Statistical Sample Size Determination Methods for Inspections of Engineering Systems

Abstract

A statistical sample size determination (SSD) method is designed for the maintenance of engineering components of similar structure within an overall system. The maintenance problem is defined as a sequential decision-making process, in which the optimal sample sizes are derived by an approach based on the value of information (VoI) concept. Firstly, various sample size determination methods are summarized, and their advantages and disadvantages are discussed. This comparison highlights that, in many cases, the VoI-based approach is superior to traditionally used methods. Existing standards for engineering components are then categorized, based on the comparison, and the rationale behind each standard is described. Potential advantages of using a VoI-based approach are suggested and discussed. Secondly, the theoretical superiority of VoI-based methods is demonstrated in the context of a diagnostic inspection problem, in which the traditional SSD method, the hypothesis-testing approach, can be defined. After the hypothesis-testing context is translated into a sequential decision-making problem, theoretical and numerical results are compared for the VoI-based and traditional methods. Thirdly, the models for condition-based maintenance problems are defined with a time-dependent degradation process called the gamma process. The models mathematically describe how temporal and parameter uncertainties of the degradation process affect the VoI-based analysis. Computational calculation techniques are introduced and compared with each other. Additionally, the model is generalized as a dynamic programming problem and formulated as a multiple-inspection problem. Finally, the effectiveness of the SSD approach is demonstrated through application to an actual degrading system. Based on data from nuclear power plants, numerical analyses are shown for both single and two inspection cases. The results provide operators with guidelines for maintenance and inspection policies that minimize the expected cost throughout the remaining lifetime of the system.