An alternative approach to test process capability for unilateral specification with subsamples

Abstract

Process capability indices are useful management tools, which provide common quantitative measures on manufacturing capability and production quality. The indices C_PU and C_PL are designed specifically for processes with one-sided manufacturing specifications. The majority of the results obtained so far related to the distributional properties of the estimated capability indices were derived based on the assumption of possessing a single sample. However, a common practice in process control is to estimate the process capability indices by using the past ‘in control’ data from several subsamples. In order to use previous in-control data from multiple subsamples to make correct decisions regarding process capability, the distribution of the estimated capability index based on multiple subsamples should be available. In this paper, we develop a capability testing procedure with one-sided specifications using a Bayesian approach based on subsamples collected over time from an in-control process. By applying the proposed testing procedure, the practitioners can make reliable decisions to determine whether their processes meet the pre-set capability requirement when a daily based or weekly based production control plan is implemented for monitoring process stability.

Keywords:

• Bayesian approach
• Multiple subsamples
• Posterior probability
• Testing procedure
• Unilateral specification limit