Evaluating Six Sigma failure rate for inverse Gaussian cycle times

Six Sigma is a quality philosophy and methodology that aims to achieve operational excellence and delighted customers. The cost of poor quality depends on the sigma quality level and its corresponding failure rate. Six Sigma provides a well-defined target of 3.4 defects per million. This failure rate is commonly evaluated under the assumption that the process is normally distributed and its specifications are two-sided. However, these assumptions may lead to implementation of quality-improvement strategies that are based on inaccurate evaluations of quality costs and profits. This paper defines the relationship between failure rate and sigma quality level for inverse Gaussian processes. The inverse Gaussian distribution has considerable applications in describing cycle times, product life, employee service times, and so on. We show that for these processes attaining Six Sigma target failure rate requires higher quality efforts than for normal processes. A generic model is presented to characterise cycle times in manufacturing systems. In this model, the asymptotic production is described by a drifted Brownian motion, and the cycle time is evaluated by using the first passage time theory of a Wiener process to a boundary. The proposed method estimates the right efforts required to reach Six Sigma goals.