Sofia Panagiotidou

Optimal preventive maintenance for equipment with two quality states and general failure time distributions

We present an economic model for the optimization of preventive maintenance in a production process with two quality states. The equipment starts its operation in the in-control state but it may shift to the out-of-control state before failure or scheduled preventive maintenance. The time of shift and the time of failure are generally distributed random variables. The two states are characterized by different failure rates and revenues. We first derive the structure of the optimal maintenance policy, which is defined by two critical values of the equipment age that determine when to perform preventive maintenance depending on the actual (observable) state of the process. We then provide properties of the optimal solution and show how to determine the optimal values of the two critical maintenance times accurately and efficiently. The proposed model and, in particular, the behavior of the optimal solution as the model parameters and the shift and failure time distributions change are illustrated through numerical examples.

Inventory management of multiple items with irregular demand: A case study

We present the case of a Greek commercial enterprise facing the problem of managing the inventories of thousands of different items, supplied by more than 20 European and Asian manufacturers and sold to a large number of different-type customers. A key feature of the problem is that the demand for the vast majority of items is intermittent and lumpy, thus not allowing the use of the usual normal or Poisson distributions. The paper describes the solutions given to several practical problems in the course of developing an easy-to-use yet effective and all-encompassing inventory control system. Emphasis is placed on the accurate modeling of demand by means of a gamma distribution with a probability mass at zero or a package Poisson distribution for very-slow-moving items. Using those models and simple quantitative tools we develop an efficient procedure for approximate but quite accurate determination of the base stock levels that achieve the desired fill rates in the proposed periodic review system. We briefly describe the computerized implementation of the new system and the very encouraging results.

An economically designed, integrated quality and maintenance model using an adaptive Shewhart chart

This paper proposes a model for the economic design of a variable-parameter (Vp) Shewhart control chart used to monitor the mean in a process, where, apart from quality shifts, failures may also occur. Quality shifts result in poorer quality outcome, higher operational cost and higher failure rate. Thus, removal of such quality shifts, besides improving the quality of the outcome and reducing the quality cost, is also a preventive maintenance (PM) action since it reduces the probability of a failure and improves the equipment reliability. The proposed model allows the determination of the scheme parameters that minimize the total expected quality and maintenance cost of the procedure. The monitoring mechanism of the process employs an adaptive Vp-Shewhart control chart. To evaluate the effectiveness of the proposed model, its optimal expected cost is compared against the optimum cost of a fixed-parameter (Fp) chart.

Optimal procurement and sampling decisions under stochastic yield of returns in reverse supply chains

We study the problem of optimizing the sampling and procurement decisions in a remanufacturing system under stochastic yield of returns in a single-period setting. Returned products are characterized by uncertainty regarding their ability to be successfully remanufactured. This uncertainty is formulated as a variable probability of each returned unit in a batch to be remanufacturable (returns yield). We study the impact of returns yield on the optimal procurement policy and the benefits of sampling inspection of returns prior to the procurement decision. It is shown that sampling inspection improves the procurement decisions since it allows the Bayesian updating of the prior information regarding the returns yield. We derive analytical expressions for the determination of the economically optimal procurement quantity and structural properties that facilitate the optimization procedure and provide useful insights. The determination of the economically optimal sample size is also discussed and the benefits of sampling are illustrated through numerical examples.

Evaluation of maintenance policies for equipment subject to quality shifts and failures

We develop an economic model for the optimization of maintenance procedures in a production process with two quality states. In addition to deteriorating with age, the equipment may experience a jump to an out-of-control state (quality shift), which is characterized by lower production revenues and higher tendency to failure. The times to quality shift and failure are allowed to be generally distributed random variables. We consider two types of maintenance: minimal maintenance (MM) that upgrades the quality state of the equipment without affecting its age and perfect preventive maintenance (PM) that fully upgrades the equipment to the as-good-as-new condition. We derive the expression for the expected profit per time unit and we investigate, through a large number of numerical examples, the type of the optimal solution. It is concluded that in practically every case the optimal maintenance policy is an extreme one: it either calls for immediate MM as soon as a quality shift occurs (active policy) or it allows operation in the out-of-control state until the time of a scheduled PM action (passive policy).

Joint optimization of spare parts ordering and maintenance policies for multiple identical items subject to silent failures

In this paper the joint maintenance and spare parts ordering problem for more than one identical operating items is studied. The operating items may suffer two types of silent failures: a minor failure, which results in item malfunctioning, and a major failure, which renders the item completely out-of-function. Inspections are periodically held to detect any failures and the inspected items are preventively maintained, repaired or replaced according to their condition. Two ordering policies are investigated to supply the necessary spare parts: a periodic review and a continuous review policy. The expected total maintenance and inventory cost per time unit is derived and the proposed models are optimized for real case data. In addition, the sensitivity of the proposed models is studied through numerical examples and the effect of some key problem characteristics on the optimal decisions is discussed.

Optimal integrated process control and maintenance under general deterioration

We develop an integrated Statistical Process Control (SPC) and preventive maintenance (PM) model for three-state processes (two operational states and a non-operational failure state) taking into account the interrelation between quality degradation and proneness to complete failure. No restriction is placed on the distributions of the times to quality shifts and failures and different types of inspection policies and tools are allowed signifying a wide practical applicability of the model. The proposed scheme leads to significant economic improvement compared to: (a) independently obtained SPC and PM policies, which treat quality shifts and failures in isolation, and (b) approximate models, which assume Markovian deterioration.

Joint optimization of manufacturing/remanufacturing lot sizes under imperfect information on returns quality.

The increased quality volatility that characterizes returned used products in reverse supply chains, has led both academic research and industrial practice to support the establishment of, preferably fast and inexpensive, procedures for the quality assessment of returns. To this end, an initial classification of returns is typically performed based on some easily acquirable usage information, which is inherently - yet not always perfectly - related to their quality. Despite the criticality of the returns classification process and its impact on the reverse supply chain operation and profitability, little work has been done on the determination of the optimal threshold values, used to classify returns into different quality categories, taking into account the inevitable quality assessment inaccuracies. Motivated by multiple related reports from industrial applications, in the present paper the problem of optimizing the returns classification process under partial quality information in a hybrid manufacturing/remanufacturing facility is studied. More specifically, analytical models for the joint optimization of the new and returned products lot-sizing decisions are developed, based on usage information of returns which is only indirectly related to their remanufacturability. Our analysis provides useful insights on the value of information regarding the quality of returns under an indicator-based initial classification process. Numerical evidence on the economic superiority of the proposed models under alternative quality patterns of returns is also provided.

The variable sampling interval control chart for finite-horizon processes

The requirement to be globally competitive requires companies to have a high level of flexibility to allow for the production of a large variety of products. To limit work-in-process, decision makers periodically schedule according to a make-to-order management strategy i.e. the production of finite batches of the same product code. Scheduling calls for frequent set up activities, which require the reconfiguration of a manufacturing process, and allows manufacturers to switch between different codes. This can limit the production horizon of one product code to a few hours or shifts. In this context, efficient online quality control monitoring using control charts is strategic to eliminate scrap or rework and to meet the demand at the time specified by the production plan. The design of control charts for a process with a limited production horizon is a challenge for statistical process control practitioners. Under this framework, this article investigates the issues related to the implementation of the Variable Sampling Interval (VSI) Shewhart control chart in a process with finite production horizon. When the production horizon is finite, the statistical properties of a control chart are known to be a function of the number of scheduled inspections. In the case of a VSI control chart, the quality practitioner cannot fix the number of inspections a priori due to the stochastic nature of the sampling interval selection. Therefore, the aim of this article is to propose a new Markov chain approach for the exact computation of the statistical performance of the VSI control chart in processes with an unknown and finite number of inspections. The proposed approach is general and does not depend on the monitored sample statistic. With reference to the process mean monitoring, an extensive numerical analysis compares the performance of the VSI chart to the Variable Sample Size and Fixed Sampling Rate z charts. Numerical results show that the VSI chart outperforms other charts for moderate to large shift sizes. An illustrative example shows the implementation of the VSI chart in a short run producing a finite batch of mechanical parts.

A Bayesian model for the joint optimization of quality and maintenance decisions

We develop a model for the economic design of a Bayesian control chart for monitoring a process mean. The process may randomly suffer failures that result in a non-operating state, and thus call for an immediate corrective maintenance action, as well as assignable causes that shift the process mean to an undesirable level. Quality shifts, apart from poorer quality outcome and higher operational cost, also result in higher failure rate. Consequently, their removal, besides improving the outcome quality and reducing the quality-related cost, is also a preventive maintenance action since it reduces the probability of a failure. The proposed Bayesian model allows the determination of the design parameters that minimize the total expected quality and maintenance cost per time unit. The effectiveness of the proposed model is evaluated through the comparison of its expected cost against the optimum expected cost of the simpler variable-parameter Shewhart chart. Copyright