This dissertation consists of three projects focused on seasonal recurrent event prediction, electronic circuit troubleshooting and the development of an open source software, RSpice, respectively. Big challenges when making recurrent event prediction include (1) the recurrent event rate may show a seasonal pattern and the pattern may also be affected by locations; (2) individual level variabilities can also affect the recurrent event rate. We present a general methodology to solve these challenges by using hierarchical clustering for the seasonal patterns and introducing random effects into our models. These help us in improving both the model fitting and prediction performance. This work is illustrated with two motivating product warranty applications in Chapter 2. Electronic circuits are widely used in industry, and the troubleshooting process of an electronic circuit based on previous experience may suggest a replacement of the whole circuit or some components, however, the failure of the circuit may just due to a less number of specific electronic components. The unnecessary removal of components can increase the costs significantly. Motivated by finding a more precise and faster troubleshooting procedure based on limited data, we propose the use of data simulation and Bayesian inference in circuit troubleshooting in Chapter 3. In the third project (Chapter 4), we address challenges that arise when doing data simulation and Bayesian inference in the second project (Chapter 3). In order to do exploratory analysis of an electronic circuit and make inference on which specific electronic components cause the failure of a circuit, we need to use a circuit simulator, ngspice, to generate the response (e.g., voltage values

at specified nodes of a circuit) given the circuit setup. We also need to ensure that the component values generated by Bayesian inference algorithm can be passed to the circuit simulator and the output from the circuit simulator can be passed back to the algorithm for evaluation interactively. We present our work of writing an R package called RSpice to accomplish the above tasks.