3.1. Process monitoring in context¶
In the first section we learned about visualizing data, then we moved on to reviewing univariate statistics. This section now combines both topics, showing how to create a system that monitors a single, univariate, value from any process. These monitoring systems are easily implemented online, and generate great value for companies that use them in day-to-day production. This is one of their greatest advantages: almost no training is required to interpret the visualization and secondly the human eye can quickly pick up any patters or trends in the plots; both expected and unexpected patterns.
Monitoring charts are a graphical tool, enabling anyone to rapidly detect a problem by visual analysis. The next logical step after detection of a problem is to diagnose it, but we will cover diagnosis in the section on latent variable models.
This section is the last section where we deal with univariate data; after this section we start to use and deal with 2 or more variables.
3.1.1. Usage examples¶
The material in this section is used whenever you need to rapidly detect problems. It has tangible application in many areas - in fact, you have likely encountered these monitoring charts in areas such as a hospital (monitoring a patient’s heart beat), stock market charts (for intraday trading), or in a processing/manufacturing facility (control room computer screens).
Co-worker: We need a system to ensure an important dimension on our product is stable and consistent over the entire shift.
Yourself: We know that as the position of a manufacturing robot moves out of alignment that our product starts becoming inconsistent; more variable. How can we quickly detect this slow drift in alignment and predict when to stop the process and perform preventative maintenance?
Manager: the hourly average profit, and process throughput is important to the head-office; can we create a system for them to track that?
Potential customer: what is your process capability - we are looking for a new supplier that can provide a low-variability raw material for us with Cpk of at least 1.6, preferably higher.
Note: process monitoring is mostly reactive and not proactive. So it is suited to incremental process improvement, which is typical of most improvements. However, using the monitoring charts to make proactive changes to avoid a bigger problem later in time is certainly possible by adding additional rules and calculations to the plots. For example, rules to forecast a few steps ahead, with prediction intervals, can be easily added.
We point out in the next section that process monitoring is not a feedback control system. So that section should be read in the context of thinking reactively and proactively (in a feed forward anticipatory manner).
3.1.2. What we will cover¶
We will consider 3 main charts after introducing some basic concepts: Shewhart charts, CUSUM charts and (exponentially weighted moving average) charts. The EWMA chart has an adjustable parameter that captures the behaviour of a Shewhart chart at one extreme and a CUSUM chart at the other extreme, or a combination of both is possible by settings this parameter on a sliding scale.
Concepts and acronyms that you must be familiar with by the end of this section:
Shewhart chart, CUSUM chart and EWMA chart
Phase 1 and phase 2 when building a monitoring system
Type 1 and type 2 errors
LCL and UCL
Cp and Cpk
Real-time implementation of monitoring systems
3.2. References and readings¶
Recommended: Box, Hunter and Hunter, Statistics for Experimenters, Chapter 14 (2nd edition)
Recommended: Montgomery and Runger, Applied Statistics and Probability for Engineers.
Hunter, J.S. “The Exponentially Weighted Moving Average”, Journal of Quality Technology, 18 (4) p 203 - 210, 1986.
MacGregor, J.F. “Using On-Line Process Data to Improve Quality: Challenges for Statisticians”, International Statistical Review, 65, p 309-323, 1997.