Other important concept behind SPC is what Shewhart called the rational subgroup concept.
Subgroups should be rational.
A rational subgroup is a group in which all of the observations are generated under conditions in which only random effects are responsible for the observed variation [Nelson (1988),Wheeler(2004),and Hawkins and Olwell (1998)].
Subgroups must be representative of process performance.
Subgroups or samples should be selected so that if special causes are present,the chance for differences between subgroups will be maximized,while the chance for differences within a subgroup will be minimized.
Usually time order is a good basis for the selection because it allows detecting time related assignable causes.
In general the approaches to construct rational subgroups expressed by Montgomery (1985) are as follows:
1-Samples consisting of units produced at the same time or as closely together as possible.
This approach is used to detect process shifts.
2-Each sample is a random sample of all process output over the sampling interval.
This approach is used to make decisions about the acceptance of all products that have been produced since the last sample.
3-If several machines pool their output into a common stream the control charts should be applied to the individual streams to avoid confusing the origin of assignable causes.
Subgroups should ensure the presence of a normal distribution for the sample means
In general,the larger the sample size, the better the distribution is represented by the normal curve. In practice,sample sizes of four or more ensure a good approximation to normality.
Subgroups should ensure good sensitivity to the detection of assignable causes.
The larger the sample size,the more likely that a shift of a given magnitude will be detected.
Subgroups should be rational.
A rational subgroup is a group in which all of the observations are generated under conditions in which only random effects are responsible for the observed variation [Nelson (1988),Wheeler(2004),and Hawkins and Olwell (1998)].
Subgroups must be representative of process performance.
Subgroups or samples should be selected so that if special causes are present,the chance for differences between subgroups will be maximized,while the chance for differences within a subgroup will be minimized.
Usually time order is a good basis for the selection because it allows detecting time related assignable causes.
In general the approaches to construct rational subgroups expressed by Montgomery (1985) are as follows:
1-Samples consisting of units produced at the same time or as closely together as possible.
This approach is used to detect process shifts.
2-Each sample is a random sample of all process output over the sampling interval.
This approach is used to make decisions about the acceptance of all products that have been produced since the last sample.
3-If several machines pool their output into a common stream the control charts should be applied to the individual streams to avoid confusing the origin of assignable causes.
Subgroups should ensure the presence of a normal distribution for the sample means
In general,the larger the sample size, the better the distribution is represented by the normal curve. In practice,sample sizes of four or more ensure a good approximation to normality.
Subgroups should ensure good sensitivity to the detection of assignable causes.
The larger the sample size,the more likely that a shift of a given magnitude will be detected.
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