Should Observations Be Grouped for Effective Process Monitoring?

Abstract

When control charts are used to monitor processes to detect special causes, it is usually assumed that a special cause will produce a sustained shift in a process parameter that lasts until the shift is detected and the cause is removed. However, some special causes may produce a transient shift in a process parameter that lasts only for a short period of time. Control charts are usually based on samples of n ≥ 1 observations using a sampling interval of fixed length, say d. When n > 1, the usual practice, based on the so-called rational subgroups concept, is to take a concentrated sample at one time point at the end of the sampling interval d, but another option is to disperse the sample over the interval d. In this paper, we investigate the question of whether it is better to use n = 1, or to use n > 1 and either concentrated or dispersed samples. The objective of monitoring is assumed to be the detection of special causes that may produce either a sustained or transient shift in the process mean %mU and/or process standard deviation σ. It is assumed that the sampling rate in terms of the number of observations per unit time is fixed, so that the ratio n/d is fixed. The best sampling strategy depends on the type of control chart being used, so Shewhart and cumulative sum (CUSUM) charts are considered. For both types of control charts, a combination of two charts is investigated; one chart is designed to monitor μ, and the other is designed to monitor σ. The overall conclusion is that it is best to take samples of n = 1 and use a CUSUM chart combination. The Shewhart chart combination with the best overall performance is based on n > 1, but this combination has inferior statistical performance compared with the CUSUM chart combination.

• Average Time to Signal
• Concentrated Sampling
• Cumulative Sum Control Charts
• Dispersed Sampling
• Exponentially Weighted Moving-Average Control Charts
• Shewhart Control Charts
• Statistical Process Control
• Steady State
• Sustained Shift
• Transient Shift
• 100% Inspection

Additional information

Notes on contributors

Marion R. Reynolds

Dr. Reynolds is a Professor in the Departments of Statistics and Forestry. He is a Member of ASQ. His email address is [email protected].

Zachary G. Stoumbos

Dr. Stoumbos is Associate Professor and Chair of the Department of Management Science and Information Systems and a member of the Rutgers Center for Operations Research (RUTCOR). He is a Senior Member of ASQ. His email address is [email protected].