A Renewal-Process Approach to Continuous Sampling Plans

Abstract

A class of continuous sampling plans (CSP's) that switch between full and partial inspection of items in a production line is formulated in terms of discrete renewal processes. The renewal-theory framework facilitates studying both the long-run average outgoing quality (AOQ) and the average outgoing quality in a short production run of length t, AOQ(t). Renewal theory also leads to a computable approximation, AOQ*(t), to AOQ(t). By simulation it is found that AOQ greatly overestimates AOQ(t), for short runs, while the approximation AOQ*(t) is found to be sufficiently accurate in situations corresponding to actual practice. Formulas are derived enabling one to compute AOQ and AOQ*(t) for the Dodge sampling plans CSP-1 through CSP-5. Numerical illustrations for selected CSP's are presented.

KEY WORDS:

• Continuous sampling plans
• Average outgoing quality
• Inspection by attributes
• Quality control
• Renewal process
• Renewal interval