Sampling on successive occasions to re-estimate future asset management expenditure

Abstract

Sampling schemes are used by the utilities such as electricity and water to assess the condition of their networks, and hence to predict future expenditure. Frequently the assessment process has to be carried out on a regular basis, e.g. every 5 years. However there is little published literature to provide guidance as to how much resampling to undertake, how to use the extra information gained and how accurate the results are likely to be. Therefore this paper describes simple linear and quadratic regression models for predicting future condition and investigates their performance. As this investigation requires all items to have a full condition history, a deterioration model is developed to generate this information.

Introduction

A major cost commitment for distribution utilities is maintaining their network in a satisfactory condition. Therefore it is important to be able to accurately asses the condition of the network and to predict the likely expenditure for several years ahead both for a company’s own financial planning and for submissions to government regulators, e.g. as a part of the UK water industry’s Asset Management Plan (Lindley, 1992). As network assets are widely spread and can be inaccessible, e.g. buried in the ground, not every item can be inspected in detail. Instead a sampling programme is normally initiated and the conditions of the unsampled items are estimated by comparing their characteristics with those of the sampled items. Metcalfe (1991) discusses the use of classical stratified sampling while Bayesian approaches are described in O’Hagan, 1997, Freeman et al., 1996.

Usually this network assessment and prediction of future expenditure is not a one-off task, but gets repeated at regular intervals, e.g. every 5 years for the UK water industry’s submission to the regulator. Instead of starting from scratch each time, benefit can be obtained from incorporating the earlier samples into the prediction process, and this is especially important when predicting the condition (and so expenditure) in a few years time. However various questions now arise, e.g. How to combine the information from samples at different times?, How much overlap should there be between samples carried out at different times? Relatively little guidance for Asset Managers has been published on these questions. One approach would be to model the deteriorating condition but deterioration modelling (Ansell et al., 1998) usually assumes condition data has been collected on quite a few occasions. When this is the case, deterioration curves (Shahin et al., 1987, Livneh, 1998) or models such as Markov Decision Processes (Wirahadikusumah et al., 1999) can be fitted to the data.

We are interested in the case when sampling has occurred on only two or three occasions. Note that we choose to avoid the approach of combining items of different ages together as construction quality may have varied over time. For example, studies suggest that the percentage of sewers built in the 1940s that are in a poor state is higher than the percentage for those built in the 1920s. Therefore this paper investigates using a simple extrapolation method as an alternative to having a complex deterioration model. Where sampling is carried out on only two occasions, a linear model is used, and where sampling is carried out on three occasions, a quadratic model is employed. In order to analyse the method, items whose condition is known every year are needed. Unfortunately this requirement is rarely met as items that can have this information readily available (e.g. pumps) are often not the kind of items that have to be sampled in order to estimate network condition. (If the inspection cost was low, then which items to sample is less of an issue as the cost of inspecting everything is not prohibitive.) Therefore simulated data sets are analysed so as to gain a better understanding of the capabilities of the approach. A deterioration model was developed for generating these simulated data sets.