An approach for improvements on the attribute npx$np_x$ control chart

Abstract

This paper proposes an attribute control chart named 𝑛𝑝 𝜇 𝑥(𝐼) which is used for monitoring the process mean value of a variable (𝑋) by employing sequential sample sizes of 𝑛 𝑎 , 𝑛 𝑏 with 𝑛 𝑎 > 𝑛 𝑏 . Each item is classified as approved or not according to a discriminant limit (𝑤 𝑖 , 𝑖 = 𝑎, 𝑏) using a GO/NO GO gauge. In the end of inspection we'll have 𝑌 𝑎 and 𝑌 𝑏 items classified as disapproved. Whenever 𝑌 𝑎 > 𝑈𝐶𝐿 𝑛 𝑎 or 𝑌 𝑏 > 𝑈𝐶𝐿 𝑛 𝑏 , the process is judged to be out of control and after adjustments in the process, the inspection is always restarted with a sample size of 𝑛 𝑎 . The parameters used in the construction of the 𝑛𝑝 𝜇 𝑥(𝐼) control chart were obtained through a search for values that optimize their performance, such that can compete with the standard attribute 𝑛𝑝 𝑥 chart and the traditional 𝑋 control chart. The performances were compared in terms of average run length (𝐴𝑅𝐿) in scenarios of shift sizes (𝛿) in the process mean. A numerical example illustrates its application.