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Prediction problems raised in uncertain environments require different solution approaches such as grey prediction models, which consider uncertainty in information and also enable the use of small data sets. The purpose of this paper is to investigate the comparative performances of grey prediction models (GM) and Markov chain integrated grey models in a demand prediction problem.

The modeling process of grey models is initially described, and then an integrated model called the Grey-Markov model is presented for the convenience of applications. The analyses are conducted on a monthly demand prediction problem to demonstrate the modeling accuracies of the GM (1,1), GM (2,1), GM (1,1)-Markov, and GM (2,1)-Markov models.

Numerical results reveal that the Grey-Markov model based on GM (2,1) achieves better prediction performance than the other models.

It is thought that the methodology and the findings of the study will be a significant reference for both academics and executives who struggle with similar demand prediction problems in their fields of interest.

The novelty of this study comes from the fact that the GM (2,1)-Markov model has been first used for demand prediction. Furthermore, the GM (2,1)-Markov model represents a relatively new approach, and this is the second paper that addresses the GM (2,1)-Markov model in any area.

The purpose of this paper is to review the Fuzzy Markov development for assessing the structural integrity of buried transportation bridges. In doing so, the appropriateness of Fuzzy Markov will be assessed, leading to the subsequent model.

This research will utilize the Fuzzy Markov techniques as the conceptual framework. Such methodology is further supported via the utilization and evaluation of 30 buried transportation bridges using the developed Fuzzy Markov model.

Subsequently, through a developed Fuzzy Markov model, this research found that as the basis of structural resilience, specific matrices for age-dependent transition probability can be compiled using conditional survival probabilities in the various structural states; as the basis of structural integrity, specific environmental and economic schemes can also be established based on inspection intervals, intervention systems and failure phases; exact inspection and maintenance intervals can be scheduled to further prolong an asset’s life; and clear and early warning signs can also be formulated for immediate intervention when the structural integrity of the asset are indeed compromised.

The gap within the literature currently surrounds the limitation of computational analysis for some buried structures such as bridges. Specifically, to streamline such evaluation and regimes, a Fuzzy Markov is developed and reviewed.

The purpose of this paper is to propose a state dependent stochastic Markov model for availability analysis of process plant instead of traditional time dependent model.

The traditional concepts of system performance measurement and reliability (namely, binary; two-state concepts) are observed to be inadequate to characterize performance of complex system components. Availability analysis considering an intermediate state, such as a degraded state, provides a better alternative mechanism for system performance mapping. The availability model provides a better assessment of failure and repair characteristics for equipment in the sub-system and its overall performance. In addition to availability analysis, this paper also discusses the preventive maintenance (PM) program to achieve target availability. In this model, the degraded state is considered as a PM state. Using Markov analysis the optimum maintenance interval is determined.

Markov process provides an easier way to measure the performance of the process facility. This study also revealed that the maintenance interval has a major influence in the availability of a process facility as well as in maintaining target availability. The developed model is also applicable to the varying target availability as well as having the capability to handle even the reconfigured process systems.

Considering the degraded state as an operative state, a higher availability of the plant is predicted. The consideration of the degraded state of the system makes the availability estimation more realistic and acceptable. Availability quantification, target availability allocation and a PM model are exemplified in a sub-system of an liquefied natural gas facility.

The unique features of the present study are; Markov modeling approach integrating availability and PM; optimum PM interval determination of stochastically degrading components based on target availability; consideration of three-state systems; and consideration of increasing failure rates.

Asset intensive process industries are under immense pressure to achieve promised return on investments and production targets. This can be accomplished by ensuring the highest level of availability, reliability and utilization of the critical equipment in processing facilities. In order to achieve designed availability, asset characterization and maintainability play a vital role. The most appropriate and effective way to characterize the assets in a processing facility is based on risk and consequence of failure. The paper aims to discuss these issues.

In this research, a risk-based stochastic modeling approach using a Markov decision process is investigated to assess a processing unit's availability, which is referred as the risk-based availability Markov model (RBAMM). RBAMM will not only provide a realistic and effective way to identify critical assets in a plant but also a method to estimate availability for efficient planning purposes and resource optimization.

A unique risk matrix and methodology is proposed to determine the critical equipment with direct impact on the availability, reliability and safety of the process. A functional block diagram is then developed using critical equipment to perform efficient modeling. A Markov process is utilized to establish state diagrams and create steady-state equations to calculate the availability of the process. RBAMM is applied to natural gas absorption process to validate the proposed methodology. In the conclusion, other benefits and limitations of the proposed methodology are discussed.

A new risk-based methodology integrated with Markov model application of the methodology is demonstrated using a real-life application.

Degraded failures and sudden critical failures are quite prevalent in industries. Degradation processes commonly belong to Weibull family and critical failures are found to follow exponential distribution. Therefore, it becomes important to carry out reliability and availability analysis of such systems. From the reported literature, it is learnt that models are available for the situations where the degraded failures as well as critical failures follow exponential distribution. The purpose of this paper is to present models suitable for reliability and availability analysis of systems where the degradation process follows Weibull distribution and critical failures follow exponential distribution.

The research uses Semi-Markov modeling using the approach of method of stages which is suitable when the failure processes follow Weibull distribution. The paper considers various states of the system and uses state transition diagram to present the transition of the system among good state, degraded state and failed state. Method of stages is used to convert the semi-Markov model to Markov model. The number of stages calculated in Method of stages is usually not an integer value which needs to be round off. Method of stages thus suffers from the rounding off error. A unique approach is proposed to arrive at failure rates to reduce the error in method of stages. Periodic inspection and repairs of systems are commonly followed in industries to take care of system degradation. This paper presents models to carry out reliability and availability analysis of the systems including the case where degraded failures can be arrested by appropriate inspection and repair.

The proposed method for estimating the degraded failure rate can be used to reduce the error in method of stages. The models and the methodology are suitable for reliability and availability analysis of systems involving degradation which is very common in systems involving moving parts. These models are very suitable in accurately estimating the system reliability and availability which is very important in industry. The models conveniently cover the cases of degraded systems for which the model proposed by Hokstad and Frovig is not suitable.

The models developed consider the systems where the repair phenomenon follows exponential and the failure mechanism follows Weibull with shape parameter greater than 1.

These models can be suitably used to deal with reliability and availability analysis of systems where the degradation process is non-exponential. Thus, the models can be practically used to meet the industrial requirement of accurately estimating the reliability and availability of degradable systems.

A unique approach is presented in this paper for estimating degraded failure rate in the method of stages which reduces the rounding error. The models presented for reliability and availability analyses can deal with degradable systems where the degradation process follows Weibull distribution, which is not possible with the model presented by Hokstad and Frovig.

The purpose of this paper is to investigate whether Markov mixture of normals (MMN) model is a viable approach to modeling financial returns.

This paper adopts the full Bayesian estimation approach based on the method of Gibbs sampling, and the latent state variables simulation algorithm developed by Chib.

Using data from the S&P 500 index, the paper first demonstrates that the MMN model is able to capture the unconditional features of the S&P 500 daily returns. It further conducts formal model comparisons to examine the performance of the Markov mixture structures relative to two well‐known alternatives, the GARCH and the t‐GARCH models. The results clearly indicate that MMN models are viable alternatives to modeling financial returns.

The univariate MMN structure in this paper can be generalized to a multivariate setting, which can provide a flexible yet practical approach to modeling multiple time series of assets returns.

Given the encouraging empirical performance of the MMN models, it is hopeful that the MMN models will have success in some interesting financial applications such as Value‐at‐Risk and option pricing.

The paper explicitly formulates the Gibbs sampling procedures for estimating MMN models in a Bayesian framework. It also shows empirically that MMN models are able to capture the stylized features of financial returns. The MMN models and their estimation method in this paper can be applied to other financial data, especially in which tail probability is of major interest or concern.

The purpose of this paper is to deal with the different phases of volatility behavior and the dependence of the variability of the time series on its own past, models allowing for heteroscedasticity like autoregressive conditional heteroscedasticity (ARCH), generalized autoregressive conditional heteroscedasticity (GARCH), or regime‐switching models have been suggested by reserachers. Both types of models are widely used in practice.

Both regime‐switching models and GARCH are used in this paper to model and explain the behavior of crude oil prices in order to forecast their volatility. In regime‐switching models, the oil return volatility has a dynamic process whose mean is subject to shifts, which is governed by a two‐state first‐order Markov process.

The GARCH models are found to be very useful in modeling a unique stochastic process with conditional variance; regime‐switching models have the advantage of dividing the observed stochastic behavior of a time series into several separate phases with different underlying stochastic processes.

The regime‐switching models show similar goodness‐of‐fit result to GARCH modeling, while has the advantage of capturing major events affecting the oil market. Daily data of crude oil prices are used from NYMEX Crude Oil market for the period 13 February 2006 up to 21 July 2009.

Pavement deterioration prediction models play a crucial role in determining maintenance strategies and future funding needs. While deterioration prediction models have been studied extensively in the past, applications of these models to local street networks have been limited. This study aims to address this gap by sharing the results of network level deterioration prediction models developed at a local level.

Network level pavement deterioration prediction models are developed using Markov chains for the local street network in Syracuse, New York, based on pavement condition rating data collected over a 15-year time period. Transition probability matrices are generated by calculating the percentage of street sections that transition from one state to another within one duty cycle. Bootstrap sampling with replacement is used to numerically generate 95% confidence intervals around the transition probability values.

The overall local street network is divided into three cohorts based on street type (i.e. avenues, streets and roads) and two cohorts based on pavement type. All cohorts demonstrated very similar deterioration trends, indicating the existence of a fast-paced deterioration mechanism for the local street network of Syracuse.

This study contributes to the body of knowledge in deterioration modeling of local street networks, especially in the absence of key predictor variables. Furthermore, this study introduces the use of bootstrap sampling with replacement method in generating confidence intervals for transition probability values.

Urinary incontinence (UI) is a common chronic health condition, a problem specifically among elderly women that impacts quality of life negatively. However, UI is usually viewed as likely result of old age, and as such is generally not evaluated or even managed appropriately. Many treatments are available to manage incontinence, such as bladder training and numerous surgical procedures such as Burch colposuspension and Sling for UI which have high success rates. The purpose of this paper is to analyze which of these popular surgical procedures for UI is effective.

This research employs randomized, prospective studies to obtain robust cost and utility data used in the Markov chain decision model for examining which of these surgical interventions is more effective in treating women with stress UI based on two measures: number of quality adjusted life years (QALY) and cost per QALY. Treeage Pro Healthcare software was employed in Markov decision analysis.

Results showed the Sling procedure is a more effective surgical intervention than the Burch. However, if a utility greater than certain utility value, for which both procedures are equally effective, is assigned to persistent incontinence, the Burch procedure is more effective than the Sling procedure.

This paper demonstrates the efficacy of a Markov chain decision modeling approach to study the comparative effectiveness analysis of available treatments for patients with UI, an important public health issue, widely prevalent among elderly women in developed and developing countries. This research also improves upon other analyses using a Markov chain decision modeling process to analyze various strategies for treating UI.

The purpose of this paper is to analyze the historical gas allocation pattern for seeking appropriate arrangement and utilization of potentially insufficient natural gas supply available in Pakistan up to 2030.

This study presents Markov chain-based modeling of historical gas allocation data followed by its validation through error evaluation. Structural prediction using classical Chapman–Kolmogorov method and varying-order polynomial regression in the historical transition matrices are presented.

Markov chain model reproduces the terminal state vector with 99.8 per cent accuracy, thus demonstrating its validity for capturing the history. Lower order polynomial regression results in better structural prediction compared with higher order ones in terms of closeness with Markov approach-based prediction.

The data belongs to a certain geographic region with specific gas demand and supply profile. The proposition may be tested further by researchers to check the validity for other comparable structural predictions/analyses.

This study can facilitate policy-making in the field of natural gas allocation and management in Pakistan specifically and other comparable countries generally.

Two major literature gaps filled through this study are: first, Markov chain model becomes stationary when projected using Chapman–Kolmogorov relation in terms of a fixed, average transition matrix resulting in an equilibrium state after a finite number of future steps. Second, most of the previous studies analyze various gas consumption sectors individually, thus lacking integrated gas allocation policy.