Tool 42: Control Chart - -R (Variable)

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
	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.

Example of tool application