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

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.