Development of statistical theory in reliability engineering: A survey

Statistical theory and its applications have played a significant role in the advancement of methodology and techniques for solving various problems in reliability engineering. Different criteria of aging have been introduced for modelling and characterizations of wear properties. Some real life engineering reliability operations arising in maintenance and replacement policies formulations are investigated as convolution, mixture and formation of coherent systems. Shock models are studied for shocks arriving according to Poisson process and causing damages with specific form of aging. Cumulative damage models have been also studied by many researchers. Statistical hypotheses testing are used to test whether a certain, censored or uncensored data has exponential or a specific aging propety.In this paper we present a unified state of the art type of survey for the research and developments in these problems. In particular we expose the main recent contributions, trace the trend of research and highlight the possible direction of further research.     

Transient rate matrix determination for the complex system

This paper presents new techniques dealing with the reliability of complex systems. A power station reliability assessment model is used to illustrate the approach. Before calculating the state transient probabilities for the overall electrical power plant, the failure and repair rates of each generating unit are needed. These two coefficients can form a transition rate matrix, which represents each generator. To form the overall system a special technique is required. In the present study the direct‐differentiation and the Kronecker algebra methods are used to form the overall transition rate matrix, which represents the whole system. Forming the overall system is the first part (major part) of the current study. The second part is to calculate the state transient probabilities, following the Adams method. Two electric power plants from the State of Bahrain are analysed as examples. Copyright © 2001 John Wiley & Sons, Ltd.     

Reliability study of two engineering models using LU decomposition

This paper presents two different methods — LU decomposition and Runge–Kutta — for reliability engineering assessment. These methods are used to calculate the steady-state probabilities and frequencies of two different engineering models. The effect of the different methods is shown on the simple numerical examples by comparing the steady-state probabilities and frequencies of both models. The paper concludes that the LU decomposition method is useful to practicing engineers and students of reliability concepts. Also, the final results for both methods is almost the same.     

New better than renewal-used classes of life distributions

The concept of stochastic dominance in economics is used to compare the conditional life distribution of a used device that has lived until time t/spl ges/0 and its life distributions at time t=0. This comparison gives two classes of life distributions namely, the NBRU class of life distribution and its dual. Relations of these classes to existing criteria of aging and some of their closure properties under reliability operations are studied. The preservation of these aging properties for the survival probability under the homogeneous shock model process are investigated.     

Estimation of the Maximum Annual Loads Modeling for Kingdom of Bahrain

The present paper proposes the impact of the air temperature on electricity demand as expected. It is clear that the annual maximum load is recorded versus the years starting by the year 2009 up to 2012. At present, the graph fitting technique is applied with some mathematical and computational tools based on the actual values of the years 2009 up to 2012 considering the lower values, the higher values and the average values of the annual maximum loads for Kingdom of Bahrain. For the three scenarios, the models are obtained by curve fitting technique. As well, the model of actual loads is obtained finally which has mostly the closest values obtained.     

Prediction of reliability of broadcasting transmitter systems

This paper shows that the SPICE circuit simulation program is a useful tool for predicting the reliability of broadcasting transmitters. A broadcasting system formed of two transmitters fed from a common power supply unit is considered as a vehicle to illustrate the use of the proposed technique. Agreement between the steady-state probabilities obtained using the proposed technique are compared with results obtained using the Laplace transform method     

Flow graph development method

The present paper demonstrates the use of graph theory to find the steady state behaviour of multi-state systems described by Markov models.Two applications are demonstrated and compared with results obtained by Laplace Transform technique. The agreement between the two techniques appears to be excellent.The developed method is also compared with another method which uses the graph theory to calculate the steady state probabilities.     

MATCHING OF SEPARATELY EXCITED DC MOTORS TO PHOTOVOLTAIC GENERATORS FOR MAXIMUM POWER OUTPUT

This paper addresses the matching of separately excited dc motors to photovoltaic generators (PVG) for maximum power output. The dc motor is used to drive a centrifugal water pump. A PVG is a nonlinear device having insolation dependent I–V (current–voltage) characteristic, and hence a natural mismatch exists between the motor loads and the PVG. Therefore, considering the high initial cost of PVG, it is of vital importance to develop an appropriate matching process, to utilize PVG efficiently. In this article a procedure is developed to express the field current of the motor directly in terms of the maximum power point current and voltage of the PVG. It is shown that by adjusting the field current according to the developed relation, the motor is forced to follow the maximum power trajectory of the PVG, i.e. the input power of the motor is always equal to the maximum output power of the PVG at any available solar insolation. The effect of temperature on the I–V characteristic of the PVG is neglected at this stage. Finally a general expression is proposed relating the optimum field current directly to the available insolation level, which may be used as base for best matching.     

The prerequisite for competition in the restructured wholesale Saudi electricity market

Protection of customers against monopoly is the first and main objective of the Saudi Electricity and Co-generation Regulatory Authority (ECRA). The second important objective, as recommended by the present study, is regulating natural monopoly businesses [Saudi electricity national grid (SENG) and Saudi electricity distribution (SED)] in addition to promoting real competition in competitive businesses [power supply providers (PSPs) and customer service providers (CSPs)]. Another four main objectives of ECRA are to promote the efficient use of energy and natural resources, to ensure a reasonable rate of return for PSPs and CSPs and at the same time to be fair to end-users, to ensure reasonable charges to SENG and SED services to be adequate for them to run the organization in a break-even manner and to maintain the system's security and reliability. The present paper discusses the way to improve and restructure the Saudi electricity market.     

Comparison between state probabilities and availabilities of four-state and five-state models using Laplace transform and matrix multiplication methods

When it is required to study the behaviour of any system after start-up or repair, transient solutions are particularly important. Also, these solutions become necessary when the behaviour need to be studied over a fixed period of time during which the system is required to perform a given mission. There are a number of methods available to solve the first order differential equations of any system, including: the Laplace Transform method, and the Matrix Multiplication method. Both methods are used in this paper to calculate the state-probabilities for four-state and five-state models, respectively, and the results are compared. A comparison is also made between the system “availability” and “unavailability” for both four-state and five-state models using the Laplace Transform and the Matrix Multiplication methods.