International Journal of Industrial Engineering & Production Research

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Abstract: Stochastic models such as mixture models, graphical models, Markov random fields and hidden Markov models have key role in probabilistic data analysis. In this paper, we used Gaussian mixture model to the pixels of an image. The parameters of the model were estimated by EM-algorithm.

  In addition pixel labeling corresponded to each pixel of true image was made by Bayes rule. In fact, a new numerically method was introduced for finding the maximum a posterior estimation by using EM-algorithm and Gaussians mixture distribution. In this algorithm, we were made a sequence of priors, posteriors were made and then converged to a posterior probability that is called the reference posterior probability. Maximum a posterior estimated can determine by the reference posterior probability which can make labeled image. This labeled image shows our segmented image with reduced noises. We presented this method in several experiments.

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  Stochastic models such as mixture models, graphical models, Markov random fields and hidden Markov models have key role in probabilistic data analysis. In this paper, we have learned Gaussian mixture model to the pixels of an image. The parameters of the model have estimated by EM-algorithm.

  In addition pixel labeling corresponded to each pixel of true image is made by Bayes rule. In fact, we introduce a new numerically method of finding maximum a posterior estimation by using EM-algorithm and Gaussians mixture distribution. In this algorithm, we have made a sequence of priors, posteriors and they converge to a posterior probability that is called the reference posterior probability. Maximum a posterior estimated can determine by the reference posterior probability that will make labeled image. This labeled image shows our segmented image with reduced noises. We show this method in several experiments.

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  In the classical versions of “Best Choice Problem”, the sequence of offers is a random sample from a single known distribution. We present an extension of this problem in which the sequential offers are random variables but from multiple independent distributions. Each distribution function represents a class of investment or offers. Offers appear without any specified order. The objective is to accept the best offer. After observing each offer, the decision maker has to accept or reject it. The rejected offers cannot be recalled again. In this paper, we consider both cases of known and unknown parameters of the distribution function of the class of next offer. Two optimality criteria are considered, maximizing the expected value of the accepted offer or the probability of obtaining the best offer. We develop stochastic dynamic programming models for several possible problems, depending on the assumptions. A monotone case optimal policy for both criteria is proved. We also show that the optimal policy of a mixed sequence is similar to the one in which offers are from a single density .

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In this research, the decision on belief (DOB) approach was employed to analyze and classify the states of uni-variate quality control systems. The concept of DOB and its application in decision making problems were introduced, and then a methodology for modeling a statistical quality control problem by DOB approach was discussed. For this iterative approach, the belief for a system being out-of-control was updated by taking new observations on a given quality characteristic. This can be performed by using Bayesian rule and prior beliefs. If the beliefs are more than a specific threshold, then the system will be classified as an out-of-control condition. Finally, a numerical example and simulation study were provided for evaluating the performance of the proposed method.

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In order to perform Preventive Maintenance (PM), two approaches have evolved in the literature. The traditional approach is based on the use of statistical and reliability analysis of equipment failure. Under statistical-reliability (S-R)-based PM, the objective of achieving the minimum total cost is pursued by establishing fixed PM intervals, which are statistically optimal, at which to replace or overhaul equipments or components. The second approach involves the use of sensor-based monitoring of equipment condition in order to predict occurrence of machine failure. Under condition-based (C-B) PM, intervals between PM works are no longer fixed, but are performed only “when needed”. It is obvious that Condition Based Maintenance (CBM) needs an on-line inspection and monitoring system that causes CBM to be expensive. Whenever this cost is infeasible, we can develop other methods to improve the performance of traditional (S-R)-based PM method. In this research, the concept of Bayesian inference was used. The time between machine failures was observed, and with combining Bayesian Inference with (S-R)-based PM, it is tried to determine the optimal checkpoints. Therefore, this approach will be effective when it is combined with traditional (S-R)-based PM, even if large number of data is gathered.

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The Weibull distribution has been widely used in survival and engineering reliability analysis. In life testing experiments is fairly common practice to terminate the experiment before all the items have failed, that means the data are censored. Thus, the main objective of this paper is to estimate the reliability function of the Weibull distribution with uncensored and censored data by using Bayesian estimation. Usually it is assigned prior distributions for the parameters (shape and scale) of the Weibull distribution. Instead, we assign prior distributions for the reliability function for a fixed time, that is, for the parameter of interest. For this, we propose different non-informative prior distributions for the reliability function and select the one that provides more accurate estimates. Some examples are introduced to illustrate the methodology and mainly to investigate the performance of the prior distributions proposed in the paper. The Bayesian analysis is conducted based on Markov Chain Monte Carlo (MCMC) methods to generate samples from the posterior distributions

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