A Simple Discrete Approximation for the Renewal Function

Background: The renewal function is widely useful in the areas of reliability, maintenance and spare components inventory planning. Its calculation relies on the type of the probability density function of component failure times which can be, regarding the region of the component lifetime, modelled either by the exponential or by one of the peak-shaped density functions. For most peak-shaped distribution families the closed form of the renewal function is not available. Many approximate solutions can be found in the literature, but calculations are often tedious. Simple formulas are usually obtained for a limited range of functions only. Objectives: We propose a new approach for evaluation of the renewal function by the use of a simple discrete approximation method, applicable to any probability density function. Methods/Approach: The approximation is based on the well known renewal equation. Results: The usefulness is proved through some numerical results using the normal, lognormal, Weibull and gamma density functions. The accuracy is analyzed using the normal density function. Conclusions: The approximation proposed enables simple and fairly accurate calculation of the renewal function irrespective of the type of the probability density function. It is especially applicable to the peak-shaped density functions when the analytical solution hardly ever exists

Availability Analysis of the Integrated Maintenance Technique based on Reliability, Risk, and Condition in Power Plants

The availability of power plants is of utmost importance in a power system. The availlability of a power plant is determined by its reliability and maintainability, which results from the plant’s maintenance program. Commonly used maintenance techniques for power plants include reliability-centered maintenance (RCM), risk-based maintenance (RBM), and condition-based maintenance (CBM) as well as their combination. This study aims to analyze the respective system availability that results from each of the three maintenance techniques and examines the system availability of the integrated maintenance technique, which is based on reliability, risk, and condition. The availability analysis is performed by developing a mathematical model based on the maintenance programs produced by each maintenance technique. The availabilities of the RCM, RBM, CBM, and integrated maintenance techniques are 81.56%, 81.02%, 84.92%, and 90.07%, respectively

A Stochastic Process Study of Two-Echelon Supply Chain with Bulky Demand Process Incorporating cost Sharing Coordination Strategies

This research considers a single-item two-echelon supply chain facing a sequence of stochastic bulky customer demand with random order inter-arrival time and random demand size. The demand process is a general renewal process and the cost functions for both parties involve the renewal function and its integral. The complexity of the general renewal function causes the computational intractability in deciding the optimal order quantities, so approximations for the renewal function and its integral are introduced to address the computational complexity. Asymptotic expansions are commonly used in the literature to approximate the renewal function and its integral when the optimal decisions are relatively large compared to the mean of the inter-renewal time. However, the optimal policies do not necessarily fall in the asymptotic region. So the use of asymptotic expansions to approximate the renewal function and its integral in the cost functions may cause significant errors in decision making. To overcome the inaccuracy of the asymptotic approximation, this research proposes a modified approximation. The proposed approximation provides closed form functions for the renewal function and its integral which could be applied to various optimization problems such as inventory planning, supply chain management, reliability and maintenance. The proposed approximations are tested with commonly used distributions and applied to an application in the literature, yielding good performance. By applying the proposed approximation method to the supply chain cost functions, this research obtains the optimal policies for the decentralized and the centralized cases. The numerical results provide insights into the cost savings realized by the centralization of the supply chain compared to the decentralized case. Furthermore, this research investigates coordination schemes for the decentralized case to improve the utilities of parties. A cost sharing mechanism in which the vendor offers the retailer a contract as a compensation of implementing vendordesired inventory policy is investigated. The sharing could be realized by bearing part of the retailer’s inventory holding cost or fixed cost. The contract is designed to minimize the vendors cost while satisfying the individual rationality of the retailer. Other forms of coordination mechanisms, such as the side payment and delayed payment, are also discussed

Safety and Reliability - Safe Societies in a Changing World

The contributions cover a wide range of methodologies and application areas for safety and reliability that contribute to safe societies in a changing world. These methodologies and applications include: - foundations of risk and reliability assessment and management - mathematical methods in reliability and safety - risk assessment - risk management - system reliability - uncertainty analysis - digitalization and big data - prognostics and system health management - occupational safety - accident and incident modeling - maintenance modeling and applications - simulation for safety and reliability analysis - dynamic risk and barrier management - organizational factors and safety culture - human factors and human reliability - resilience engineering - structural reliability - natural hazards - security - economic analysis in risk managemen