncertainty exists because of lack of data, lack of resources, and lack of understanding. We cannot measure everything, so there are always unknowns. Even measurements include measurement errors. Also, we do not always have enough resources to analyze the data obtained. In addition, we do not have a full understanding of how the world, or the universe, works (Park 2011). Every day we find ourselves in situations where we must make many decisions, big or small. We tend to make the decisions based on a prediction, despite knowing that it is uncertain. For instance, imagine how many decisions are made by people every day based on the probability of it raining tomorrow (i.e., based on the weather forecast). To have a good basis for making a decision, it is of critical importance to correctly model the uncertainty in the forecast. In the oil and gas industry, uncertainties are large and complex. Oil and gas fields have been developed and operated despite tremendous uncertainty in a variety of areas, including undiscovered media and unpredictable fluid in the subsurface, wells, unexpected facility and equipment costs, and economic, political, international, environmental, and many other risks. Another important aspect of uncertainty modeling is the feasibility of verifying the uncertainty model with the actual results. For example, in the weather forecast it was announced that the probability of raining the next day was 20%. And the next day it rained. Do we say the forecast was wrong? Can we say the forecast was right? In order to make sure the uncertainty model is correct; we should strictly verify all the assumptions and follow the mathematically, statistically, proven-to-be-correct methodology to model the uncertainty (Caers et al. 2010; Caers 2011). In this paper, we show an effective, rigorous method of modeling uncertainty in the expected performance of potential field development scenarios in the oil and gas field development planning given uncertainties in various domains from subsurface to economics. The application of this method is enabled by using technology as described in a later section.

Modeling the Context of the Problem Domain of Time Series with Type-2 Fuzzy Sets

Data analysis in the context of the features of the problem domain and the dynamics of processes are significant in various industries. Uncertainty modeling based on fuzzy logic allows building approximators for solving a large class of problems. In some cases, type-2 fuzzy sets in the model are used. The article describes constructing fuzzy time series models of the analyzed processes within the context of the problem domain. An algorithm for fuzzy modeling of the time series was developed. A new time series forecasting scheme is proposed. An illustrative example of the time series modeling is presented. The benefits of contextual modeling are demonstrated.