Np(X) Control Chart for Monitoring the Mean with Estimated Parameters

• Activity Number: 391 - Improving Quality
• Type: Contributed
• Date/Time: Wednesday, August 10, 2022 : 8:30 AM to 10:20 AM
• Sponsor: Quality and Productivity Section
• Author(s): Felipe Schoemer Jardim* and Mariana Cristina de Oliveira and Marcela Aparecida Guerreiro Machado de Freitas and Carlos Junior and Subha Chakraborti
• Companies: Fluminense Federal University (UFF) and São Paulo State University (UNESP) and São Paulo State University (UNESP) and São Paulo State University (UNESP) and University of Alabama
• Keywords: Parameter Estimation; False Alarm Rate; Average Run Length; Attribute Control Charts; np Control Chart

Abstract

Control charts are powerful tools used by many industries to monitor some quality characteristics (qc) and detect special causes of variation. If it is impractical to represent the qc numerically, attribute control charts, such as the np chart, are often used to monitor the number of nonconforming units. Attribute control charts are considered simpler, faster, and cheaper than variable control charts (such as the Xbar chart) because they do not require measuring some quality characteristic, instead, practitioners just need to count the number of nonconforming units in a sample. Due to this reason, the np control chart is also used to monitor not only the number of nonconforming units but also the process mean. This is known as the np(x) chart. However, the existing studies on the performance of np(x) chart do not consider the practical case where the parameters (such as p), needed to calculate the control limits, must be estimated. With this background as motivation, in this paper, we show that the ARL may be significantly different than what is nominally expected if parameter estimation is not taken into account in the designing of the chart. Some solutions are provided.