Editing Control chart (section)

==Types of charts==

{| class="wikitable"
 ! Chart
 ! Process observation
 ! Process observations relationships
 ! Process observations type
 ! Size of shift to detect
|-
| [[Xbar and R chart|<math>\bar x</math> and R chart]]
| Quality characteristic measurement within one subgroup
| Independent
| Variables
| Large (≥ 1.5σ)
|-
| [[Xbar and s chart|<math>\bar x</math> and s chart]]
| Quality characteristic measurement within one subgroup
| Independent
| Variables
| Large (≥ 1.5σ)
|-
| [[Shewhart individuals control chart]] (ImR chart or XmR chart)
| Quality characteristic measurement for one observation
| Independent
| Variables<sup>†</sup>
| Large (≥ 1.5σ)
|-
| [[Three-way chart]]
| Quality characteristic measurement within one subgroup
| Independent
| Variables
| Large (≥ 1.5σ)
|-
| [[p-chart]]
| Fraction nonconforming within one subgroup
| Independent
| Attributes<sup>†</sup>
| Large (≥ 1.5σ)
|-
| [[np-chart]]
| Number nonconforming within one subgroup
| Independent
| Attributes<sup>†</sup>
| Large (≥ 1.5σ)
|-
| [[c-chart]]
| Number of nonconformances within one subgroup
| Independent
| Attributes<sup>†</sup>
| Large (≥ 1.5σ)
|-
| [[u-chart]]
| Nonconformances per unit within one subgroup
| Independent
| Attributes<sup>†</sup>
| Large (≥ 1.5σ)
|-
| [[EWMA chart]]
| [[Exponentially weighted moving average]] of quality characteristic measurement within one subgroup
| Independent
| Attributes or variables
| Small (< 1.5σ)
|-
| [[CUSUM]] chart
| Cumulative sum of quality characteristic measurement within one subgroup
| Independent
| Attributes or variables
| Small (< 1.5σ)
|-
| [[Time series]] model
| Quality characteristic measurement within one subgroup
| Autocorrelated
| Attributes or variables
| N/A
|-
| [[Regression control chart]]
| Quality characteristic measurement within one subgroup
| Dependent of process control variables
| Variables
| Large (≥ 1.5σ)
|}

<sup>†</sup>Some practitioners also recommend the use of Individuals charts for attribute data, particularly when the assumptions of either binomially distributed data (p- and np-charts) or Poisson-distributed data (u- and c-charts) are violated.<ref name = "Wheeler2000">{{cite book | last = Wheeler | first = Donald J. | title = Understanding Variation: the key to managing chaos | page = [https://archive.org/details/understandingvar00dona/page/140 140] | year = 2000 | publisher = SPC Press | isbn = 978-0-945320-53-1 | url = https://archive.org/details/understandingvar00dona/page/140 }}</ref> Two primary justifications are given for this practice. First, normality is not necessary for statistical control, so the Individuals chart may be used with non-normal data.<ref name="Staufer2010a">{{cite web | last = Staufer | first = Rip | title = Some Problems with Attribute Charts | publisher = [[Quality Digest]]|url=http://www.qualitydigest.com/inside/quality-insider-article/some-problems-attribute-charts.html | access-date = 2 Apr 2010}}</ref> Second, attribute charts derive the measure of dispersion directly from the mean proportion (by assuming a probability distribution), while Individuals charts derive the measure of dispersion from the data, independent of the mean, making Individuals charts more robust than attributes charts to violations of the assumptions about the distribution of the underlying population.<ref name="WheelerSPC">{{cite web | last = Wheeler | first = Donald J. | title = What About Charts for Count Data? | publisher = [[Quality Digest]] | url = http://www.qualitydigest.com/jul/spctool.html | access-date = 2010-03-23}}</ref> It is sometimes noted that the substitution of the Individuals chart works best for large counts, when the binomial and [[Poisson distribution]]s approximate a normal distribution. i.e. when the number of trials {{math|<var>n</var> > 1000}} for p- and np-charts or {{math|<var>λ</var> > 500}} for u- and c-charts.

Critics of this approach argue that control charts should not be used when their underlying assumptions are violated, such as when process data is neither normally distributed nor binomially (or Poisson) distributed. Such processes are not in control and should be improved before the application of control charts. Additionally, application of the charts in the presence of such deviations increases the [[Type I and type II errors|type I and type II error]] rates of the control charts, and may make the chart of little practical use.{{Citation needed|date=April 2010}}