ESTIMATING THE RELIABILITY OF A NEW CONSUMER PRODUCT USING USER SURVEY DATA AND RELIABILITY TEST DATA

Because new products enter the market rapidly, estimating their reliability is challenging due to insufficient historical data. User survey data about similar devices (e.g., older versions of the new device) can be used as the prior information in a Bayesian analysis integrated with evidence in the form of product returns, reliability tests, and other reliability data sources to improve reliability estimation and test specification of the new product. User surveys are usually designed for purposes other than reliability estimation. Therefore, extracting reliability information from these surveys may be tricky or impossible. Even when possible, the extracted reliability information contains significant uncertainties. This dissertation introduces the critical elements of a reliability-informed user survey and offers methods for collecting them. A generic and flexible mathematical approach is then proposed. This approach uses the survey and reliability test data of similar products, for example, an older generation of the same product as prior knowledge. Then it combines them through a formal Bayesian analysis with the reliability test data to estimate the life distribution of the new product. The approach models continuous life distributions for products exposed to many damage-induced cycles. It proposes discrete life distribution models for products whose failures occur within several damaging cycles. The actual cycles for various applicable damaging stress profiles are converted into the equivalent (pseudo) cycles under a reference stress profile. When damage-induced cycles are estimated from user surveys, they may involve biases, as is the nature of most nontechnical users’ responses. This bias is minimized using an approach based on the Kullback-Leibler divergence method. The survey data and other evidence from similar products are then combined with the test data of the new product to estimate the parameters of the reliability model of the new product. The dissertation developed approaches to design reliability test specifications for a new product with unknown failure modes. The number of samples, stress levels, and the number of cycles for the accelerated life test are determined based on the manufacturer’s requirements, including the desired warranty time, the desired reliability with some confidence level at the warranty time, and the maximum number of samples. The actual use conditions (i.e., actual stress profiles and usage cycles) are grouped using clustering techniques. The centers of clusters are then used to design frequency-accelerated or stress-accelerated reliability tests. The application of the proposed reliability estimation approach and the test specification design approach is illustrated and used to validate the proposed algorithms using the simulated datasets for a hypothetical handheld electronic device with the failure mode of cracking caused by accidental drops. The proposed approaches can adequately estimate the reliability model and design test specifications for a wide range of consumer products. These approaches require reliability data about an existing product that is similar to the new product, however

Advances in System Identification and Stochastic Optimization

This work studies the framework of systems with subsystems, which has numerous practical applications, including system reliability estimation, sensor networks, and object detection. Consider a stochastic system composed of multiple subsystems, where the outputs are distributed according to many of the most common distributions, such as Gaussian, exponential and multinomial. In Chapter 1, we aim to identify the parameters of the system based on the structural knowledge of the system and the integration of data independently collected from multiple sources. Using the principles of maximum likelihood estimation, we provide the formal conditions for the convergence of the estimates to the true full system and subsystem parameters. The asymptotic normalities for the estimates and their connections to Fisher information matrices are also established, which are useful in providing the asymptotic or finite-sample confidence bounds. The maximum likelihood approach is then connected to general stochastic optimization via the recursive least squares estimation in Chapter 2. For stochastic optimization, we consider minimizing a loss function with only noisy function measurements and propose two general-purpose algorithms. In Chapter 3, the mixed simultaneous perturbation stochastic approximation (MSPSA) is introduced, which is designed for mixed variable (mixture of continuous and discrete variables) problems. The proposed MSPSA bridges the gap of dealing with mixed variables in the SPSA family, and unifies the framework of simultaneous perturbation as both the standard SPSA and discrete SPSA can now be deemed as two special cases of MSPSA. The almost sure convergence and rate of convergence of the MSPSA iterates are also derived. The convergence results reveal that the finite-sample bound of MSPSA is identical to discrete SPSA when the problem contains only discrete variables, and the asymptotic bound of MSPSA has the same order of magnitude as SPSA when the problem contains only continuous variables. In Chapter 4, the complex-step SPSA (CS-SPSA) is introduced, which utilizes the complex-valued perturbations to improve the efficiency of the standard SPSA. We prove that the CS-SPSA iterates converge almost surely to the optimum and achieve an accelerated convergence rate, which is faster than the standard convergence rate in derivative-free stochastic optimization algorithms