Question

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Discuss the rational subgroup concept and the part that it plays in the design of control charts. Also, explain whether, when taking samples or subgroups from a process, you should seek to have assignable causes occurring within the subgroups or between them.

Answer 1

A fundamental idea in the use of control charts is the collection of sample data according to what Shewhart called the rational subgroup concept. To illustrate this concept, suppose that we are using an x control chart to detect changes in the process mean. Then the rational subgroup concept means that subgroups or samples should be selected so that if assignable causes are present, the chance for differences between subgroups will be maximized, while the chance for differences due to these assignable causes within a subgroup will be minimized. When control charts are applied to production processes, the time order of production is a logical basis for rational subgrouping. Even though time order is preserved, it is still possible to form subgroups erroneously. If some of the observations in the sample are taken at the end of one shift and the remaining observations are taken at the start of the next shift, then any differences between shifts might not be detected. Time order is frequently a good basis for forming subgroups because it allows us to detect assignable causes that occur over time. Two general approaches to constructing rational subgroups are used. In the first approach, each sample consists of units that were produced at the same time (or as closely together as possible). Ideally, we would like to take consecutive units of production. This approach is used when the primary purpose of the control chart is to detect process shifts. It minimizes the chance of variability due to assignable causes within a sample, and it maximizes the chance of variability between samples if assignable causes are present. It also provides a better estimate of the standard deviation of the process in the case of variables control charts. This approach to rational subgrouping essentially gives a snapshot of the process at each point in time where a sample is collected.

I would want assignable causes to occur between subgroups and would prefer to select samples as close to consecutive as possible. If assignable causes occur within the subgroup, this may cause the range or the sample standard deviation of the observations within the sample to be relatively large, resulting in wider limits on the x control chart and making the process appear to be in statistical control. In most SPC applications, process changes will not be self-correcting, but will require action to return the process to its usual performance level. The probability of detecting a change (and therefore initiating a corrective action) will be maximized by taking observations in a sample as close together as possible