Reliability Analysis for Degrading Systems with 100% Quality Inspection after Burn-In

Introduction

Intensive global competition and higher customer expectations have required modern manufacturers to develop products with enhanced levels of quality and reliability in shorter production cycles at reduced costs. Quality and reliability are inherently related in a sense that quality inspection and monitoring decisions impact anticipated reliability and failure time distributions. Therefore, under time and budget constraints, integrated models should be developed to consider quality/manufacturing variability and reliability simultaneously. Especially for degrading characteristics, important decisions including burn-in, quality inspection and preventive maintenance should be incorporated into an integrated model considering process/physical variability and associated failure mechanisms. For various degradation models, this paper analyzes failure time distributions considering the impacts of burn-in and quality inspection. The developed reliability models can be readily used for optimizing burn-in, quality inspection and maintenance decisions.

Reliability modeling for degrading characteristics is one of the most effective analytical tools that has attracted considerable attentions from researchers in statistics and reliability since the early 1990s (Carey, & Koenig, 1991; Lu, & Meeker, 1993). It is an effective alternative to estimate failure-time distributions and predict reliability when failure data is insufficient due to time and budget constraints. Degradation modeling can be widely applied to many applications, such as wear on rubbing surfaces of MEMS devices (Tanner, & Dugger, 2003) and crack growth on microstructures of Nitinol stents (Pelton, Schoroeder, Mitchell, Gong, Barney, & Robertson, 2008). The major advantages of degradation modeling include: (1) it requires a shorter time for testing and analysis, compared with traditional reliability analysis that often takes an unacceptable long time to obtain failure data, (2) it can provide a closer understanding of physical/chemical failure mechanisms so as to improve reliability behavior of products (Tseng, Hamada, & Chiao, 1995), and (3) it is the scientific foundation for implementing advanced maintenance strategies, such as predictive maintenance or condition-based maintenance (Grall, Dieulle, Berenguer, & Roussignol, 2002).

Previous studies on degradation-based reliability have been focused on developing physics-based degradation models (e.g., Arrhenius law or corrosion initiation equation) (Elsayed, 2000), estimating time-to-failure distributions and parameters in degradation models (Bae, Kuo, & Kvam, 2007; Gebraeel, 2006; Gebraeel, & Lawley, 2008; Gebraeel, Lawley, Li, & Ryan, 2005; Lu et al., 1993), and investigating degradation processes under random environments (Kharoufeh, 2003; Singpurwalla, 1995). For example, Lu and Meeker developed statistical methods for using degradation measures to estimate time-to-failure distributions for a broad class of degradation models (Lu et al., 1993). Bae et al. investigated the resulting lifetime distribution from selected degradation model. Simple additive and multiplicative models with single random effects were featured (Bae et al., 2007). Gebraeel et al. estimated residual life distributions based on sensory-updated data using a neural network approach (Gebraeel et al., 2008), a Bayesian approach (Gebraeel et al., 2005), and for components with exponential degradation patterns (Gebraeel, 2006). Singpurwalla provided an overview of a class of stochastic failure models that can be used for systems affected by dynamic environments (Singpurwalla, 1995). Kharoufeh derived the explicit probability distribution of the random failure time for single-unit systems that deteriorate continuously and additively due to the influence of a random environment modeled as a general, finite-state Markov process (Kharoufeh, 2003).