Six Sigma Tool Navigator: The Master Guide for Teams

2017-07-07 02:10:07

Tool 42: Control Chart—-R (Variable)

AKA

N/A

Classification

Analyzing/Trending (AT)

Tool description

A control chart is a graph that plots randomly selected data over time in order to determine if a process is performing to requirements or is, therefore, under statistical control. The chart displays whether a problem is caused by an unusual or special cause (correctable error) or is due to chance causes (natural variation) alone.

Typical application

To determine if a process is performing to upper and lower control-limit requirements (process is kept in control).

To monitor process variations over time, with regard to both special or chance causes.

To identify opportunities for improving quality and to measure process improvement.

To serve as a quality measurement technique.

Problem-solving phase

→	Select and define problem or opportunity
→	Identify and analyze causes or potential change
	Develop and plan possible solutions or change
→	Implement and evaluate solution or change
→	Measure and report solution or change results
	Recognize and reward team efforts

Typically used by

2	Research/statistics
	Creativity/innovation
4	Engineering
	Project management
1	Manufacturing
	Marketing/sales
	Administration/documentation
	Servicing/support
3	Customer/quality metrics
	Change management

links to other tools

before

Variance Analysis

Sampling Methods

Observation

Checksheet

Events Log

after

Process Capability Ratios

Standard Deviation

Descriptive Statistics

Process Analysis

Work Flow Analysis (WFA)

Notes and key points

Types of Control Charts
Data Required	For Specific Chart
Quantitative Variable Data Continuous or measurements Example: size, downtime, dimensions, activities per day, etc.	– R chart† (average and range "R" of samples) – S chart (average and standard deviations "S" of samples)
Qualitative Attribute Data Discrete or counts Example: Complaints, rework, missed due dates, delays, rejects, etc.	c chart‡ (number of defects in a subgroup) np chart (number of defective units in a subgroup) p chart‡‡ (percentage defective) μ chart (defects per unit)

Most commonly used charts:

†For variable data:	-R Chart
‡For attribute data:	c Chart
‡‡For attribute data:	p Chart

Note: For a description of other charts refer to a reference on statistical process control (SPC).

-R Chart (variable data)

Sample data: Random sampling, minimum (20) samples, minimum (5) data points in each subgroup.

Calculations: See -R Chart example

Table of Factors for & R Charts
Data Points in Subgroup (n)	Factors for Chart	Factors for R Chart
Data Points in Subgroup (n)	A2	Upper-D3	Lower-D4
2	1.880	0	3.268
3	1.023	0	2.574
4	.729	0	2.282
5	.577	0	2.114

6	.483	0	2.004
7	.419	.076	1.924
8	.373	.136	1.864
9	.337	.184	1.816
10	.308	.223	1.777

Step-by-step procedure

STEP 1 Determine the type of variance control chart to be used. See example Connector Wire (variables control chart—type -R).

STEP 2 Collect at least 20 samples of data, 5 measurements per sample. Sampling should be random and according to a set frequency over a period of time.

STEP 3 Prepare a type -R Chart and record collected data as shown. See example chart.

STEP 4 After all 20 subgroups (samples) have been recorded, perform all required calculations. See notes and key points above for example.

STEP 5 Plot and connect plotted points to draw trendlines. Verify that trendline points reflect recorded averages () and ranges (R).

STEP 6 Analyze plotted data for significant variance or patters.