Toni Lupo

Determination of Pareto frontier in multi-objective maintenance optimization

Abstract The objective of a maintenance policy generally is the global maintenance cost minimization that involves not only the direct costs for both the maintenance actions and the spare parts, but also those ones due to the system stop for preventive maintenance and the downtime for failure. For some operating systems, the failure event can be dangerous so that they are asked to operate assuring a very high reliability level between two consecutive fixed stops. The present paper attempts to individuate the set of elements on which performing maintenance actions so that the system can assure the required reliability level until the next fixed stop for maintenance, minimizing both the global maintenance cost and the total maintenance time. In order to solve the previous constrained multi-objective optimization problem, an effective approach is proposed to obtain the best solutions (that is the Pareto optimal frontier) among which the decision maker will choose the more suitable one. As well known, describing the whole Pareto optimal frontier generally is a troublesome task. The paper proposes an algorithm able to rapidly overcome this problem and its effectiveness is shown by an application to a case study regarding a complex series–parallel system.

ELECTRE III to dynamically support the decision maker about the periodic replacements configurations for a multi-component system

The problem tackled by the present paper concerns the selection of the elements of a repairable and stochastically deteriorating multi-component system to replace (replacements configuration) during each scheduled and periodical system stop within a finite optimization cycle, by ensuring the simultaneous minimization of both the expected total maintenance cost and the system unavailability. To solve the considered problem, a combined approach between multi-objective optimization problem (MOOP) and multi-criteria decision making (MCDM) resolution techniques is proposed. In particular, the @e constraint method is used to single out the optimal Pareto frontier whereas the ELECTRE III multi-criteria decision support method is proposed to support the selection of the replacements configuration that represents the best compromise among the considered objectives. The proposed approach is sequentially applied at each scheduled system stop by allowing the dynamic updating of the information about the decisional context in which the decision maker has to operate. To illustrate the whole procedure a numerical case study is solved for different hypothesized scenarios related to the importance attributed by the decision maker to the system unavailability and the maintenance cost objectives.

An Effective Double Sampling Scheme for the c Control Chart

In the present paper is developed a statistical process control inspection procedure based on a new simple-to-implement and effective double sampling scheme for the c control chart, aimed at the minimization of the number of inspected observation units and warranting fixed levels for the type I and II error risks. In particular, the formulations of the false alarm risk α, the power P of the chart, and the expected number of inspected observation units for the developed inspection procedure are given, whereas a macro of Microsoft Excel is adopted to solve the tackled problem. In order to illustrate the application of the developed approach and to investigate on the influence of several operating parameters, numerical examples are carried out and the related considerations are given. Finally, by comparing the performance of the developed inspection procedure with that of the related classic c chart scheme, meaningful reduction of the number of the inspected observation units can be achieved by adopting the proposed approach. Copyright

A Multi-Objective Approach to Optimize a Periodic Maintenance Policy

The present paper proposes a multi-objective approach to find out an optimal periodic maintenance policy for a repairable and stochastically deteriorating multi-component system over a finite time horizon. The tackled problem concerns the determination of the system elements to replace at each scheduled and periodical system inspection by ensuring the simultaneous minimization of both the expected total maintenance cost and the expected global system unavailability time. It is assumed that in the case of system elements failure they are instantaneously detected and repaired by means of minimal repair actions in order to rapidly restore the system. A nonlinear integer mathematical programming model is developed to solve the treated multi-objective problem, whereas the Pareto optimal frontier is described by the Lexicographic Goal Programming and the e-constraint methods. To explain the whole procedure, a case study is solved and the related considerations are given.

Economic Design Approach for an SPC Inspection Procedure Implementing The Adaptive C Chart

The present paper proposes a design approach for a statistical process control (SPC) procedure implementing a c control chart for non-conformities, with the aim to minimize the hourly total quality-related costs. The latter take into account the costs arising from the non-conforming products while the process is in-control and out-of-control, for false alarms, for assignable cause locations and system repairs, for sampling and inspection activities and for the system downtime. The proposed economic optimization approach is constrained by the expected hourly false alarms frequency, as well as the available labor resource level. A mixed integer non-linear constrained mathematical model is developed to solve the treated optimization problem, whereas the Generalized Reduced Gradient Algorithm implemented on the solver of Microsoft Excel is adopted to resolve it. In order to illustrate the application of the developed procedure, a numerical analysis based on a fractional factorial design scheme, to investigate on the influence of several operating and costs parameters, is carried out, and the related considerations are given. Finally, the obtained results show that only few parameters have a meaningful effect on the selection of the optimal SPC procedure. Copyright

Comparing the Economic Effectiveness of Various Adaptive Schemes for the c Chart

In an attempt to improve the effectiveness of statistical process control (SPC) procedures, a variety of adaptive schemes has been developed in the last decades. However, considering control charts for attributes, relatively few works about adaptive schemes have been proposed, and most of them were proposed only recently. The common characteristic of those schemes is that one or more chart parameters are allowed to adaptively vary during the SPC operations according to the sampling information history, typically the current point plotted on the chart. In this way, the adaptive schemes are smarter than the related static ones, but they are also more complicated in terms of implementation. The purpose of the present work is to evaluate and compare the economic performance of the main adaptive schemes of a control chart for attributes, in order to derive conclusions on their relative effectiveness. In particular, the analysis is focused on the c chart that is used to monitor the total nonconformities number in an inspection unit. A numerical comparative study, based on a fractional factorial design scheme, to investigate on the influence of several operating and costs parameters, is carried out, and the related considerations are given. The obtained results show that the chart parameter having the most impact on the economic performance is the sampling interval. Therefore, in most cases, the use of a c chart with adaptive sampling intervals is the better choice than other adaptive schemes, which are also more complicated in terms of implementation. Copyright

ECONOMIC-STATISTICAL DESIGN APPROACH FOR A VSSI X-BAR CHART CONSIDERING TAGUCHI LOSS FUNCTION AND RANDOM PROCESS SHIFTS

Economic design approaches of control charts are commonly based on the assumption that various cost parameters values and the occurrence risk of assignable causes have to be a priori known with precision. However, in real operative contexts, such parameters can be really difficult to accurately estimate, especially considering costs arising from out-of-control conditions of the process. As consequence, pure economic design approaches can involve chart schemes with low statistical performance. To overcome such limitation, it is herein proposed a multi-objective economic-statistical design approach for an adaptive X-bar chart. In particular, such approach aims at the minimization of both the total quality related costs and the out-of-control average run length, in such a way assuring an optimal trade-off between economic and statistical performance of the related control procedure. Moreover, for a robust design approach, the mean shift is considered as a random variable. A mixed integer nonlinear constrained mathematical model is formulated to solve the treated problem, whereas the Pareto optimal frontier is described by the e-constraint method. In order to show the employment of the proposed approach, an illustrative example is developed and the related considerations are given. Finally, some sensitivity analysis is also performed to investigate the effects of operative and costs parameters on chart parameters.

A Multi‐Objective Design Approach for the c Chart Considering Taguchi Loss Function

The present paper proposes a multi-objective design approach for the c chart, considering in the optimization process of the chart parameters both the statistical and the economic objectives. In particular, the minimization of the hourly total quality related costs is the considered objective to carry out the economic goal, whereas the statistical objective is reached by the minimization the out-of-control average run length of the chart. A mixed integer non-linear constrained mathematical model is formulated to solve the treated multi-objective optimization problem, whereas the Pareto optimal frontier is described by the e-constraint method. In order to show the employment of the proposed approach, an illustrative example is developed and the related considerations are given. Finally, some sensitivity analysis is also performed to investigate the effects of operative and costs parameters on the chart performance. Copyright

The New Nino Capability Index for Dynamic Process Capability Analysis

The process capability analysis is a crucial activity to evaluate if the process outcome meets the design specifications. Classically, such analysis is performed by verifying the in-control condition of the process and evaluating suitable capability indices, by assuming the process in-control steady-state condition. However, the in-control period of the process characterizes only a part of the system functioning cycle, the one with the lower defective rate. In particular, the system functioning cycle is also characterized by the out-of-control period, during which a greater defective rate is produced, and such increasing is not considered by the widely adopted capability indices. As consequence, the classical approaches to perform the process capability analysis involves an overestimation of the process capability level. For this reason, in order to overcome the previously described limitation, in the present paper it is proposed a new capability index based on the real defective rate of the process. Thus, such new index is able to estimate the real process capability level. Finally, in order to compare the new index to the conventional Cp capability index, a numerical comparison study related to a process capability analysis is carried out, and the related practical considerations are given. Copyright

An effective opportunistic maintenance policy for a global service

The aim of the present paper is to develop a model for an effective maintenance policy with refer to a global service contract between a services provider company and a company for the waste management. The contract requires, with fixed performance levels of the service, the supplying of a mandatory set of maintenance services on a set of waste compactors vehicles of the outsourcer company. In particular, the service provider (SP) must perform corrective maintenance actions and the replacement of the fault parts. The tackled problem concerns the determination of an effective opportunistic maintenance policy in order to assure the required service performance levels at the minimum global maintenance cost. The problem is mathematically formulated by a constrained partition model that becomes difficult or very hard to solve by mathematical approach for large practical systems as that one here considered. For this reason, in order to solve the proposed problem of maintenance services optimisation, a genetic approach is developed.