Quality Advisor

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Data Analysis Tools

Tools for analyzing and interpreting data so that areas to improve become apparent.

What type of data do I have?

Variables charts (measurement data)

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Consists of measurements of a characteristic, such as length, weight, density, time, or pressure.

Control charts Is your process stable and in control?
X-bar & range Use this if your data has a subgroup size of 2-10 observations.
X-bar & sigma Use this if your data has a subgroup size of 11 or more observations.
X-MR Use this if your data has a subgroup size of 1 observation.
Median Use this to analyze measurement data when you want to plot all observations.
Run chart Use this to see trends and patterns if there is not enough data for a control chart.
Histogram Use this to determine if your data has a normal distribution.
Capability analysis Use this to determine if your process is capable of producing output within specification limits.

 

Attributes (counts data)

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Consists of defects per item (nonconformities) or the number of defective items (nonconforming). For example, the number of non-working parts in sample or the number of blemishes counted on an individual part.

Control charts Is your process stable and in control?
np-chart Use this if your data is a count of nonconforming units and the subgroups are all the same size.
p-chart Use this if your data is a count of nonconforming units and the subgroup size varies.
c-chart Use this if your data is a count of nonconformities and the subgroups are all the same size.
u-chart Use this if your data is a count of nonconformities and the subgroup size varies.
Capability analysis Use this to determine capability for attributes data.

 

Pareto (counts in categories)

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Consists of a count of items or occurrences, such as the number of defective items, the number of scratches on a door panel, or how often a specific problem occurs.

Pareto diagram Use this to analyze counts that are in categories.

 

Rare event

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Use this when other control charts are not effective to determine if your process is stable.

g-chart Use this if your count data occurs infrequently. It is used by counting the number of events between rarely-occurring error or a nonconforming incident.
t-chart Use this if your error or non-nonconforming incident occurs infrequently. Each point on the chart represents an amount of time that has passed since the prior nonconforming incident occurred.

 

Interpreting quality charts

Quality Advisor

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Data Collection Tools

A resource for data collection tools, including how to collect data, how much to collect, and how frequently to collect it.

Sampling

A tool used to indicate how much data to collect and how often it should be collected.

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Operational Definition

A clear, concise, detailed definition of a measure.

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Improving Measurement Accuracy with Gage R&R

Gage R&R refers to testing the repeatability and reproducibility of the measurement system.

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Formulas and Tables

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Process performance indices

Process performance indices use sigma of the individuals.

Pp

Pp for one-sided specifications

If you are using one sided specifications, use the following formulas to determine the Cp:

Upper specification

Lower specification

Ppk

Where:

Zmin is the smaller of Zupper and Zlower.

Using sigma of the individuals:

Pr

Formulas and Tables

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Capability indices

Capability indices use estimated sigma.

Cp

Cp for one-sided specifications

If you are using one sided specifications, use the following formulas to determine the Cp:

Upper specification

Lower specification

Cr

Cpk

f-cpk

Where:

Zmin is the smaller of Zupper and Zlower.

Using estimated sigma:

Cpm

Where: sigma for cpm

T = specification target (nominal)

Xi = a given individual reading of ” i ”

n = total number of individual readings

= symbol for summation

Formulas and Tables

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t-chart formula

The t-chart formula:

Formulas and Tables

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g-chart formula

The g-chart formula:

Formulas and Tables

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c-chart formulas

The c-chart formula (for number of nonconformities, from subgroups of a constant size):

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u-chart formula

The u-chart formula (for number of nonconformities from subgroups that can vary in size):

Formulas and Tables

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p-chart formulas

The p formula (for the proportion of nonconforming units from subgroups that can vary in size):

f-p-bar

To calculate control limits for the p-chart: