Economical control chart with supplementary rules to monitor the average number of defects

• Published in: International journal of advanced manufacturing technology Vol. 76; no. 5-8; pp. 881 - 891
• Main Authors: Sena da Rocha, André Luiz, Guedes de Medeiros, Pledson, Lee Ho, Linda
• Format: Journal Article
• Language: English
• Published: London Springer London 01-02-2015; Springer Nature B.V
• Subjects: CAE) and Design; Computer-Aided Engineering (CAD; Control charts; Control limits; Defects; Engineering; Industrial and Production Engineering; Inspection; Markov chains; Mechanical Engineering; Media Management; On-line systems; Original Article; Process controls; Warning; Markov chain; On-line process control; Average number of defects; Number of defects per inspected item; Poisson distribution; Warning limit
• ISSN: 0268-3768; 1433-3015
• DOI: 10.1007/s00170-014-6237-1

This study proposes a procedure for an on-line process control system to monitor the average number of defects using a Shewhart-like chart with two sets of limits (viz., control and warning limits). After the production of
m
units, the
m
th item is inspected. If the number of defects exceeds the upper control limit or if, in a sequence of the last
h
inspections, all inspected items exhibit a number of defects between the warning and control limits, then the process is stopped for adjustment; otherwise, production continues. The properties of an ergodic Markov chain are used to obtain an expression for the average cost per item produced. The inspection interval (
m
), warning and control limits (
W
and
C
, respectively), and the sequence size (
h
) are determined by minimizing the average cost per produced item. A numerical example illustrates the proposed procedure.