Process capability indices (PCIs) are widely used to measure whether an in-control process conforms to manufacturing specifications. The normal distribution is assumed in most traditional applications of PCIs. Nevertheless, it is not uncommon that some quality characteristics have skewed distributions. In such cases, the gamma distribution is an appropriate model and percentile-based PCIs for the gamma process have been studied in the literature. In practical applications of PCIs, it is important to select an appropriate distribution between the normal and the gamma distributions based on historical data. In this study, we first construct a hypothesis test for model discrimination between the normal and the gamma distributions. Asymptotic distribution of the test statistic under the gamma process is derived. We then consider statistical inference for the percentile-based PCIs under the gamma process. The maximum likelihood method is used for point estimation and the method of generalized pivotal quantities is used for interval estimation. We demonstrate the proposed methods by a practical example.
- Generalized confidence interval
- Generalized pivotal quantity
- Probability of correct selection
- Quality control
- Ratio of maximized likelihoods