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The purpose of this paper is to use Bayesian probability theory to analyze the software reliability model with multiple types of faults. The probability that all faults are detected and corrected after a series of independent software tests and correction cycles is presented. This in turn has a number of applications, such as how long to test a software, estimating the cost of testing, etc.

The use of Bayesian probabilistic models, when compared to traditional point forecast estimation models, provides tools for risk estimation and allows decision makers to combine historical data with subjective expert estimates. Probability evaluation is done both prior to and after observing the number of faults detected in each cycle. The conditions under which these two measures, the conditional and unconditional probabilities, are the same is also shown. Expressions are derived to evaluate the probability that, after a series of sequential independent reviews have been completed, no class of fault remains in the software system by assuming the prior distribution as Poisson and binomial.

From results in Sections 4 and 5 it can be observed that the conditional and unconditional probabilities are the same if the prior probability distribution is Poisson and binomial. In these cases the confidence that all faults are deleted is not a function of the number of faults observed during the successive reviews but it is a function of the number of reviews, the detection probabilities and the mean of the prior distribution. This is a remarkable result because it gives a circumstance in which the statistical confidence from a Bayesian analysis is actually independent of all observed data. From the result in Section 4 it can be seen that exponential formula could be used to evaluate the probability that no fault remains when a Poisson prior distribution is combined with a multinomial detection process in each review cycle.

The paper is part of research work for a PhD degree.

The purpose of this paper is to develop a monitoring multiple-stream processes control chart with a finite mixture of probability distributions in the manufacture industry.

Data were collected during production of a wheat-based dough in a food industry and the control charts were developed with these steps: to collect the master sample from different production batches; to verify, by graphical methods, the quantity and the characterization of the number of mixing probability distributions in the production batch; to adjust the theoretical model of probability distribution of each subpopulation in the production batch; to make a statistical model considering the mixture distribution of probability and assuming that the statistical parameters are unknown; to determine control limits; and to compare the mixture chart with traditional control chart.

A graph was developed for monitoring a multi-stream process composed by some parameters considered in its calculation with similar efficiency to the traditional control chart.

The control chart can be an efficient tool for customers that receive product batches continuously from a supplier and need to monitor statistically the critical quality parameters.

Much has been written about probabilistic methods of risk analysis and about the probability distributions required for its use. This paper demonstrates a method known as the probability of acceptance error approach using simple scenarios in which the only variable tested by a probability distribution is rental growth but in which other variables such as discount rate, capitalisation rate and holding period are also tested. In particular, the sensitivity of the probability distribution chosen for the rental growth values is discussed where both the rental growth values themselves and the probability distributions are normally distributed and also where they have a skewed distribution. It is shown that for current market projections for rental growth great accuracy in the selection of a probability distribution is not required. It is also shown that assumptions about independence or serial correlation of cash flows may be similarly treated and that the probability of acceptance error may be described as a range having independence and serial correlation as the two extremes. The range usually turns out to be fairly narrow. The most sensitive item in the calculations is, as expected, the discount rate. The above findings are demonstrated in a series of appendices.

Actual costs frequently deviate from the estimated costs in either favorable or adverse direction in construction projects. Conventional cost evaluation methods do not take the uncertainty and correlation effects into account. In this regard, a simulation-based cost risk analysis model, the Correlated Cost Risk Analysis Model, previously has been proposed to evaluate the uncertainty effect on construction costs in case of correlated costs and correlated risk-factors. The purpose of this paper is to introduce the detailed evaluation of the Cost Risk Analysis Model through scenario and sensitivity analyses.

The evaluation process consists of three scenarios with three sensitivity analyses in each and 28 simulations in total. During applications, the model’s important parameter called the mean proportion coefficient is modified and the user-dependent variables like the risk-factor influence degrees are changed to observe the response of the model to these modifications and to examine the indirect, two-sided and qualitative correlation capturing algorithm of the model. Monte Carlo Simulation is also applied on the same data to compare the results.

The findings have shown that the Correlated Cost Risk Analysis Model is capable of capturing the correlation between the costs and between the risk-factors, and operates in accordance with the theoretical expectancies.

Correlated Cost Risk Analysis Model can be preferred as a reliable and practical method by the professionals of the construction sector thanks to its detailed evaluation introduced in this paper.

Choice under risk has a large stochastic (unpredictable) component. This chapter examines five stochastic models for binary discrete choice under risk and how they combine with “structural” theories of choice under risk. Stochastic models are substantive theoretical hypotheses that are frequently testable in and of themselves, and also identifying restrictions for hypothesis tests, estimation and prediction. Econometric comparisons suggest that for the purpose of prediction (as opposed to explanation), choices of stochastic models may be far more consequential than choices of structures such as expected utility or rank-dependent utility.

The purpose of this paper is to discuss the application of a method for combining multiple criteria based on the transformation of numerical evaluations into probabilities of preference. It is applied to compare failure risks and to measure efficiency in the retail trade sector.

The main conceptual aspect of the method employed is taking into account uncertainty. Its other important feature is allowing for the combination of evaluations in terms of joint probabilities. This avoids the need of assigning weights to the criteria. In the context of failure modes and effects analysis (FMEA) it provides a probabilistic derivation for priority scores. An application of FMEA to the sector of services is discussed. Another area of application investigated is the assessment of efficiency.

Details of the application of the probabilistic composition in the evaluation of modes of failure and in the comparison of operational efficiencies of retail stores are evidenced.

The study is limited to the retail market. Other factors might be considered in the reliability analysis and other inputs and outputs might be added to the productivity evaluation. The extension of the study to other cases and sectors is straightforward.

Features of the evaluation of modes of failure and of productivity in the retail sector are revealed.

The main contribution of this paper is showing how to use a probabilistic framework to measure efficiency in services management.

The purpose of this paper is to examine people’s understanding and evaluation of uncertainty intervals produced by experts as part of a quality assurance procedure of large public projects.

Three samples of educated participants (employees in a large construction company, students attending courses in project management and judgment and decision making, and judges of district and appeal courts) answered questionnaires about cost estimates of a highway construction project, presented as a probability distribution.

The studies demonstrated additivity neglect of probabilities that are graphically displayed. People’s evaluations of the accuracy of interval estimates revealed a boundary (a “cliff”) effect, with a sharp drop in accuracy ratings for outcomes above an arbitrary maximum. Several common verbal phrases (what “can” happen, is “entirely possible” and “not surprising”) which might seem to indicate expected outcomes were regularly used to describe unlikely values near or at the top of the distribution (an extremity effect).

All judgments concerned a single case and were made by participants who were not stakeholders in this specific project. Further studies should compare judgments aided by a graph with conditions where the graph is changed or absent.

Experts and project managers cannot assume that readers of cost estimates understand a well-defined uncertainty interval as intended. They should also be aware of effects created by describing uncertain estimates in words.

The studies show how inconsistencies in judgment affect the understanding and evaluation of uncertainty intervals by well-informed and educated samples tested in a maximally transparent situation. Readers of cost estimates seem to believe that precise estimates are feasible and yet that costs are usually underestimated.