A discounted model for a repairable system with continuous state space

We examine repairable systems with a continous state space and partial repair options, carried out at fixed times $n=1,2,...$. Every time interval $[n,n+1)$ there is a manufacturing cost and a repair cost. These cost functions are not restricted to the class of bounded functions in this study. Conditions are found under which a control-limit replacement policy minimizes the discounted cost. Hence these conditions guarantee that there is an optimal policy under the discounted cost criterion which does not use partial repairs. We explicitly explain how to derive this optimal policy

Optimising Age-Replacement and Extended Non-Renewing Warranty Policies in Lifecycle Costing

This paper analyses the life cycle cost of equipment protected by both base and extended warranty policies from a consumer's perspective. We assume that the equipment has two types of failure: minor and catastrophic. A minor failure can be corrected with minimal repair whereas a catastrophic failure can only be removed by a replacement. It is assumed that equipment is maintained at no charge to the consumer during the warranty period, whereas the consumer is fully charged for any maintenance on failures after the extended warranty expires. We formulate the expected life cycle cost of the equipment under a general failure time distribution, and then for special cases we prove that the optimal replacement and extended warranty policies exists where the expected life cycle cost per unit time is minimised. This is examined with numerical examples. © 2011 Elsevier B.V. All rights reserved

Selective maintenance optimisation for series-parallel systems alternating missions and scheduled breaks with stochastic durations

This paper deals with the selective maintenance problem for a multi-component system performing consecutive missions separated by scheduled breaks. To increase the probability of successfully completing its next mission, the system components are maintained during the break. A list of potential imperfect maintenance actions on each component, ranging from minimal repair to replacement is available. The general hybrid hazard rate approach is used to model the reliability improvement of the system components. Durations of the maintenance actions, the mission and the breaks are stochastic with known probability distributions. The resulting optimisation problem is modelled as a non-linear stochastic programme. Its objective is to determine a cost-optimal subset of maintenance actions to be performed on the components given the limited stochastic duration of the break and the minimum system reliability level required to complete the next mission. The fundamental concepts and relevant parameters of this decision-making problem are developed and discussed. Numerical experiments are provided to demonstrate the added value of solving this selective maintenance problem as a stochastic optimisation programme

A Periodicity Metric for Assessing Maintenance Strategies

Organised by: Cranfield UniversityThe maintenance policy in manufacturing systems is devised to reset the machines functionality in an economical fashion in order to keep the products quality within acceptable levels. Therefore, there is a need for a metric to evaluate and quantify function resetting due to the adopted maintenance policy. A novel metric for measuring the functional periodicity has been developed using the complexity theory. It is based on the rate and extent of function resetting. It can be used as an important criterion for comparing the different maintenance policy alternatives. An industrial example is used to illustrate the application of the new metric.Mori Seiki – The Machine Tool Company; BAE Systems; S4T – Support Service Solutions: Strategy and Transitio

Decline and repair, and covariate effects

The failure processes of repairable systems may be impacted by operational and environmental stress factors. To accommodate such factors, reliability can be modelled using a multiplicative intensity function. In the proportional intensity model, the failure intensity is the product of the failure intensity function of the baseline system that quantifies intrinsic factors and a function of covariates that quantify extrinsic factors. The existing literature has extensively studied the failure processes of repairable systems using general repair concepts such as age-reduction when no covariate effects are considered. This paper investigates different approaches for modelling the failure and repair process of repairable systems in the presence of time-dependent covariates. We derive statistical properties of the failure processes for such systems

Some contributions to modeling usage sensitive warranty servicing strategies and their analyses

Providing a warranty as a part of a product\u27s sale is a common practice in industry. Parameters of such warranties (e.g., its duration limits, intensity of use) must be carefully specified to ensure their financial viability. A great deal of effort has been accordingly devoted in attempts to reduce the costs of warranties via appropriately designed strategies to service them. many such strategies, that aim to reduce the total expected costs of the warrantor or / and are appealing in other ways such as being more pragmatic to implement - have been suggested in the literature. Design, analysis and optimization of such servicing strategies is thus a topic of great research interest in many fields. In this dissertation, several warranty servicing strategies in two-dimensional warranty regimes, typically defined by a rectangle in the age-usage plane, have been proposed, analyzed and numerically illustrated. Two different approaches of modeling such usage sensitive warranty strategies are considered in the spirit of Jack, Iskandar and Murthy (2009) and Iskandar (2005). An `Accelerated Failure Time\u27 (AFT) formulation is employed to model product degradation resulting due to excessive usage rate of consumers. The focus of this research is on the analysis of warranty costs borne by the manufacturer (or seller or third party warranty providers) subject to various factors such as product\u27s sale price, consumer\u27s usage rate, types and costs of repair actions. By taking into account the impact of the rate of use of an item on its lifetime, a central focus of our research is on warranty cost models that are sensitive to the usage rate. Specifically, except the model in Chapter 4 where the rate at which an item is used is considered to be a random variable; all other warranty servicing policies that we consider, have usage rate as a fixed parameter, and hence are policies conditional on the rate of use. Such an approach allows us to examine the impact of a consumer\u27s usage rate on the expected warranty costs. For the purpose of designing warranties, exploring such sensitivity analysis may in fact suggest putting an upper limit on the rate of use within the warranty contract, as for example in case of new or leased vehicle warranties. A Bayesian approach of modeling 2-D Pro-rated warranty (PRW) with preventive maintenance is considered and explored in the spirit of Huang and Fang (2008). A decision regarding the optimal PRW proportion (paid by the manufacturer to repair failed item) and optimal warranty period that maximizes the expected profit of the rm under different usage rates of the consumers is explored in this research. A Bayesian updating process used in this context combines expert opinions with market data to improve the accuracy of the parameter estimates. The expected profit model investigated here captures the impact of juggling decision variables of 2-D pro-rated warranty and investigates the sensitivity of the total expected profit to the extent of mis-specification in prior information