individual moving range (i-mr) charts the swiss army knife of process charts€¦ · ·...

Individual Moving Range (I-MR) Charts

The Swiss Army Knife of Process Charts

SPC Selection Process

Choose Appropriate

Control Chart

typeof data

type ofattribute

data

subgroupsize

I – MR Chart

X – R Chart

X – S Chart

C Chart U ChartNP

ChartP Chart

typeof defect

type ofsubgroups

ATTRIBUTE CONTINUOUS

DEFECTS DEFECTIVES

VARIABLECONSTANT CONSTANT VARIABLE

1 2-9 10+

Number of Incidences

Incidences per Unit

Number of Defectives

Proportion Defectives

Individuals &

Moving Range

Mean & Range

Mean & Std. Dev.

Sample size

2I-MR XBarR Charts Coventry Healthcare – Larry Dyer MBB

Individual Moving Range (I-MR Chart)

• Control charts for variables data

• Monitors the process over time

• Individual Chart

– Plots each measurement as a separate data point

– Each data point stands on its own (subgroup size = 1)

• Moving Range Chart

– Uses a default value of 2, which means each data point plots the

difference (range) between two consecutive data points as they come

from the process in sequential order

– There will be one less data point in the Moving Range chart than the

Individual chart


Sample Individual Moving Range Chart

4

645750433629221581

180

160

140

120

100

Observation

In

div

idu

al

Va

lue

_X=134.24

UC L=165.38

LC L=103.10

645750433629221581

40

30

20

10

0

Observation

Mo

vin

g R

an

ge

__MR=11.71

UC L=38.25

LC L=0

1

111

1

I-MR Chart of Systolic Blood Pressure

I-MR XBarR Charts Coventry Healthcare – Larry Dyer MBB

Xbar-R Charts

• Control charts for variables data

• Monitors the process over time

• The distribution does not have to be approximately normal

• Based on the average of a series of observations, called a subgroup

• Monitors the variation between observations in the subgroup over

time

• The larger the subgroup, the more sensitive the chart will be to

shifts, providing a Rational Subgroup can be formed

5I-MR XBarR Charts

What is arational subgroup?

Coventry Healthcare – Larry Dyer MBB

What is it and where does it come from?

Rational Subgroup Items which were produced under the same conditions When possible, formed by using consecutive units Each subgroup’s statistics are compared to the control limits,

and patterns of variation between subgroups are analyzed

Picture a Stable Distribution A group of objects containing a characteristic of

interest

Distribution


Where do Subgroups Come From?

Subgroup:• A subset of the distribution of interest

Subgroup 1

Subgroup 2

Subgroup 3

Subgroup N

…


Sample Xbar-R Chart

8I-MR XBarR Charts

191715131197531

110

105

100

95

90

Sample

Sa

mp

le M

ea

n

__X=99.69

UC L=109.33

LC L=90.05

191715131197531

48

36

24

12

0

Sample

Sa

mp

le R

an

ge

_R=28.63

UC L=51.99

LC L=5.27

Xbar-R Chart of Glucose Readings


When to Use I-MR/Xbar-R

• I-MR

– When you have a limited number of individual measurements

• Xbar-R

– When you can collect measurements in groups (subgroups) of between

two and ten observations

• For subgroup sizes greater than ten

– Use Xbar / Sigma charts

• Must have data that is time-ordered


Interpreting R Charts

• Always look at the Range chart first

– Control limits on the I-MR are derived from the change in range (moving

range)

– The control limits on the Xbar-R chart are derived from the average

range

– If the Range chart is out of control, then the control limits on the

Individual and X-bar chart are meaningless.

• Look for out of control points

– Special causes must be eliminated

– There should be more than five distinct values plotted

– No single value should appear more than 25% of the time


I-MR Chart

• Looking at the moving range chart, what does the out of control

point tell you?

11

28252219161310741

8

6

4

2

0

Observation

In

div

idu

al

Va

lue

_X=3.5

UC L=7.810

LC L=-0.810

28252219161310741

6.0

4.5

3.0

1.5

0.0

Observation

Mo

vin

g R

an

ge

__MR=1.621

UC L=5.295

LC L=0

1

I-MR Chart of Individual


Interpreting R Charts

• Average charts become more sensitive to process changes as the

subgroup size is increased

12I-MR XBarR Charts

What doesthat mean?


Sensitive to Process Changes

• As the subgroup size increases the control limits of the range chart

increase

• Range Chart

– UCL – 42.86

– LCL – 0

13I-MR XBarR Charts

• Range Chart

– UCL – 52.99

– LCL – 5.27


191715131197531

110

105

100

95

90

Sample

Sa

mp

le M

ea

n

__X=99.69

UC L=109.33

LC L=90.05

191715131197531

48

36

24

12

0

SampleS

am

ple

Ra

ng

e

_R=28.63

UC L=51.99

LC L=5.27

Xbar-R Chart of Glucose Readings (Subgroup Size 9)

554943373125191371

120

110

100

90

80

Sample

Sa

mp

le M

ea

n

__X=99.69

UC L=116.72

LC L=82.65

554943373125191371

40

30

20

10

0

Sample

Sa

mp

le R

an

ge

_R=16.65

UC L=42.86

LC L=0

1

Xbar-R Chart of Glucose Readings (Subgroup Size 3)

Interpreting Individual/Xbar Charts

• Individual/Xbar Charts

Interpret the points on the X-bar chart relative to the control limits and

Run Tests

Look for out of control points

Look for obvious non-random behavior

• Averages in the Xbar Chart cannot be compared to requirements

14I-MR XBarR Charts

What doesthat mean?


Xbar-R Cannot Be Compared to Requirements

• Both charts use same data set

• Look at the control limits on the Individual and Xbar Charts

– UCL – 131.17

– LCL – 68.2

15I-MR XBarR Charts

16314512710991735537191

140

120

100

80

60

Observation

In

div

idu

al

Va

lue

_X=99.69

UC L=131.17

LC L=68.20

16314512710991735537191

40

30

20

10

0

Observation

Mo

vin

g R

an

ge

__MR=11.84

UC L=38.68

LC L=0

I-MR Chart of Glucose Readings

191715131197531

110

105

100

95

90

Sample

Sa

mp

le M

ea

n

__X=99.69

UC L=109.33

LC L=90.05

191715131197531

48

36

24

12

0

Sample

Sa

mp

le R

an

ge

_R=28.63

UC L=51.99

LC L=5.27

Xbar-R Chart of Glucose Readings

– UCL – 109.33

– LCL – 90.05

Individual Readings Same Readings in Subgroups of 9


General Steps for Constructing I-MR Charts

The Control Chart Cookbook

1. Select characteristic (critical “X” or CTQ) to be charted

2. Determine the purpose of the chart

3. Select data-collection points

4. Determine the measurement method/criteria

5. Drop the data into Minitab or other charting software


Questions?


Run Tests – Western Electric Rules

Average

UCL

LCL

-1

-2

+1

+2

Average

UCL

LCL

-1

-2

+1

+2

Average

UCL

LCL

-1

-2

+1

+2

Average

UCL

LCL

-1

-2

+1

+2

Average

UCL

LCL

-1

-2

+1

+2

Average

UCL

LCL

-1

-2

+1

+2

Average

UCL

LCL

-1

-2

+1

+2

Average

UCL

LCL

-1

-2

+1

+2

Average

UCL

LCL

-1

-2

+1

+2

Average

UCL

LCL

-1

-2

+1

+2

Average

UCL

LCL

-1

-2

+1

+2

Average

UCL

LCL

-1

-2

+1

+2

Average

UCL

LCL

-1

-2

+1

+2

Average

UCL

LCL

-1

-2

+1

+2

Average

UCL

LCL

-1

-2

+1

+2

Average

UCL

LCL

-1

-2

+1

+2

Average

UCL

LCL

-1

-2

+1

+2

Average

UCL

LCL

-1

-2

+1

+2

One or more observations occurring more than 3 Standard Deviations from the average, i.e. any points occurring above or below the Control Limits.

Two out of three consecutive observations, all on the same side of the average and occurring more than two Standard Deviations away form the average.

Fifteen consecutive observations occurring within one Standard Deviation from the average.

Four out of five consecutive observations, all on one side of the Center Line occurring more than one Standard Deviation from the average.

Eight consecutive observations on one side of the average.

Eight consecutive observations that are more than one Standard Deviation from the average.

Fourteen consecutive observations that alternate up and down.

Six consecutive observations that trend downward or upward.


individual moving range (i-mr) charts the swiss army knife of process charts€¦ · ·...

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