Profit Analysis of a Two Unit Cold Standby System Operating Under Different Weather Conditions Subject t o Inspection

A system, or unit, is said to be working under normal weather conditions if the system is working under prescribed conditions as defined/stated by the definition of reliability of system/unit, otherwise the system is said to be working in abnormal weather conditions. For example, if a car with the capacity for five persons is carrying more than five persons, it will be said to be working under abnormal weather conditions. Another example, if a hydraulic machine having the capacity to lift a maximum weight of 500 tons is lifting a weight of 600 tons, then the machine is working under abnormal weather conditions. Hence, in this situation, work done by the machine is out of its capacity and the machine is working in abnormal weather conditions. If the machine is working within the capacity of the stated conditions, it is said to be working in normal weather conditions. The main purpose of this paper is to analyze the profit of a two-unit system called the standby system that is working under different weather conditions in an inspection facility. There is a single perfect server who visits the system immediately whenever required. A server inspects the unit before repair/replacement of the failed unit. All the mechanical activities done by the server are only possible during normal weather conditions. There are two possibilities after inspection of the unit; either repair of the unit is feasible or not feasible. If repair of the unit is not feasible, then the unit will be replaced immediately by a new unit. Otherwise, the repaired unit works as a new unit. The operative unit undergoes preventive maintenance after a specific (maximum) operation time. All random variables are statistically independent. The failure rate and the rate by which the system undergoes for preventive maintenance are constant whereas the inspection rate, repair rate, and maintenance rate follow negative exponential distributions. The expressions for several reliability measures are derived in steady state conditions using the regenerative point technique and semi-Markov process. The graphical behavior of MTSF, availability and profit function, has been depicted with respect to preventive maintenance rate for arbitrary values of other parameters and costs

A Repairable System Supported by Two Spare Units and Serviced by Two Types of Repairers

We study a one-unit repairable system, supported by two identical spare units on cold standby, and serviced by two types of repairers. The model applies, for instance, to ANSI (American National Standard Institute) centrifugal pumps in a chemical plant, and hydraulic systems in aviation industry. The failed unit undergoes repair either by an in-house repairer within a random or deterministic patience time, or else by a visiting expert repairer. The expert repairs one or all failed units before leaving, and does so faster but at a higher cost rate than the regular repairer. Four models arise depending on the number of repairs done by the expert and the nature of the patience time. We compare these models based on the limiting availability , and the limiting profit per unit time , using semi-Markov processes, when all distributions are exponential. As anticipated, to maximize , the expert should repair all failed units. To maximize a suitably chosen deterministic patience time is better than a random patience time. Furthermore, given all cost parameters, we determine the optimum number of repairs the expert should complete, and the optimum patience time given to the regular repairer in order to maximize

Mathematical Modeling and Simulation in Mechanics and Dynamic Systems

The present book contains the 16 papers accepted and published in the Special Issue “Mathematical Modeling and Simulation in Mechanics and Dynamic Systems” of the MDPI “Mathematics” journal, which cover a wide range of topics connected to the theory and applications of Modeling and Simulation of Dynamic Systems in different field. These topics include, among others, methods to model and simulate mechanical system in real engineering. It is hopped that the book will find interest and be useful for those working in the area of Modeling and Simulation of the Dynamic Systems, as well as for those with the proper mathematical background and willing to become familiar with recent advances in Dynamic Systems, which has nowadays entered almost all sectors of human life and activity

Reliability applied to maintenance

The thesis covers studies conducted during 1976-79 under a Science Research Council contract to examine the uses of reliability information in decision-making in maintenance in the process industries. After a discussion of the ideal data system, four practical studies of process plants are described involving both Pareto and distribution analysis. In two of these studies the maintenance policy was changed and the effect on failure modes and frequency observed. Hyper-exponentially distributed failure intervals were found to be common and were explained after observation of maintenance work practices and development of theory as being due to poor workmanship and parts. The fallacy that constant failure rate necessarily implies the optimality of maintenance only at failure is discussed. Two models for the optimisation of inspection intervals are developed; both assume items give detectable warning of impending failure. The first is based upon constant risk of failure between successive inspections 'and Weibull base failure distribution~ Results show that an inspection/on-condition maintenance regime can be cost effective even when the failure rate is falling and may be better than periodiC renewals for an increasing failure situation. The second model is first-order Markov. Transition rate matrices are developed and solved to compare continuous monitoring with inspections/on-condition maintenance an a cost basis. The models incorporate planning delay in starting maintenance after impending failure is detected. The relationships between plant output and maintenance policy as affected by the presence of redundancy and/or storage between stages are examined, mainly through the literature but with some original theoretical proposals. It is concluded that reliability techniques have many applications in the improvement of plant maintenance policy. Techniques abound, but few firms are willing to take the step of faith to set up, even temporarily, the data-collection facilities required to apply them. There are over 350 references, many of which are reviewed in the text, divided into chapter-related sectionso Appendices include a review of Reliability Engineering Theory, based on the author's draft for BS 5760(2) a discussion of the 'bath-tub curves' applicability to maintained systems and the theory connecting hyper-exponentially distributed failures with poor maintenance practices