8-1

IsProcessCapable

?

IsProcessCapable

?TheQualityImprovementModel

Use SPC to Maintain Current Process

Collect & Interpret

Data

Select Measures

Define Process

IsProcessCapable

?

IsProcessCapable

?

Improve Process

Capability

IsProcessStable

?

Investigate & Fix

Special Causes

No

Yes

No

Yes

Is Process Capable?

Purpose:Determine the adequacy of the process with respect to customer /management needs.

8-2

IsProcessCapable

?

IsProcessCapable

?Capable Process

A stable process that meets customer requirements.

8 22 242 4 6 10 12 14 16 18 20 26 28 30 32

Run Order

UCL

CL

LCL

Control Chart

Lower Spec Upper SpecTarget

Histogram

Capability assessments for unstable processes, may not be indicative of how the process is actually performing.

8-3

IsProcessCapable

?

IsProcessCapable

?

Assessing Process Capability

Counting Measures The average percent defectives. The average number of defects.

Instrument Measures Comparing both the center of the process and the

process variation

8-4

IsProcessCapable

?

IsProcessCapable

?

Capability Assessment for Counting Measures

“Order Entry Process”

Is this process adequate as is?

Should it be improved?

Week123456789

1011121314151617181920

Total

# Errors15221810139

2712242288

26162010169

1520

320

0

5

10

15

20

25

30

35

5 10 15 20

Avg=16.0

LCL=4.0

UCL=28.0

Week

Numberof Errors

Control Chart

8-5

IsProcessCapable

?

IsProcessCapable

?

Measures of Process CapabilityCp = Specification Range

True Process Range = USL - LSL

6c

Cpk =

Distance from process averageto closest specification limit

12 True Process Range

= min (USL - x , x - LSL)3c

Problem: We are assuming the process has a target that is in the center of the specification range, and that the process is in fact centered on that target.

Note: a negative result is possible if the process average is outside specifications

Benefits: • Optimal values are attained by running exactly between specs. • Can (must) be used for 1-sided specifications

Cp < 1.0 Process is not capable of meeting specsCp = 1.0 Process is marginally capableCp > 1.0 Process is capable of meeting specs

Cpk < 1.0 Process is not capable of meeting specsCpk = 1.0 Process is marginally capableCpk > 1.0 Process is capable of meeting specs

Warning: Capability assessments for unstable processes, may not be indicative of how the process is actually performing.

8-6

IsProcessCapable

?

IsProcessCapable

?

How much material is out of spec? In the short term? In the long term?

USLUSLLSLLSL

Process Capability

8-7

IsProcessCapable

?

IsProcessCapable

?Process Capability Ratios

Voice of The Customer

Voice of The Process

USLUSLLSLLSL

8-8

IsProcessCapable

?

IsProcessCapable

?Process Capability - The Strategy

Centering –The Process Is On Target

Spread – Reduce The Variation

LSL USL

DefectsDefects

8-9

IsProcessCapable

?

IsProcessCapable

?

2 Key Metrics for Measuring Capability

C Min( X-LSL

3

USL- X

3pk

, )

c

LSLUSLCp

6

c c

Process Capability Ratios

8-10

IsProcessCapable

?

IsProcessCapable

?Process Capability Ratios - Concept

Total ToleranceC

Process Spreadp

c

LSLUSLCp

6

8-11

IsProcessCapable

?

IsProcessCapable

?

A Short-term Capability study covers a relatively short period of time (days, weeks) generally consisting of 30 to 50 data points. The actual number depends on the subject under study.

Is The ProcessIn Control ?

Is It Producing Defects ?

35302520151050

39

34

29

24

Observation Number

Indi

vidu

al V

alu

e

I Chart for C1

X=30.60

3.0SL=37.36

-3.0SL=23.84

CP & CPK Measure Short-term Capability

8-12

IsProcessCapable

?

IsProcessCapable

?

A long-term capability study covers a relatively long period of time (weeks, months) generally consisting of 100-200 data points. Again, the actual amount depends

on the subject under study.

Is The ProcessIn Control ?

Is It Producing Defects ?

100500

50

40

30

20

Observation Number

Indi

vidu

al V

alu

e

I Chart for C3

X=33.80

3.0SL=47.12

-3.0SL=20.49

Long Term Performance

Short term Capability

8-13

IsProcessCapable

?

IsProcessCapable

?

A Further Look at Capability

Compare the estimates of the process deviations from the short-term and long-term data

What is the difference between the short-term and the long-term data?

What implication does this have in doing capability studies?

What is the difference between the short-term and the long-term data?

What implication does this have in doing capability studies?

Descriptive Statistics

Variable N Mean StdDev short term 30 30.6 2.23 long term 180 33.8 4.44

8-14

IsProcessCapable

?

IsProcessCapable

?

Measures of Process PerformanceP p = Specification Range

True Process Range = USL - LSL

6s

Ppk =

Distance from process averageto closest specification limit

12 True Process Range

= min (USL - x , x - LSL)3s

Problem: We are assuming the process has a target that is in the center of the specification range, and that the process is in fact centered on that target.

Note: a negative result is possible if the process average is outside specifications

Benefits: • Optimal values are attained by running exactly between specs. • Can (must) be used for 1-sided specifications

P p < 1.0 Process Performance is not meeting specsP p = 1.0 Process Performance is marginally meeting specsP p > 1.0 Process Performance is meeting specs

Ppk < 1.0 Process Performance is not meeting specsPpk = 1.0 Process Performance is marginally meeting specsPpk > 1.0 Process Performance is meeting specs

8-15

IsProcessCapable

?

IsProcessCapable

?

Performance vs. Capability

These data show that the process, if well controlled can perform much better than it currently is

5040302010

14

13

12

11

10

Index

CO

2-S

hrt

CO2 Levels for 55 Time PointsDays Sales Outstanding for 55 Days

DS

O

8-16

IsProcessCapable

?

IsProcessCapable

?Capability vs. Performance

5040302010

14

13

12

11

10

Index

CO

2-S

hrt

CO2 Levels for 55 Time PointsDays Sales Outstanding for 55 Days

DS

O

Process Performance: Total Variation including

shifts and drifts

(Pp & Ppk)

Capability: Only random or short term variability

(Cp & Cpk)

8-17

IsProcessCapable

?

IsProcessCapable

?

Process Performance Ratios

The P-family of indices are computationally the same as the C-family of ‘capability’ indices, but use the observed

long-term standard deviation.

P Min( X-LSL

3

USL- X

3pk

, )

s

LSLUSLpP

6

s s

8-18

IsProcessCapable

?

IsProcessCapable

?

WARNING!!!WARNING!!!Statistical Assumptions Made In Capability

Studies

1. Data Comes From a Stable ProcessData Comes From a Stable Process If not, work towards getting the process in

control Don’t despair, you can still make some

assumptions about your process in the mean time

2. Data are Normally DistributedData are Normally Distributed If not, transform it (ask the instructor)

If Items #1 and #2 aren’t met, results will be misleading