Novel Approaches to Prediction of a Future Number of Failures Based on Previous In-Service Inspections

Novel Approaches to Prediction of a Future Number of Failures Based on Previous In-Service Inspections

Nicholas A. Nechval (University of Latvia, Latvia) and Konstantin N. Nechval (Transport and Telecommunication Institute, Latvia)
DOI: 10.4018/978-1-5225-3035-0.ch011
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Abstract

In this chapter, we present novel approaches to predictions of the number of failures that will be observed in a future inspection of a sample of units, based only on the results of the previous in-service inspections of the same sample. The failure-time of such units is modeled with a distribution from a two-parameter Weibull distribution. The different cases of parametric uncertainty are considered. The pivotal quantity averaging approach proposed here for constructing point prediction and simple prediction limits emphasizes pivotal quantities relevant for eliminating unknown parameters from the problems and represents a special case of the method of invariant embedding of sample statistics into a performance index applicable whenever the statistical problem is invariant under a group of transformations, which acts transitively on the parameter space. For illustration, a numerical example is given.
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Introduction

This chapter extends the results of Nelson (2000) through the use of novel approaches to prediction of a future number of failures based on previous in-service inspections. Nelson's prediction limits were motivated by the following application.

Nuclear power plants contain large heat exchangers that transfer energy from the reactor to steam turbines. Such exchangers typically have 10,000 to 20,000 stainless steel tubes that conduct the flow of steam. Due to stress and corrosion, the tubes develop cracks over time. Cracks are detected during planned inspections. The cracked tubes are subsequently plugged to remove them from service. To develop efficient inspection and plugging strategies, plant management can use a prediction of the added number of tubes that will need plugging by a specified future time.

Nelson (2000) presents the procedures to obtain predictions for the number of failures that will be observed in a future inspection of a sample of units, based only on the results of the first in-service inspection of the same sample. The failure-time of such units is modeled with a two-parameter Weibull distribution indexed by scale and shape parameters β and δ, respectively. The case is considered when the scale parameter β is unknown, but the shape parameter δ is known.

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