Topic 9:

Quality and the Toyota System

1. Quality Costs2. Statistical Process Control3. Six Sigma4. Just in Time Production

Philip Crosby

• Former VP of quality control at ITT corp.• Wrote “Quality is Free: The Art of Making Quality

Certain”• Proposed: “Zero Defects” as the goal for quality

– “Consider the AQL you would establish on the product you buy. Would you accept an automobile that you knew in advance was 15% defective? %5? 1%? 1/2%? How about nurses that care for newborn babies? Would an AQL of 3% on mishandling be too rigid?”

– “Mistakes are caused by lack of knowledge and lack of attention”

Crosby’s Quality Postures

0

24

68

1012

1416

18

20

Reported Actual

UncertAwakeEnlightWisdomCertain

• Uncertainty– We don’t know why we have problems

with quality• Awakening

– It is absolutely necessary to always have problems with quality

• Enlightenment– Through management commitment and

quality improvement we are identifying and resolving our problems

• Wisdom– Defect prevention is a routine part of our

operation• Certainty

– We know why we don’t have problems with qualityC

ost

of Q

ual

ity

as a

% o

f sa

les

Categories of Quality Costs

• Prevention costs

– Costs associated with preventing defects

• Appraisal costs

– Costs associated with assessing quality within a productive system

• Internal failure costs

– Costs associated with losses from disposal of or fixing quality problems

• External failure costs

– Costs associated with releasing poor quality into the demand stream

• Cost of yield loss• cost to send your

employees to quality training

• warranty costs associated with unplanned product repair

• cost of a new automated quality testing device

• cost of rework• loss of market share due

to a national product purity scandal

• litigation cost due to product defect

Rework / Elimination of Flow Units

Step 1 Test 1 Step 2 Test 2 Step 3 Test 3

Rework

Step 1 Test 1 Step 2 Test 2 Step 3 Test 3

Step 1 Test 1 Step 2 Test 2 Step 3 Test 3

Rework: Defects can be corrected

by same or other resource Leads to variability

Loss of Flow units: Defects can NOT be corrected

Leads to variability To get X units, we have to

start X/y units

Calculation of Yield Loss

• B(1-d1)(1-d2)(1-d3)…(1-dn) = m• Thus: B=m/(1-d1)(1-d2)(1-d3)…(1-dn)• Where:

– di = proportion of defectives generated by operation i– n = number of operations– m = number of finished products– B = raw material started in process

Example:1000 finished product needed from a flow cell4 operations generating 2%,3%,5%,3% proportion

defective respectively.How many units must be started in the process?

Quality Costs

2% 5%3% 3% 1000

1142 1119 1086 1031

31553323

Not just the mean is important, but also the variance

Need to look at the distribution function

The Concept of Consistency:Who is the Better Target Shooter?

Common Cause Variation (low level)

Common Cause Variation (high level)

Assignable Cause Variation

• Need to measure and reduce common cause variation• Identify assignable cause variation as soon as possible

Two Types of Causes for Variation

W. Edwards Deming

• Quality is first a management responsibility

• There are two keys to ongoing quality improvement– Employee training– Reacting to process data in real time

• Variation is the disease and SPC/SQC tools are the cure

SPC Objectives

• Insure high quality production by reducing and controlling process variation.

• Identify types of process variation.– Common cause variation: small, random

forces that continually act on a process – Special cause: variation that may be

assigned to abnormal, unpredictable forces • Take action whenever a process is judged to

have been influenced by special causes.

A General SPC Procedure

• Periodically select from the process a sample of items, inspect them, and note the result.

• Because of common or special causes, the results of every sample will vary. Determine whether the cause of the variation is common or special.

• Take action depending on what was determined in step 2.

This procedure is enacted through the use of control charts

Time

ProcessParameter

Upper Control Limit (UCL)

Lower Control Limit (LCL)

Center Line

• Track process parameter over time - mean - percentage defects

• Distinguish between - common cause variation (within control limits) - assignable cause variation (outside control limits)

• Measure process performance: how much common cause variation is in the process while the process is “in control”?

Statistical Process Control: Control Charts

Charting Continuous Variables

• The Xbar-R Chart: tracks the mean and range of a variable calculated from a fixed sample

• The Xbar-S Chart: tracks the mean and standard deviation of a variable calculated from a large sample

The Xbar-R Chart• Collect sample data by sub-group (normally containing 2 - 5 data

points): record the continuous variable under study.• Compute the mean and range for each sub-group:

• Calculate average mean and average range • Compute and draw control limits:

• Plot mean and range for each subgroup.

RAxLCLUCLxx 2/

smallestestln xxR

n

xxxx

arg

21 ...

RDLCL

RDUCL

R

R

3

4

Number of Observations in Subgroup

(n)

Factor for X-bar Chart

(A2)

Factor for Lower

control Limit in R chart

(D3)

Factor for Upper

control limit in R chart

(D4)

Factor to estimate Standard

deviation, (d2)

2 1.88 0 3.27 1.128 3 1.02 0 2.57 1.693 4 0.73 0 2.28 2.059 5 0.58 0 2.11 2.326 6 0.48 0 2.00 2.534 7 0.42 0.08 1.92 2.704 8 0.37 0.14 1.86 2.847 9 0.34 0.18 1.82 2.970

10 0.31 0.22 1.78 3.078

Parameters for Creating X-bar Charts

Example of an Xbar-R ChartSub-group

Obs1

Obs2

Obs3

Obs4

Obs5

Mean Range

123456789

10.

25

14.013.213.513.913.013.713.913.414.413.3

13.3

12.613.312.812.413.012.012.113.612.412.4

12.8

13.212.713.013.312.112.512.713.012.212.6

13.0

13.113.412.813.112.212.413.412.412.412.9

12.3

12.112.112.413.213.312.413.013.512.512.8

12.2

TotalMean

13.0012.9412.9013.1812.7212.6013.0213.1812.7812.80

12.72

323.5012.94

1.91.31.11.51.21.71.81.22.20.9

1.1

33.801.35

Each data point is the pulling force applied to a glass strand before breaking

For 5 obs.

D3=0 D4=2.114 A2=0.577

Example (cont)

For this example, the control limits reduce to:

0)35.1(0

86.2)35.1(114.2

16.12&72.13

35.1)577(.94.12/

R

R

xx

LCL

UCL

LCLUCL

1

Sub-group

2

3

Ran

ge

12

Sub-group

13

14

Mea

n

The Xbar-s Chart• Similar to Xbar-r chart except that a larger sample is

taken.

• The calculation of control limits may include a sample standard deviation as an estimate of the population standard deviation.

• Control limits are calculated :

sAxLCLUCLxx 3/

sBLCL

sBUCL

s

s

3

4

Process capability measure

• Estimate standard deviation:• Look at standard deviation relative to specification limits• Don’t confuse control limits with specification limits: a process can be out of control, yet be incapable

= R / d 2

3

Upper Specification Limit (USL)

LowerSpecificationLimit (LSL)

X-3A X-2A X-1AX X+1A

X+2 X+3A

X-6BX X+6B

Process A(with st. dev A)

Process B(with st. dev B)

6

LSLUSLC p

x Cp P{defect} ppm

1 0.33 0.317 317,000

2 0.67 0.0455 45,500

3 1.00 0.0027 2,700

4 1.33 0.0001 63

5 1.67 0.0000006 0,6

6 2.00 2x10-9 0,00

The Statistical Meaning of Six Sigma

Control Limits and Specification Limits

• Control limits of a quality characteristic represent natural variation in a process

• Specification limits indicate acceptable variation set by the customer

• The process capability index is useful in comparison:

• The capability index may be adjusted to to consider how well the process is “centered” within the limits

6

LSLUSLC p

)1( kCC ppk K=2 |design target - process average | / specification range

Process Capability Example

USL=10

LSL=9.5

= .02

167.4)02(.6

5.910

pC

9.5 10.0

8334.)8.1(167.4 pkC

K=2 |9.75 - 9.95| / .5 = .8

PC Example (cont)

USL=10

LSL=9.5

= .02

167.4)02(.6

5.910

pC

9.5 10.0

917.3)16.1(167.4 pkC

K=2 |9.75 - 9.79| / .5 = .16

Charting Discrete Attributes

• Charts that track the number of units defective– P Chart: fraction of a sample that is defective

given different sample sizes– NP Chart: fraction of a sample that is

defective given constant sample sizes

pUCL= + 3

pLCL= - 3

SizeSample

pp )1( =

• Estimate average defect percentage

• Estimate Standard Deviation

• Define control limits

• Divide time into: - calibration period (capability analysis) - conformance analysis

1 300 18 0.0602 300 15 0.0503 300 18 0.0604 300 6 0.0205 300 20 0.0676 300 16 0.0537 300 16 0.0538 300 19 0.0639 300 20 0.067

10 300 16 0.05311 300 10 0.03312 300 14 0.04713 300 21 0.07014 300 13 0.04315 300 13 0.04316 300 13 0.04317 300 17 0.05718 300 17 0.05719 300 21 0.07020 300 18 0.06021 300 16 0.05322 300 14 0.04723 300 33 0.11024 300 46 0.15325 300 10 0.03326 300 12 0.04027 300 13 0.04328 300 18 0.06029 300 19 0.06330 300 14 0.047

p =0.052

=0.013

=0.091=0.014

Period n defects p

Attribute Based Control Charts: The p-chart

0.000

0.020

0.040

0.060

0.080

0.100

0.120

0.140

0.160

0.180

13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

Attribute Based Control Charts: The p-chart

Example of a P Chart

Sub-groupNumber

Sub-groupSize (n)

Number ofDefectives

(np)

PercentDefective(np/n)100

UCL LCL

123456.

Total

11522021065220255

5925

1518235

1815

610

13.08.2

11.07.78.25.9

10.3

18.816.516.621.616.516.0

1.84.14.00.04.14.6

Note: control limits calculated assuming z=3

Quantities of light bulbs are tested to see if they function

Example of a P Chart (cont)

For this example, the control limits reduce to:

)304(.3

103.0924.

3103.nn

5

10

15

20

25

Per

cent

Def

ecti

ve

UCL

LCL

p

Sub-group

The NP Chart

• Similar to the P Chart except assumes constant sample size

• Calculation of the control limits must be performed only once

nplineCenter

)1(/ pnpznpLCLUCL

Discrete Attributes (cont)

• Charts that track the number of defects in one or more units– U Chart: defects in a variable sized sample

volume– C Chart: defects in a fixed sized sample

The U Chart

• Collect sample data: for each sample record the number of units sampled (n) and the number of defects (c)

• Compute the number of defects per unit for each sample sub-group: (u = c/n)

• Calculate the mean defects per unit:

• Compute and draw control limits• Plot u

n

cu

n

uzuLCLUCL /

The C Chart

• Similar to the U Chart except assumes constant sample size

• Calculation of the control limits must be performed only once

ClineCenter

CzCLCLUCL /

Example of a C ChartSub-groupNumber

Number ofDefects

Sub-groupNumber

Number ofDefects

123456789

10

7534382343

11121314151617181920

Total

6327247423

82

Note: control limits calculated assuming z=3

In this example, a data point represents the number of rips found in 5 yards of nylon fabric

Example of a C ChartFor this example, the control limits reduce to: 1.431.4/

1.4

LCLUCL

C

5

10

Def

ecti

ves

UCL

C

Sub-group

We assume the process is in an “in control” state when:

• Points are within the control limits• Consecutive groups of points do not take a particular form.

– Runs on one side of the central line (7 out of 7, 10 out of 11, or 12 out of 14)

– Trends of a continued rise or fall of points (7 out of 7)– Periodicity or same pattern repeated over equal interval– Hugging the central line (most points within the center half of

the control zone)– Hugging the control limits (2 out of 3, 3 out of 7, or 4 out of

10 points within the outer 1/3 zone)

Statistical Process Control

CapabilityAnalysis

ConformanceAnalysis

Investigate forAssignable Cause

EliminateAssignable Cause

Capability analysis • What is the currently "inherent" capability of my process when it is "in control"?

Conformance analysis• SPC charts identify when control has likely been lost and assignable cause variation has occurred

Investigate for assignable cause• Find “Root Cause(s)” of Potential Loss of Statistical Control

Eliminate or replicate assignable cause• Need Corrective Action To Move Forward

How do you get a Six Sigma Process?

Step 1: Do Things Consistently

ISO 9000 can be very helpful

Step 2: Reduce Variability in the Process

Taguchi: Even small deviations are quality losses. It is not enough to look at “Good” vs “Bad” Outcomes. Only looking at good vs bad wastes

opportunities for learning; especially as failures become rare (closer to six sigma) you

need to learn from the “near misses”

Step 3: Accommodate Residual Variability Through Robust Design

Double-checking and Fool-proofing

CUSTOMER FOCUS

CONTINUOUSIMPROVEMENT

MANAGEMENTCOMMITMENT & LEADERSHIP

EMPLOYEEINVOLVEMENT

ANALYTICALPROCESSTHINKING

MGT BY FACTEMPOWERMENT

PL

AN

NIN

GT

RA

ININ

G

A Systems View of Total Quality Management

Toyota Production System

• Pillars:

1. just-in-time, and

2. autonomation, or automation with a human touch

• Practices:– setup reduction (SMED)– worker training– vendor relations– quality control– foolproofing (baka-yoke)– many others

JIT Implementation

• Adopt goal to eliminate all forms of waste

• Improve workplace cleanliness and order

• Promote flow manufacturing

• Level production requirements

• Improve and standardize all process steps

The Seven Zeros

• Zero Defects: To avoid delays due to defects. (Quality at the

source)

• Zero (Excess) Lot Size: To avoid “waiting inventory” delays.

(Usually stated as a lot size of one.)

• Zero Setups: To minimize setup delay and facilitate small lot sizes.

• Zero Breakdowns: To avoid stopping tightly coupled line.

• Zero (Excess) Handling: To promote flow of parts.

• Zero Lead Time: To ensure rapid replenishment of parts (very

close to the core of the zero inventories objective).

• Zero Surging: Necessary in system without WIP buffers.

Cross Training and Plant Layout

• Cross Training:– Adds flexibility to inherently inflexible system– Allows capacity to float to smooth flow– Reduces boredom– Fosters appreciation for overall picture– Increase potential for idea generation

• Plant Layout:– Promote flow with little WIP– Facilitate workers staffing multiple machines– U-shaped cells

• Maximum visibility• Minimum walking• Flexible in number of workers• Facilitates monitoring of work entering and leaving cell• Workers can conveniently cooperate to smooth flow

and address problems

U-Shaped Manufacturing Cell

Inbound Stock Outbound Stock

Kanban

• Definition: A “kanban” is a sign-board or card in Japanese and is the name of the flow control system developed by Toyota.

• Role:

Kanban is a tool for realizing just-in-time. For this tool to work fairly well, the production process must be managed to flow as much as possible. This is really the basic condition. Other important conditions are leveling production as much as possible and always working in accordance with standard work methods.

• – Ohno 1988• Push vs. Pull: Kanban is a “pull system”

– Push systems schedule releases– Pull systems authorize releases

One-Card Kanban

Outbound stockpoint

Outbound stockpoint

Productioncards

Completed parts with cards enter outbound stockpoint.

When stock is removed, place production card in hold box.

Production card authorizes start of work.

The Lessons of JIT

– The production environment itself is a control

– Operational details matter strategically

– Controlling WIP is important

– Speed and flexibility are important assets

– Quality can come first

– Continual improvement is a condition for survival