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An approach to maintenance optimization where safety issues are important

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Abstract

The starting point for this paper is a traditional approach to maintenance optimization where an object function is used for optimizing maintenance intervals. The object function reflects maintenance cost, cost of loss of production/services, as well as safety costs, and is based on a classical cost–benefit analysis approach where a value of prevented fatality (VPF) is used to weight the importance of safety. However, the rationale for such an approach could be questioned. What is the meaning of such a VPF figure, and is it sufficient to reflect the importance of safety by calculating the expected fatality loss VPF and potential loss of lives (PLL) as being done in the cost–benefit analyses? Should the VPF be the same number for all type of accidents, or should it be increased in case of multiple fatality accidents to reflect gross accident aversion?

In this paper, these issues are discussed. We conclude that we have to see beyond the expected values in situations with high safety impacts. A framework is presented which opens up for a broader decision basis, covering considerations on the potential for gross accidents, the type of uncertainties and lack of knowledge of important risk influencing factors. Decisions with a high safety impact are moved from the maintenance department to the “Safety Board” for a broader discussion. In this way, we avoid that the object function is used in a mechanical way to optimize the maintenance and important safety-related decisions are made implicit and outside the normal arena for safety decisions, e.g. outside the traditional “Safety Board”.

A case study from the Norwegian railways is used to illustrate the discussions.

Introduction

Most maintenance optimization models focus on costs of planned and corrective maintenance, but do not explicitly incorporate the safety risk dimension, see for example the overview of models in Valdez-Flores and Feldman [1], Wang [2], and Aven and Jensen [3]. There is however an increasing number of models linking maintenance and safety risks. It is acknowledged that safety is a main concern for determining the right level and type of the maintenance activities. For some early work on this topic, see Vatn et al. [4] and the references therein. A more recent contribution is Aven and Castro [5].

The present paper adds to this research area by addressing the problem of using methods based on traditional cost–benefit type of analyses and using expected values. The problem is that safety risk measures are not justified only by reference to computed expected values. Uncertainties need to be taken into account, and in this paper we present a framework for how to carry out the maintenance optimization in a practical decision-making setting taking the uncertainties into account.

The need for seeing beyond expected values in risk management has been noted also earlier, see e.g. Aven and Vinnem [6] and Aven [7]. However, the implication of this observation in a practical maintenance optimization context does not seem to have been addressed before. How should we extend the existing models and methods being used for maintenance optimization to properly reflect risks and uncertainties in a practical setting? This is the key issue discussed in the present paper.

In maintenance optimization, the traditional approach is to determine an optimal maintenance policy, minimising the average cost per unit of time in the long run or the total expected discounted costs. To simplify our analysis in this paper, we restrict attention to the average cost case and models where the objective is to determine a fixed time (interval) τ, after which the unit is renewed (overhauled, replaced), i.e. is as good as new.

The suggested approach has similarities with procedures adopted in other sectors and in particular the medical sector, as noted by one of the reviewers of the present paper. In the medical sector, one applies screening for several diseases, like breast cancer and colorectal cancer. The issue in screening is to determine when and how often to start screening. The idea is that the early detection of cancer will make it possible to obtain a successful treatment. On the other hand, there are also negative aspects related to screening, in the form of false positives and costs for the screening. As a support for the decision-making one calculates the average costs per life year saved, and trade-off curves of costs versus number of lives saved are computed. An independent board, e.g. a governmental health board, then makes a decision. Their decision is based on the expected value calculations as well as factors not covered by the analytical approach.

The relation between maintenance and safety is basically described by three elements: (i) the maintenance of components will generally increase the component reliability and hence the safety level, (ii) failures are often introduced during execution of maintenance, and (iii) accident often occurs during maintenance. This paper mainly focuses on the first of these elements. The two other elements are also important, and structural approaches such as task analysis and safe job analysis are often recommended to reduce the negative impact of maintenance.

The paper is organized as follows. First, in Section 2, we review the traditional approach to maintenance optimization, restricted to the special case mentioned above. We use an example from the Norwegian railways to illustrate the discussions. Then in Section 3, we discuss some of the main problems of this traditional approach, and this discussion provides the basis for the framework presented in Section 4. In Section 5, the railway example is used to show how the framework works. The final section, Section 6, discusses the framework and the example case, and concludes.

Section snippets

Review of a traditional approach to maintenance optimization

We search for a preventive maintenance interval τ optimizing the object function c(τ), expressing the average total cost per unit time. The unit is renewed after time τ. Let PMCost denote the cost per preventive maintenance action, and let M(τ) be the total expected cost of corrective maintenance, safety cost and cost related to loss of production/deliverability. Hence,c(τ)=PMCost/τ+M(τ)/τ

The cost term M(τ) depends on the specific model analysed. For the discussion below we assume that we can

Discussion of critical issues of this approach

There are several aspects of the classical approach to maintenance optimization that need further discussion.

A framework for maintenance optimization

In the following, we propose a framework for maintenance optimization where decisions with a high safety impact are moved from the maintenance department to the “Safety Board” for a broader discussion. However, since maintenance optimization involves hundreds or thousands of decisions it is not manageable to have these kinds of discussions for all decisions. The Safety Board is involved at several important steps of the maintenance optimization. First in a more general discussion of priority

Railway examples

In this section, we discuss some aspects that typically will be part of the discussion between the Maintenance Department and the Safety Board in the process of establishing a new maintenance program. The objective is not to present all the details about the optimization, but rather to highlight what principal issues those are to be discussed. Important aspects are as follows:

  • 1.

    Qualitative aspects of the analysis, e.g. barrier analysis.

  • 2.

    Sensitivity analysis of critical assumptions and quantities

Final remarks and conclusions

In the scientific literature, maintenance optimization has for several decades been treated as a problem to optimize some object function. Usually, the models and procedures presented introduce general cost parameters, where there are no explicit discussions on how e.g. safety is treated. One way to include safety in the optimization is to introduce cost figures such as VPF. However, our position is that important safety decisions should not be based on the result of some optimization process.

Acknowledgements

The authors are grateful to two anonymous reviewers for valuable comments and suggestions to an earlier version of this paper.

References (12)

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