A Bivariate Model for Markov Manpower Planning Systems

This paper reports on the successful development and implementation of an interactive manpower scheduling and planning system for a children’s mental health facility in a large urban hospital centre in Montreal, Canada. This service employs approximately 120 professionals who meet the nursing and therapy needs of between 70 and 100 children at any one time, with a yearly through-put of approximately 120 patients. The system is based on the patient as a central entity and is designed to improve the patient flow and resource scheduling process and to permit the evaluation of policy options in real time.

This paper presents an optimum workforce-size model which determines the minimum number of excess workers (overstaffing) as well as the minimum total recruitment cost during a specified planning horizon. The model is an extension of other existing dynamic programming models for manpower planning in the sense that it strikes a balance between overstaffing and understaffing at each stage of the computations. The model also considers a manpower planning system in which the employment level has upper and lower bounds. The employment level varies from one period to another while the cost incurred in each period depends only on recruitment size and the overstaffing cost from an earlier stage. A mathematical problem is formulated and solved to illustrate the model numerically.KEYWORDS: Workforce-size, dynamic programming, Optimum, Overstaffing and Understaffing.

Computation of bounds for transient measures of large rewarded Markov models using regenerative randomization

In this paper a novel Voter Based Markov model will be presented for evaluation of the reliability in a multi-port power electronic interface. In the new Markov model, a new technique called Voter Based State Reduction (VBSR) technique will be introduced for reducing the number of states in Failure Mode and Effect Analysis (FMEA). The VBSR technique will simplify the reliability analysis of power electronic systems. It will also make the results of the reliability assessment more meaningful. In order to show the effectiveness of the proposed model, reliability of a Multi-port Power Electronics Interface (MPEI) will be evaluated using both conventional and Voter based Markov model. Comparison of FMEA and reliability evaluation results between conventional Markov model and the new Voter Based Markov model confirms the effectiveness of the proposed method.

Stochastic bivariate time series models of waves in the North Sea and their application in simulation-based design

Markov models are commonly used for unavailability analysis of redundant systems. However, due to the exploding states of Markov models for redundant systems, the states need to be merged to simplify the computation, which is called micro-Markov models. However, how to derive the failure rates and repair rates of the newly developed micro-Markov models has not been studied thoroughly. Therefore, this paper proposes detailed explanations and rules to derive the static unavailability by the micro-Markov models for thek-out-of-n:G systems with multiple failure modes. Firstly, two properties about applying the Markov models to the repairable system with independent multiple failure modes are presented. Based on these two properties, two rules are proposed for implementing the micro-Markov models. The micro-Markov models provide the exact same results for the repairablek-out-of-n:G system with multiple independent failure modes and repair mechanisms and approximate results for systems with multiple hybrid failure modes. A case study of safety integrity verification for safety instrumented systems is provided to illustrate the application of the proposed method. The conceptual comparison and numerical examples demonstrate the reasonability and usefulness of the proposed micro-Markov models.

Queueing models provide a useful tool for predicting the performance of many service systems including computer systems, telecommunication systems, computer/communication networks and flexible manufacturing systems. Traditional queueing models predict system performance under the assumption that all service facilities provide failure-free service. It must, however, be acknowledged that service facilities do experience failures and that they get repaired. In recent years, it has been increasingly recognized that this separation of performance and reliability/availability models is no longer adequate. An exact steady-state queueing analysis of such systems is considered by several authors and is carried out by means of generating functions, supplementary variables, imbedded Markov process and renewal theory, or probabilistic techniques [1,2,7,8]. Another approach is approximate, in which it is assumed that the time to reach the steady-state is much smaller than the times to failures/repairs. Therefore, it is reasonable to associate a performance measure (reward) with each state of the underlying Markov (or semi-Markov) model describing the failure/repair behavior of the system. Each of these performance measures is obtained from the steady-state queueing analysis of the system in the corresponding state [3,5]. Earlier we have developed models to derive the distribution of job completion time in a failure-prone environment [3,4]. In these models, we need to consider a possible loss of work due to the occurrence of a failure, i.e., the interrupted job may be resumed or restarted upon service resumption. Note that the job completion time analysis includes the delays due to failures and repairs. The purpose of this paper [9] is to extend our earlier analysis so as to account for the queueing delays. In effect, we consider an exact queueing analysis of fault-tolerant systems in order to obtain the steady-state distribution and the mean of the number of jobs in the system. In particular, we study a system in which jobs arrive in a Poisson fashion and are serviced according to FCFS discipline. The service requirements of the incoming jobs form a sequence of independent and identically distributed random variables. The failure/repair behaviour of the system is modelled by an irreducible continuous-time Markov chain, which is independent of the number of jobs in the system. Let the state-space be {1,2, …, n }. When the computer system is in state i it delivers service at rate r i ≥ 0. Furthermore, depending on the type of the state, the work done on the job is preserved or lost upon entering that state. The actual time required to complete a job depends in a complex way upon the service requirement of the job and the evolution of the state of the system. Note that even though the service requirements of jobs are independent and identically distributed, the actual times required to complete these jobs are neither independent nor identically distributed, and hence the model cannot be reduced to a standard M/G/ 1 queue [8]. As loss of work due to failures and interruptions is quite a common phenomenon in fault-tolerant computer systems, the model proposed here is of obvious interest. Using our earlier results on the distribution of job completion time we set up a queueing model and show that it has the block M/G/ 1 structure. Queueing models with such a structure have been studied by Neuts, Lucantoni and others [6]. We demonstrate the usefulness of our approach by performing the numerical analysis for a system with two processors subject to failures and repairs.

Two unrepairable series structure systems with k-out-of-m:G subsystems and spares are investigated. The first one consists of a k-out-of-m:G subsystem and a series subsystem while the other consists of two k-out-of-m:G subsystems. The systems have identical components with identical lifetime distributions and the working components are suspended as soon as the systems are down. Two Markov models are proposed for the reliability analysis of such systems and closed form results on the reliability and the mean time to failure (MTTF) are presented. Numerical examples are given to illustrate the impact of several parameters on the reliability of the systems.

Application of Markovian models in the reliability analysis of dynamic systems is presented. In the context of the paper dynamic systems are systems whose stochastic behavior is changing with time. The reliability of control/safety systems coupled with the dynamics of protected or controlled systems is also analyzed. Markovian models are compared with static logic models like fault/event trees.

A robust production control policy for VLSI wafer fabrication : Sheldon X. C. Lou and Patrick W. Kager. IEEE Trans. SemiconductorMfg2(4), 159 (1989)

Safety analysis of complex technical systems currently operating in the transport sector is an urgent challenge for the global maritime industry, which suffers from a lack of information about the levels of risk and the consequences of their incorrect assessment. Among the requirements for vessel management and operations the importance of having a highly professional crew and up-to-date navigational equipment. Navigational safety is one of the components of the integral concept of “safety” for a seagoing ship. Assessment of integral safety is based on assessments of the individual safety components. In this study, the focus is on “navigational safety”, which is primarily understood as ensuring safe operation of a vessel in specific navigation conditions, ensuring safe control and maneuvering of the vessel, ship position monitoring, heading control, sufficient depth margin under the keel along the route, taking into account its actual draft and subsidence in shallow water, and sea disturbance. In the offered research on the basis of the identified states of navigational safety, the graphic model of process and matrix of transition probabilities in the general form with use of homogeneous Markov model of change of navigational safety of a vessel, with discrete time and presence of absorbing state is formed. The proposed Markov process model can be used to assess vessel navigational safety when establishing possible states of navigational safety with significant probability to assess ship safety and make decisions to ensure safe vessel operation.

The present work illustrated the reliability analysis of solar photovoltaic systems and the efficiency of medium grid-connected photovoltaic (PV) power systems with 1-out of- 2 PV panels, one out of one charge controller, 1- out of 3 batteries, 1- out of 2 inverters and one out one Distributor. The units that comprise the solar were studied. Gumbel Hougaard Family Copula method was used to evaluate the performances of solar photovoltaics. Other reliability metrics were investigated, including availability, mean time to failure, and sensitivity analysis. The numerical result was generated using the Maple 13 software. The numerical results were presented in tables, with graphs to go along with them. Failure rates and their effects on various solar photovoltaic subsystems were investigated. Numerical examples are provided to demonstrate the obtained results and to assess the influence of various system characteristics. The current research could aid companies, and their repairers overcome some issues that specific manufacturing and industrial systems repairers face.

Performance evaluation and enhancement of multistage manufacturing systems with rework loops

Most real world situations involve modelling of physical processes that evolve with time and space, especially those exhibiting high variability. Such events that have to flow with time or space are called dynamical systems. The mathematical notions of a dynamical system serves to depict the flow of causation from past into future (Kalman 1960). In this study, Markov model which is a signal model based on the Markovian property with state space approach was adopted for the analysis of dynamical systems. The Nigerian monetary exchange rate data was used in the application with the use of R statistical software package. The study incorporated the Chapman-Kolmogorov equation in the construction of absolute limiting distribution of the system via the state variables. The procedure gives an easy and effective means of analysing complex and time varying dynamical systems. The study showed that the Nigerian monetary exchange rate is ergodic with stationary probability distribution.

Hardware systems are present in many fields of human activity. Markov models are sometimes used in hardware reliability, availability, and maintainability (RAM) modeling. They are especially useful in situations in which the system we want to analyze may be modeled with several states through which the system evolves, some of them corresponding to ON states, the rest to OFF states. We provide here RAM analyses of such systems within a Bayesian framework, addressing both short-term and long-term performance.