Subjective utility with upper and lower probabilities on finite states

This article is concerned with thresholds of discrimination of preference judgments under uncertainty. We establish an axiomatic characterization for a threshold representation, where thresholds are represented by inexact measurement of subjective probabilities, i.e., upper and lower probabilities. Since upper and lower probabilities need not be additive, the representational form adopts the Choquet integration.     

Sifting the wheat from the chaff—the organization of telephone intake and the selection of social assistance inquirers in Sweden

In Sweden, the initial contact between help-seeking people and a social welfare office normally takes place over the telephone, with designated intake officers handling those aiming to apply for social assistance. Citizens seeking help are here sorted according to various eligibility criteria as well as according to different intake routines. The outcome of the sorting process is that some receive an appointment for a further assessment while others are sent away. This article describes and classifies the degree of selection at seven telephone intakes, discusses relations between the degrees of selection and reasons for selection and distinguishes several selection strategies.     

Sampling design proportional to order statistic of auxiliary variable

The sampling designs dependent on sample moments of auxiliary variables are well known. Lahiri (Bull Int Stat Inst 33:133–140, 1951) considered a sampling design proportionate to a sample mean of an auxiliary variable. Sing and Srivastava (Biometrika 67(1):205–209, 1980) proposed the sampling design proportionate to a sample variance while Wywiał (J Indian Stat Assoc 37:73–87, 1999) a sampling design proportionate to a sample generalized variance of auxiliary variables. Some other sampling designs dependent on moments of an auxiliary variable were considered e.g. in Wywiał (Some contributions to multivariate methods in, survey sampling. Katowice University of Economics, Katowice, 2003a); Stat Transit 4(5):779–798, 2000) where accuracy of some sampling strategies were compared, too.These sampling designs cannot be useful in the case when there are some censored observations of the auxiliary variable. Moreover, they can be much too sensitive to outliers observations. In these cases the sampling design proportionate to the order statistic of an auxiliary variable can be more useful. That is why such an unequal probability sampling design is proposed here. Its particular cases as well as its conditional version are considered, too. The sampling scheme implementing this sampling design is proposed. The inclusion probabilities of the first and second orders were evaluated. The well known Horvitz–Thompson estimator is taken into account. A ratio estimator dependent on an order statistic is constructed. It is similar to the well known ratio estimator based on the population and sample means. Moreover, it is an unbiased estimator of the population mean when the sample is drawn according to the proposed sampling design dependent on the appropriate order statistic.     

Subjective probabilities and utility with event-dependent preferences

This article generalizes Savage's theory to include event-dependent preferences. The state space is partitioned into finitely many events. The induced preferences over consequences are assumed independent of the underlying states within, but not across, these events. This results in an additively separable representation of preferences over acts. The dependence of the preference relation over consequences on the events is represented by event-dependent mappings of the set of consequences onto itself. Given these mappings, the preferences on acts are represented by the expectation of event-dependent utilities on the consequences with respect to unique subjective probabilities on the states.Helpful discussions with David Schmeidler are gratefully acknowledged.     

Coherent decision analysis with inseparable probabilities and utilities

This article explores the extent to which a decision maker's probabilities can be measured separately from his/her utilities by observing his/her acceptance of small monetary gambles. Only a partial separation is achieved: the acceptable gambles are partitioned into a set of belief gambles, which reveals probabilities distorted by marginal utilities for money, and a set of preference gambles, which reveals utilities reciprocally distorted by marginal utilities for money. However, the information in these gambles still enables us to solve the decision maker's problem: his/her utility-maximizing decision is the one that avoids arbitrage (i.e., incoherence or Dutch books).     

Independent attributes control chart for Markov-dependent processes

Statistical process monitoring (SPM) is a very efficient tool to maintain and to improve the quality of a product. In many industrial processes, end product has two or more attribute-type quality characteristics. Some of them are independent, but the observations are Markovian dependent. It is essential to develop a control chart for such situations. In this article, we develop an Independent Attributes Control Chart for Markov Dependent Processes based on error probabilities criterion under the assumption of one-step Markov dependency. Implementation of the chart is similar to that of Shewhart-type chart. Performance of the chart has been studied using probability of detecting shift criterion. A procedure to identify the attribute(s) responsible for out-of-control status of the process is given.     

Earthquakes occurrences estimation through a parametric semi-Markov approach

The estimation of earthquakes’ occurrences prediction in seismic areas is a challenging problem in seismology and earthquake engineering. Indeed, the prevention and the quantification of possible damage provoked by destructive earthquakes are directly linked to this kind of prevision. In our paper, we adopt a parametric semi-Markov approach. This model assumes that a sequence of earthquakes is seen as a Markov process and besides it permits to take into consideration the more realistic assumption of events’ dependence in space and time. The elapsed time between two consecutive events is modeled as a general Weibull distribution. We determine then the transition probabilities and the so-called crossing states probabilities. We conclude then with a Monte Carlo simulation and the model is validated through a large database containing real data.     

Pitman closeness,monotonicity and consistency of best linear unbiased and invariant estimators for exponential distribution under Type II censoring

Comparisons of best linear unbiased estimators with some other prominent estimators have been carried out over the last 50 years since the ground breaking work of Lloyd [E.H. Lloyd, Least squares estimation of location and scale parameters using order statistics, Biometrika 39 (1952), pp. 88–95]. These comparisons have been made under many different criteria across different parametric families of distributions. A noteworthy one is by Nagaraja [H.N. Nagaraja, Comparison of estimators and predictors from two-parameter exponential distribution, Sankhyā Ser. B 48 (1986), pp. 10–18], who made a comparison of best linear unbiased (BLUE) and best linear invariant (BLIE) estimators in the case of exponential distribution. In this paper, continuing along the same lines by assuming a Type II right censored sample from a scaled-exponential distribution, we first compare BLUE and BLIE of the exponential mean parameter in terms of Pitman closeness (nearness) criterion. We show that the BLUE is always Pitman closer than the BLIE. Next, we introduce the notions of Pitman monotonicity and Pitman consistency, and then establish that both BLUE and BLIE possess these two properties.     

Evaluation of scheduling strategies for a dynamic job shop in a tool-shared,flexible manufacturing environment

A two-phase approach is used to examine the impact of job scheduling rules and tool selection policies for a dynamic job shop system in a tool-shared, flexible manufacturing environment. The first phase develops a generalized simulation model and analyses 'simple' job scheduling rules and tool selection policies under various operating scenarios. The results from this investigation are then used to develop and analyse various bi-criteria rules in the second phase of this study. The results show that the scheduling rules have the most significant impact on system performance, particularly at high shop load levels. Tool selection policies affect some of the performance measures, most notably, proportion of tardy jobs, to a lesser degree. Higher machine utilizations can be obtained at higher tool duplication levels but at the expense of increased tooling costs and lower tool utilization. The results also show that using different processing time distributions may have a significant impact on shop performance.     

A decision support system for the selection of a casting process using analytic hierarchy process

This paper presents an Analytic Hierarchy Process (AHP) based decision support system to select the most suitable casting process for a given product. The hierarchical structure of the proposed method allows the decision maker to compare the different casting processes using the material suitability and flexibility, geometrical complexity, dimensional tolerance and surface finish of the casting, and the cost as the criteria for selection. Judgemental inconsistency of the decision maker in selecting the casting process is taken care by ensuring that the value of consistency ratio is below (0.1). A numerical example is presented to illustrate the effectiveness of the proposed methodology for selecting the suitable casting process.