Bayesian methods in quality control and software reliability

The use of statistical methods is central to improving the quality of products utilized in society today. This dissertation begins by looking at statistical modeling techniques applied to Process Capability Indices (PCI\u27s). Process Capability seeks to measure if the manufacturing process produces items meeting engineering specifications. With the advent of sophisticated measuring systems it makes more sense to look at the process capability in multiple dimensions motivating the use of multivariate process capability indices. We examine a multivariate version of a process capability index applied to a real data set.^ Software reliability models help us describe the software debugging process and measure the quality of software. Traditionally, one either models the successive times, generally CPU times, between failures or the number of failures of the soft-ware upto a given point. The models of the latter type may be described by Nonhomogeneous Poisson processes (NHPP). We present Bayesian inference for two special cases of the models of the latter type. Then we compare the different proposed models for their fit.^ Finally we look at Recapture debugging methods in software reliability. Each error when encountered is not removed from the software but merely tagged. Bayesian techniques are employed to model software reliability data in both recapture and regular (without recapture data) scenarios. Expressions for the reliability function, the mean time to failure (MTTF) are developed. We use Markov Chain Monte Carlo techniques, in particular the Gibbs Sampler and the Metropolis-Hastings algorithm which enable us to sample from analytically intractable distributions.