A practical approach for reliability prediction of pipeline systems

doi:10.1016/j.ejor.2008.07.040

European Journal of Operational Research

Volume 198, Issue 1, 1 October 2009, Pages 210-214

https://doi.org/10.1016/j.ejor.2008.07.040 Get rights and content

Abstract

Pipelines play an important role in the modern society. Failures of pipelines can have great impacts on economy, environment and community. Preventive maintenance (PM) is often conducted to improve the reliability of pipelines. Modern asset management practice requires accurate predictability of the reliability of pipelines with multiple PM actions, especially when these PM actions involve imperfect repairs. To address this issue, a split system approach (SSA) based model is developed in this paper through an industrial case study. This new model enables maintenance personnel to predict the reliability of pipelines with different PM strategies and hence effectively assists them in making optimal PM decisions.

Introduction

Pipelines are one of the most applied means to transport gas, oil and water in the world. The failures of pipelines can have huge negative impacts on business, environment and society. Therefore, the reliability of pipelines is a major concern in the field of engineering asset management and has attracted much attention of researchers in the field [1], [2], [3], [4]. When modelling the reliability of the pipelines, the existing literature largely focuses on the influences of corrosion [1], [2] and creep [3] on the pipeline failures from the material failure mechanism point of view. Very few models have considered the impact of preventive maintenance (PM) on the system reliability of pipelines.

In reality, PM is often applied to aged pipelines to reduce unexpected failures and their resultant undesirable impacts. Two commonly used PM policies include the time based preventive maintenance (TBPM) and the reliability based preventive maintenance (RBPM). In the TBPM policy, a pipeline is maintained based on scheduled PM times. The intervals between two PM actions may or may not be the same; whereas in the RBPM policy, a control limit of reliability R₀ is defined in advance. Whenever the reliability of a pipeline falls to this predefined control limit, the pipeline is preventively maintained. The purpose of PM is to improve the overall reliability of the entire pipeline. To decide a cost effective PM strategy for a pipeline, accurately predicting the reliability of the pipeline with multiple PM intervals is desired. However, to date, effective models for meeting this need have yet to be developed. The prediction is difficult because pipelines are normally complex systems. Furthermore, imperfect repairs often need to be considered. Imperfect repair in this paper indicates a system after a PM action is between as good as new and as bad as old.

A number of papers have been published to consider the influence of imperfect repairs on the reliability of a system [5], [6], [7], [8]. In [5], [6], Pham and Wang discussed eight categories of methods for treating imperfect maintenance. These methods can be further classified into two groups: (1) state rules based models and (2) improvement factor methods. The former includes (p, q) rule based model, (p(t), q(t)) rule based model, and multiple (p, q) rules based model; whereas the latter includes improvement factor method, virtual age method, shock model method, (α, β) rule and other models reviewed in [5]. In Ref. [7], Rausand and Hoyland reviewed four types of the imperfect repair models: (1) Brown and Proschan’s model; (2) failure rate reduction models; (3) age reduction models; and (4) trend renewal process. The Brown and Proschan’s model is regarded as a (p, q) rule based model in [5], [6]. The rest can fall into the group of the improvement factor method. The model given in [8] is also belong to this group although it uses two improvement factors.

The state rules based models are largely used for one-component system, and estimating the probabilities for different states is difficult. For using the improvement factor methods, a major difficulty is to estimate the improvement factors, especially for complex systems. In contrast, Ebeling [9] and Lewis [10] presented a heuristic method to predict the reliability of an asset with multiple PM intervals. In this method, PM time is a deterministic variable. This method can produce an intuitive and explicit prediction of reliability and hence very suitable for engineering applications. However, in this model, assets are assumed to have PM actions periodically, i.e., this method was developed based on TBPM only. Besides, this method cannot model the effects of different PM actions on the system reliability. It does not consider system configuration. When modelling imperfect maintenance, it uses a method similar to the improvement factor method.

To address the limitations of the existing methods, a split system approach (SSA) has been developed [11], [12] (the SSA is termed as SSM (split system model) in [11]). The SSA is different from the other methods in that it models the reliability of a system with multiple PM actions at component level. This approach considers the effects of repaired components on the system reliability and allows the changes of the reliability of the system after each PM action to be calculated rather than estimated by maintenance staff. SSA removes the assumptions on the probability of different states of a system after repairs. These assumptions were used in the state rules based models.

This paper aims to predict the reliability of pipelines with multiple imperfect PM actions using SSA through an industrial case study. The outcomes can assist industrial personnel to determine optimal PM strategy for pipelines. Both TBPM and RBPM are considered. Since the effects of PM activities on a system can be modelled using either hazard function (e.g., see [8]) or reliability function (e.g., see [9], [10]), the reliability function is used for modelling in this paper.

The rest of this paper is organised as follows. In Section 2, the industrial case is described. In Section 3, the concept of SSA is introduced and then formulae are derived for predicting the reliability of pipelines under the condition that the same part is repaired. Section 4 presents prediction results and the corresponding analysis. Conclusions are given in Section 5.

Section snippets

Case description

A water supply company needed to make an optimal maintenance strategy for a 2224 meter long steel raw water pipeline. Real world data were collected. The observation of failure history indicated that the entire pipeline could be divided into two portions: a total of 200 meter of exposed pipeline composed of pipe bridges and stream crossings and another subsystem comprising of buried pipes. Assume that all pipes in the exposed pipeline had the same failure distribution and the pipes in the 2024

Concept of SSA

From the above description of the pipeline case, it is noted that when a system is preventively maintained, often only part of its components rather than the whole system is repaired (maintained). Repair information at the component level can often assist in understanding the changes of the reliability of systems after PM actions and hence improve the maintenance outcome of these systems. The information at the component level should be considered when the reliability of a system is being

Prediction results and analysis

When applying Eqs. (11), (12) to the case study, R₁(t)₀ and R_s(t)₀ are known as Eqs. (1), (3). However, the reliability of the exposed pipeline after each PM action needs to be calculated. In principle, this reliability can also be predicted using SSA. However, the derived reliability formulae are complicated. In this paper, for simplification, an approximate formula is used to describe the reliability of the exposed pipeline after a PM action: $R_{1} (τ)_{i} = R_{1} [τ + f_{c} (t_{i} - t_{i - 1})] (i = 1, 2, \dots, n),$ where, f_c is

Conclusion

A SSA based model has been developed to predict the reliability of pipelines with multiple PM actions. The new model is able to explicitly predict the reliability changes of pipelines over a long term with multiple PM intervals. The new model is hence more suitable for supporting a long term PM decision-making for pipelines.

A PM action for a pipeline is often imperfect because normally only part of it are repaired during a PM action. The SSA based pipeline reliability prediction model can deal

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Stochastics and StatisticsA practical approach for reliability prediction of pipeline systems

Abstract

Introduction

Section snippets

Case description

Concept of SSA

Prediction results and analysis

Conclusion

Reliability Engineering and System Safety – Probabilistic Modelling of Structural Degradation

International Journal of Pressure Vessels and Piping

International Journal of Pressure Vessels and Piping

International Journal of Pressure Vessels and Piping – The 16th European Safety and Reliability Conference

European Journal of Operational Research

Stochastics and Statistics
A practical approach for reliability prediction of pipeline systems