The virus of variation, like its biological counterparts, is insidious because it's invisible. Without special tools that help make this invisible menace visible, it is impossible to make sense of variations' influence. Figure 1 serves as an example. Here, the quality characteristic of a series of parts produced by the same process are shown. Given this context, what can be said about the behavior of this process? Can future process behavior be predicted within limits?

Imbuing context with process limits

Fig 1: Time series of manufacturing data

The challenge we face with the data contained in Figure 1 is a function of the lack of context. While we may be right in the assumption that parts 1, 25, 35, 41, and 48 all serve as evidence of assignable causes of exceptional variation, without the context imbued to the data by using a process behavior chart there is no way to be sure. Thus, any affirmations or actions that assert the values highlighted in Figure 1 are “special” or “assignable” risk making one of the two types of mistakes. 

The first type of mistake, Mistake 1, confuses common causes of routine variation for assignable causes of exceptional variation. The second type of mistake, Mistake 2, confuses assignable causes of exceptional variation for common causes of routine variation. In either case, confusing noise for a signal or a signal for noise has consequences that misdirect the time and attention of technical resources away from where they are needed most. Given that time is always money in business and industry, such mistakes, when repeated over and over again, can result in extreme consequences. Alas, we can avoid these consequences and avoid making either one of the two types of mistakes by placing data in the context of a process behavior chart like the one shown in Figure 2.

Fig 2: XmR Chart of manufacturing data

Unlike the time series in Figure 1, which leaves the task of making sense of the variation exhibited by this process up to conjecture and debate, the process behavior chart in Figure 2, more accurately described as an XmR Chart, makes sense of the variation exhibited by the process with the help of the process limits. Calculated using the process data, the mean, and some numeric constants, process limits are the Voice of the Process. They serve as an empirically repeatable conjecture free way to discriminate between common causes of routine variation and assignable causes of exceptional variation. 

The process limits shown on the top graph in Figure 2, called the X Chart, are the Upper Process Limit (UPL) and Lower Process Limit (LPL). Together, these limits define how large or small a single value must be before it represents a departure from the historic mean. In Figure 2, any value that is greater than the Upper Process Limit or equal to the Lower Process Limit is a signal that assignable causes of exceptional variation have influenced process behavior. Using this criteria, there are five instances in Figure 2 where a value indicates the influence of assignable causes. This includes parts 1, 25, 35, 41, and 48. Such a finding empirically justifies the assumptions that were made about these same parts when reviewing Figure 1. That is to say, it justifies the assumption that the values associated with these parts were out of the ordinary and thus warrant further investigation. 

The process limit shown on the bottom graph in Figure 2, called the Moving Range (mR) Chart, is the Upper Range Limit (URL). The Upper Range Limit defines how large the value-to-value difference between subsequent values in a dataset must be before it represents a departure from the average moving range. In Figure 2, any value greater than the Upper Range Limit is a signal that assignable causes have influenced process behavior. Using this criteria to review Figure 2 reveals that there is one instance where a value-to-value difference is greater than the Upper Range Limit. This moving range is the product of the absolute value of the difference between the values for parts 40 and 41. It serves as evidence that the value-to-value difference between these two parts is out of the ordinary for this process and thus warrants further investigation.

The results of the analysis of the manufacturing data using the XmR Chart in Figure 2 puts the power and utility of process behavior charts on full display. Rather than get lost in conjecture and debate about what values constitute signals and what values constitute noise, process behavior charts mathematically discriminate between the two types of variation on your behalf. This ensures that the time and attention of technical resources are directed to where they are needed most. It ensures that individuals and teams avoid making either of the two types of mistakes and, in doing so, ensures efforts to improve quality and reduce costs produce results.

However, even with all this stated potential, one of the primary barriers to the use of process behavior charts in business and industry is the dearth of knowledge regarding the calculation of process limits. Thus, in service of the Broken Quality Initiatives overarching goal to address this lack of knowledge on this subject, we now turn our attention to articulating the right way to calculate process limits.