How To Draw 1,2 And 3 Sigma In The Control Chart

vii.3.three X-bar and South Charts - average and standard deviation charts for grouped data

This statlet constructs control charts for observations which are taken in subgroups (more one observation at a time). The tabs are:

Input

Summary

X-bar Chart

S Chart

Runs Rules

MA Nautical chart

EWMA Nautical chart

Capability

Instance

The example information consists of xx subgroups, each containing 5 observations. The group ways, standard deviations and sizes are specified:

Input

Three columns must be specified, containing the group means, group standard deviations, and grouping sizes:

The grouping sizes need not all be the same.

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Summary

This tab summarizes the results of the X-bar and S charts:

The pinnacle one-half of the table shows the location of the upper and lower control limits on these charts, together with a summary of how many points autumn outside the command limits. The bottom half of the table shows the estimated procedure mean and standard departure, together with the mean range:

The process parameters are estimated by

process mean = x-bar-bar

process sigma = s-bar / c₄

where x-bar is the average of the subgroup ways (weighted average if the subgroup sizes are different), s-bar is the boilerplate of the subgroup sigmas, and c_iv is a constant which is tabulated in most texts on statistical procedure control.

Options push

The Options push generates a dialog box allowing you to specify how the command limits should be computed:

Settings include:

Type of analysis - either "Initial studies", in which the information determine where the control limits are placed, or "Command to standard", which uses the specified standard mean and standard sigma to set the limits.

Use average sample size - for information from subgroups of different sizes, whether the command limits should be based on the average sample size or the private subgroup sizes.

The Initial studies fashion is normally used to determine whether or not a procedure is in a state of statistical command and to determine control limits for monitoring the process in the hereafter. The Command to standard mode is virtually often used in real-time to monitor a procedure against pre-established limits.

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X-bar Chart

This chart plots the subgroup ways with iii-sigma command limits:

Each point on the chart represents a single observation. The lines are located at:

upper control limit: hateful + iii*sigma/n^1/2

center line: x-bar-bar or specified process hateful

lower control limit: hateful - 3*sigma/n^1/2

where the hateful and sigma are estimated as described above if in "Initial studies" mode, or specified by the user if in "Control to standard" manner, and n is the subgroup size (or boilerplate subgroup size).

Any points exterior the three-sigma command limit, such as the last point in the above chart, are highlighted in red. In addition, whatever points which violate the Runs rules described below are also highlighted. In this case, 6 boosted points take been highlighted.

Options button

Y'all can specify various aspects of the control chart by pressing the Options button:

These include:

Upper control limit - if checked, an upper control limit is included on the nautical chart.

Lower control limit - if checked, a lower command limit is included on the chart.

Outer warning limits - if checked, alarm limits are drawn at the hateful +/- ii sigma.

Inner alarm limits - if checked, warning limits are drawn at the mean +/- i sigma.

Connect points - if checked, lines are drawn connecting each of the points on the chart.

Smoother - you lot may superimpose a moving boilerplate or exponentially weighted moving average (EWMA) on the chart. These smoothers are used to help estimate any trend which might be present in the data. They may also be fatigued separately using the MA and EWMA tabs. When drawn here, they use the settings of those tabs.

S Chart

This chart plots the subgroup sigmas with 3-sigma control limits:

In "Initial studies" way, the lines are placed at:

upper control limit: s-bar + 3*s-bar*(ane-c_four ²)^i/two/c₄

middle line: due south-bar

lower control limit: southward-bar - three*southward-bar*(one-c_iv ^two)^1/two/c_four

where c₄ is a abiding taken from standard tables which may exist found in any text on statistical procedure command. In "Control to standard" mode, they are placed at locations based on the specified process sigma. Whatsoever points outside the control limits are highlighted, as are any which violate the runs rules.

Options button

The options for the South chart are the same as for the 10-bar chart.

Runs Rules

This tab lists any unusual groups of points on the charts:

For a detailed give-and-take of runs rules, refer to the Individuals Nautical chart statlet.

MA Nautical chart

This tab displays a moving average chart for the subgroup means:

For a detailed give-and-take of moving average charts, refer to the Individuals Chart statlet.

EWMA Chart

This tab displays an exponentially weighted moving boilerplate chart for the subgroup means:

For a detailed discussion of exponentially weighted moving average charts, refer to the Individuals Chart statlet.

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Adequacy

This tab displays capability indices based on the estimated process sigma:

For a detailed give-and-take of adequacy indices, refer to the Individuals Chart statlet.

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