statistical process control (spc) workshop - six sigma tv - … · · 2013-03-19sixsigmatv.net...

Statistical Process Control

(SPC) Overview

SixSigmaTV.Net

SixSigmaTV.Net 2 Statistical Process Control (SPC) Workshop

SPC - Agenda

Statistical Process Control History

Review fundamentals of Control Charts

Understand the impact of variation within

your process

Construct and interpret Control Charts to

monitor process performance


Control Charts: A Brief History

• Dr. Shewhart of Bell Laboratories introduced Control Charts in 1924.

He developed a theory of variation that states there are two

components to variation:

1. Common cause - the collection of conditions inherent in any process

2. Special cause - identifiable causes or conditions directly responsible for process

shifts

• Dr. Shewhart is credited with the development of the standard

control chart based on 3 standard deviation limits to separate

common cause variation from special cause variation.

• Control Charts became widely used by the US Military during World

War II.

• Dr. Deming introduced Control Charts to the Japanese in the 1950s.

They consider this their turning point to re-building Japan after the

war and making them a formidable leader in the industrial world.


Control Charting

• What is it?

– A technique for applying statistical analysis to measure, monitor

and control processes

• When do I apply it to my process?

– To establish a baseline of performance.

– To determine if a process is stable and predictable.

– To determine if a shift has taken place.

– To avoid tampering.

– To identify impacts of process variation.

– To monitor and control critical Xs, Ys & implemented solutions.


Control Charts - Purpose

• Provide feedback on process performance

– Shows the natural variation of the process

– Provides process monitoring / feedback

– Measures the health of the process

• Identify when process performance changes

– Due to deterioration and neglect

– Due to the introduction of outside influences (“special” causes)

• Allows timely action for process adjustments

Note: Eliminating special cause variation can be one of the easiest ways to reduce variation and improve the process performance.


Control Charts – When to Use

• Define Phase – To establish a baseline of current

process performance (metrics)

• Analyze Phase – After data collection & MSA, control

charts are used to determine process variation (spread /

standard deviation), location, normality and stability

• Control Phase – To ensure improvements have positively

impacted process variation, location and stability. Also,

monitor sustained gains over long term


Control Chart Terminology

• Control - operating within natural limits without undue impact

from outside, extraneous, or “special” causes

• Control Limits - statistically calculated boundaries within which a

process in control should operate. – Identify the natural bounds of the process

– Based on the Voice of the Process

– Unrelated to customer specifications

• Control Chart - a sequential time plot tracking process

performance

2.18

7.05

11.93

1.96

3.96

5.96

7.96

9.96

11.96

13.96

0 5 10 15 20


Control Chart Terminology

• Common Cause Variation – natural variation of a process – Consistent, stable, random variability within the process

– Requires fundamental (systemic) improvement to reduce; usually more difficult to reduce

• Special Cause Variation – variation that is not natural to a process due to an outside influence (“special cause”) that may temporarily or permanently alter the process performance unless identified and addressed. – Identified by changes in process performance, outliers, or unusual patterns in the data

– Requires identifying process changes; usually easier to address and eliminate


Control Chart - Illustration

{ Normal or expected range of measures

10.04

17.58

25.11

5.40

10.40

15.40

20.40

25.40

30.40

0 5 10 15 20

Out-of-control point

Time plot of sequential process measurements


Control Limits vs. Spec Limits

Control Limits

Defined based on process

performance (+/- 3 estimated

standard deviations from the

mean).

Help determine if your process is

“in control” (without special

cause variation).

Plotted on control charts.

Change when there is a verified,

significant change to your

process.

Represent the voice of the

process.

Customer Spec Limits

Defined based on feedback

from the customer(s).

Help determine if your process

is producing defects.

Plotted on histograms (not

control charts).

Change when your customers

say they do!

Represent the voice of the

customer.

Determine product functional

requirements


Control Charts – Data Types

Variable/Continuous ( Measurable ) • Processing Cycle Time ( days, weeks, months )

• Customer Wait Time ( seconds, minutes, hours )

• Can you think of other variable data types in your organization?

Attribute / Discrete ( Defects ) • Number of Errors on Patient Records ( missing or incorrect

information )

• Can you think of other attribute data types in your organization?


Control Chart: Illustration

Common Cause Variation

Sample

Sa

mp

le M

ea

n

332925211713951

400

300

200

100

__X=262.4

UC L=408.5

LC L=116.3

Sample

Sa

mp

le R

an

ge

332925211713951

600

450

300

150

0

_R=200.5

UC L=457.4

LC L=0

Xbar-R Chart of Distance

Subgroup Variation


The Family of Control Charts

• Continuous/Variable data

• X-bar/R charts for sample averages

• ImR charts for individual items

• X-bar/S charts for large samples using standard deviation

• Always measurable with a tool

– Examples: stopwatch, caliper, scale

• Attribute/Discrete

• p-chart for percent or proportions of defective items

• np-chart for number of defective items

• u-chart for defects per unit

• c-chart for number of defects

• Operational definitions are always required

– Examples: good/bad, pass/fail, correct/incorrect


Guidelines for Determining Control Chart Usage

Type Appropriate Data Examples of Use

c-Chart

u-Chart

c = counts of relatively infrequent events. To chart defects with

constant subgroup size.

u = counts of relatively infrequent events. To chart defects per

unit with constant or variable subgroup size.

Number of miss applied payments.

Number of lost checks.

Number of miss applied payments per week @

FC.

Number of fields missing info. on loan app.

p-Chart

np-Chart

p-Chart: To chart proportion or percent defective with subgroup

size constant or variable.

np-Chart: To chart number of defective units with constant

subgroup size. (Note: A defective may contain many defects.)

p-Chart: percent defective, percent of mis-routed

mail items from FC (sample sizes may vary),

percent of late loan payments.

np-Chart: Number of defective applications per

batch (sample sizes are constant).

I-Chart

I-MR Chart

Measurable data collected on individual items (i.e. the subgroup

size is one at any one time).

Individual charts are some of the easiest to create, and can be used

in a wide variety of situations but require larger shifts to highlight

or detect a change. Based on the standard normal distribution.

Cycle time for a process (the item may be a

single loan).

Amount of money used in the ATM per day.

Loan interest rates per day.

X bar and

Range Charts

X-Bar: displays the subgroup average. Based on standard normal

distribution.

R: range (variation) within & between the subgroups.

X-Bar and R Charts should be used in conjunction to determine

whether a process is in control.

X-Bar:

Average length of time customers wait to be

served (multiple customers used).

Cycle time for a process (in this case, a group of

loans may be monitored and the average time and

range tracked).

Control Chart Roadmap D

iscre

te D

ata

C

ontinuous D

ata


Discrete/Attribute Chart Decision Tree

C Chart defect

count

U Chart,

defects/ unit

NP Chart, #

defective

P Chart, % or

proportion

Count or Classification

(Discrete/Attribute Data)

Defects

Fixed

sample sizes

Variable

sample sizes

Defective Units

Fixed

sample sizes

Variable

sample sizes


Continuous/Variable Chart Decision Tree

Measurement

(Continuous/Variable Data)

Subgroup Size of 1

I-Chart / I-MR

Subgroup Size

2-10

X-bar & R

Subgroup Size

> 10

X-bar & S


P-Chart

• Used whenever monitoring proportion or percent

defective

• Some uses of the p-chart in transactional applications

are:

– Account errors

– Defective patient records

– Proportion of statements with errors

– Missing items


P-Chart: Exercise

A Registrar processes patient records and sends them over to Pre-Op. Construct a p-chart and see what percent of records are defective.

Day 1 2 3 4 5 6 7 8 9 10

Records 28 34 21 30 25 31 40 29 30 32

Bad 7 8 7 9 9 11 14 6 8 10

As the Patient Registrar Manager,

what are your next steps?

Day 11 12 13 14 15 16 17 18 19 20

Records 28 29 33 39 23 29 42 29 33 27

Bad 8 8 11 14 6 8 16 6 7 8

P-Chart for Errors


0.295751634

0.032260581

0.559242687

-0.100

0.000

0.100

0.200

0.300

0.400

0.500

0.600

0.700

P -

bad


U-Chart

• Used whenever monitoring number of

defects per unit.

• Some uses of the U-Chart in transactional applications

are:

– Number of account errors per customer or batch.

– Number of defects on each application processed.

– Number of errors on each patient record processed .


U-Chart: Exercise

Now that you now the percent of defective patient records being received from your Registrar, how many defects per record are we getting?

Day 1 2 3 4 5 6 7 8 9 10

Records 28 34 21 30 25 31 40 29 30 32

Defects 37 18 27 19 14 21 34 16 28 40

Day 11 12 13 14 15 16 17 18 19 20

Records 28 29 33 39 23 29 42 29 33 27

Defects 18 28 41 45 16 18 26 16 27 38

As the Pre-Op Manager,



U-Chart: Exercise

0.861

0.325

1.397

0.200

0.300

0.400

0.500

0.600

0.700

0.800

0.900

1.000

1.100

1.200

1.300

1.400

1.500

U -

defe

cts


I-MR Chart (Individual and Moving Range)

Usage when:

There is no basis for

subgrouping.

Each measurement represents

one batch.

Production rate is slow such that

measurements are easy to

gather or widely spaced in time.

I-MR chart is appropriate for continuous data and focuses

on the variation between individual measures.

0Subgroup 50 100

5

10

15

Ind

ivid

ua

l V

alu

e

Mean=10.04

UCL=16.25

LCL=3.831

0

1234

567

89

Mo

vin

g R

an

ge

1

R=2.334

UCL=7.627

LCL=0

I and MR Chart for Processing Time


ImR-Chart: Exercise

Now that you now how many defects per record you are getting, how much time is your team spending per week reworking the mistakes?

Day 1 2 3 4 5 6 7 8 9 10

Records 28 34 21 30 25 31 40 29 30 32

RW Time (hours)

2 8 6 5 3 4 6 3 2 3

Day 11 12 13 14 15 16 17 18 19 20

Records 28 29 33 39 23 29 42 29 33 27

RW Time (hours)

8 5 5 3 2 4 4 6 3 6

As the Pre-Op Manager,



ImR-Chart: Exercise – RW Time

Mean CL: 4.40

-1.199104143

9.999104143

-2.00

-1.00

0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

8.00

9.00

10.00

11.00

Ind

ivid

uals

: R

W T

ime

2.105263158

0

6.87849944

-1.00

0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

MR

: R

W T

ime


Xbar-R Chart

R chart:

Shows changes in the "within"

subgroup variation.

Asks "Is the variation in the

measurements within

subgroups stable?"

X-bar chart:

Shows changes in the average

value of the process.

Asks "Is the variation between

the averages of the subgroups

more than that predicted by

the variation within the

subgroups?"

Xbar-R chart is appropriate for continuous data when it is

practical to collect frequent samples of subgroups.

0Subgroup 10 20 30

6.5

7.5

8.5

9.5

10.5

11.5

12.5

13.5

Sa

mple

Me

an

Mean=10.09

UCL=13.08

LCL=7.108

0

5

10

Sa

mp

le R

an

ge

R=4.099

UCL=9.351

LCL=0

Xbar/R Chart for Processing Time

Most sensitive (powerful) chart for

tracking changes in the mean.


Contact Us

• SixSigmaTV.Net

• [email protected] (Master Black Belt)

• [email protected] (Master Black Belt)

• [email protected]



statistical process control (spc) workshop - six sigma tv - … · · 2013-03-19sixsigmatv.net...

Documents