s6-1 outline statistical process control (spc) control charts for variables the central limit...

S6-1

OutlineOutline Statistical Process Control (SPC)

Control Charts for Variables The Central Limit Theorem Setting Mean Chart Limits ( x-Charts) Setting Range Chart Limits (R-Charts) Using Mean and Range Charts Control Charts for Attributes Managerial Issues and Control Charts

Process Capability Acceptance Sampling

Operating Characteristic (OC) Curves Average Outgoing Quality

S6-2

When you complete this chapter, you should be able to : Identify or Define:

Natural and assignable causes of variation Central limit theorem Attribute and variable inspection Process control charts and R charts LCL and UCL p-charts and C-charts Cpk Acceptance sampling OC curve AQL and LTPD AOQ Producer’s and consumer’s risk

Learning ObjectivesLearning Objectives

x

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Learning Objectives - continuedLearning Objectives - continued

When you complete this chapter, you should be able to :

Describe or explain: The role of statistical quality control

S6-4

Operations Operations ManagementManagement

Quality and Statistical Process Quality and Statistical Process ControlControl

S6-5

In Class ExerciseIn Class ExerciseYou are the president of Hydro Message Inc. (HMI). HMI produces devises which deliver water pulsing message shower heads and hand held devices for the bath. For the following example assume 100,000 units will be produced over the life of the product.

Alternative 1: Is a simple-design hand-held. It has a 90% chance of yielding 95 good hand-helds out of every 100 manufactured. There is a 10% chance that the yield will be only 70 out of every 100. Design cost is $400,000 and manufacturing cost is $25 per unit. Expected revenue is $45/unit.

Alternative 2: Is a more complicated design. It has only a 60% chance of yielding 95 good hand-helds out of every 100 manufactured. There is a 40% chance that the yield will be only 40 out of every 100. Design cost is $700,000 and manufacturing cost is $40 per unit. Anticipated revenue is $85/unit.

S6-6

SolutionSolution

Simple Design

Complex Design

90%

10%

60%

40%

Sales = Design = Manu Cost = Exp. Value =

Do nothing = $0

S6-7

SolutionSolution

Simple Design

Complex Design

90%

10%

60%

40%

Sales = .95*$45*100,000 = $4,275,000Design = $400,000Manu Cost = 100,000 *25 = $2,500,000Exp. Value = $1,375,000

S6-8

SolutionSolution

Simple Design

Complex Design

90%

10%

60%

40%


Sales = .70*$45*100,000 = $3,150,000Design = $400,000Manu Cost = 100,000 *25 = $2,500,000Exp. Value = $250,000


Sales = .40*$85*100,000 = $3,400,000Design = $700,000Manu Cost = 100,000 *40 = $4,000,000Exp. Value = $-1,300,000

S6-9

SolutionSolutionSimple DesignEMV = (.9*1,375,000) + (.1*250,000)= $1,262,500

Complex DesignEMV = $1,505,000

90%

10%

60%

40%


Sales = .70*$45*100,000 = $3,150,000Design = $400,000Manu Cost = 100,000 *25 = $2,500,000Exp. Value = $250,000


Sales = .40*$85*100,000 = $3,400,000Design = $700,000Manu Cost = 100,000 *40 = $4,000,000Exp. Value = $-1,300,000

Complex - Simple Delta = $242,500

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Part IIPart II

Alternative 1: The simple design has virtually no chance of shocking a customer in the bath (no change required to EMV of simple design).

Alternative 2: Has a .000005/unit chance of shocking a customer in the bath. If a person is shocked in the bathtub, it is assumed they will die.

Legal has stated that each shock incident has a 20% chance of a $2,000,000 award and a 80% chance of being dismissed in a court of law due to adequate warning labels on the product.

What is the new EMV for the complex design?

S6-11

Complex Design EMV = .6 (3,195,000) + .4*(-1,380,000) = $1,365,000

Complex is still $102,500 better than the simple design. But is it worth taking the risk? What about the negative value of bad press? What about the ethical issues? Is one life worth more or less than $102,500?

60%

40%

Sales = .95*$85*100,000 = $8,075,000Design = $700,000Manu Cost = 100,000 *40 = $4,000,000Shock Cost = .95*100,000*.000005*.20*2,000,000 = $190,000Exp. Value = $3,195,000

Sales = .40*$85*100,000 = $3,400,000Design = $700,000Manu Cost = 100,000 *40 = $4,000,000Shock Cost = .40*100,000*.000005*.20*2,000,000 = $80,000Exp. Value = $-1,380,000

New information for scenario IINew information for scenario II

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Dimensions of Operations Strategy& Competitive Advantage

•Time

•Price

•Quality

•Variety

Competitive Advantage & Profit

Means to best satisfy the customer

P. 133 of text

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Ways in Which Quality Can Ways in Which Quality Can Improve ProductivityImprove Productivity

Sales Gains Improved response Higher Revenues (Prices) Improved reputation

Reduced Costs Increased productivity Lower rework and scrap costs Lower warranty costs

Increased Profits

Improved Quality

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Flow of Activities Necessary to Flow of Activities Necessary to Achieve Total Quality ManagementAchieve Total Quality Management

Organizational Practices

Quality Principles

Employee Fulfillment

Customer Satisfaction

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Traditional Traditional Quality Process (Manufacturing)Quality Process (Manufacturing)

Specifies

Need

Customer

Interprets

Need

Marketing

Designs

Product

Defines

Quality

Engineering

Produces

Product

Plans

Quality

Monitors

Quality

Operations

Quality is

Quality is

customer driven!

customer driven!

S6-16

TQMTQM

Encompasses entire organization, from supplier to customer

Stresses a commitment by management to have a continuing company-wide drive

toward excellence in all aspects of products and services that are important to the

customer.

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Organizational Practices

Quality Principles

Employee Fulfillment

Attitudes (e.g., Commitment)

How to Do

What to Do

EffectiveBusiness

EffectiveBusiness

CustomerSatisfaction

CustomerSatisfaction

AchievingAchieving Total Quality Management Total Quality Management

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Deming’s Fourteen PointsDeming’s Fourteen Points

Create consistency of purpose Lead to promote change Build quality into the products Build long term relationships Continuously improve product, quality, and

service Start training Emphasize leadership

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Deming’s Points - continuedDeming’s Points - continued Drive out fear Break down barriers between departments Stop haranguing workers Support, help, improve Remove barriers to pride in work Institute a vigorous program of education and

self-improvement Put everybody in the company to work on the

transformation

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BenchmarkingBenchmarking

Selecting best practices to use as a standard for performance

Determine what to benchmark Form a benchmark team Identify benchmarking partners Collect and analyze benchmarking information Take action to match or exceed the benchmark

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Resolving Customer ComplaintsResolving Customer ComplaintsBest PracticesBest Practices

Make it easy for clients to complain Respond quickly to complaints Resolve complaints on the first contact Recruit the best for customer service jobs

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Just-in-Time (JIT)Just-in-Time (JIT)

Relationship to quality: JIT cuts cost of quality JIT improves quality Better quality means less inventory and better,

easier-to-employ JIT system

S6-23

Just-In-Time (JIT) ExampleJust-In-Time (JIT) Example

ScrapScrap

Work in process inventory levelWork in process inventory level(hides problems)(hides problems)

Unreliable Unreliable VendorsVendors

Capacity Capacity ImbalancesImbalances

S6-24

Just-In-Time (JIT) ExampleJust-In-Time (JIT) Example

ScrapScrap

Reducing inventory revealsReducing inventory revealsproblems so they can be solved.problems so they can be solved.

Unreliable Unreliable VendorsVendors

Capacity Capacity ImbalancesImbalances

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Quality Loss Function; Distribution of Quality Loss Function; Distribution of Products ProducedProducts Produced

Low loss

High loss

Frequency

Lower Target UpperSpecification

Loss (to producing organization, customer, and society)

Quality Loss Function (a)Unacceptable

Poor

Fair

Good

Best

Target-oriented quality yields more product in the “best” category

Target-oriented quality brings products toward the target value

Conformance-oriented quality keeps product within three standard deviations

Distribution of specifications for product produced (b)

S6-26

Shows social cost ($) of deviation from target value

Assumptions Most measurable quality characteristics (e.g., length,

weight) have a target value Deviations from target value are undesirable

Equation: L = D2C L = Loss ($); D = Deviation; C = Cost

Quality Loss FunctionQuality Loss Function

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Loss

XTarget USLLSL

Loss

XTarget USLLSL

Loss = (Actual X - Target)2 • (Cost of Deviation)

Lower (upper) specification limit

Measurement

Greater deviation, more people are dissatisfied, higher cost

Quality Loss Function GraphQuality Loss Function Graph

S6-28

The specifications for the diameter of a gear are 25.00 ± 0.25 mm. If the diameter is out of specification, the gear must be scrapped at a cost of $4.00. What is the loss function?

© 1984-1994 T/Maker Co.

Quality Loss Function ExampleQuality Loss Function Example

S6-29

L = D2C = (X - Target)2C L = Loss ($); D = Deviation; C = Cost

4.00 = (25.25 - 25.00)2C Item scrapped if greater than 25.25

(USL = 25.00 + 0.25) with a cost of $4.00

C = 4.00 / (25.25 - 25.00)2 = 64 L = D2 • 64 = (X - 25.00)264

Enter various X values to obtain L & plot

Quality Loss Function SolutionQuality Loss Function Solution

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Quality Loss Function

0

100

200

300

400

500

0 10 20 30 40 50

Specification Delta Squared

Lo

ss

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Pareto Analysis of Wine Glass Pareto Analysis of Wine Glass Defects (Total Defects = 75)Defects (Total Defects = 75)

54

125 4 2

72%

88%93% 97% 100%

0

10

20

30

40

50

60

70

Scratches Porosity Nicks Contamination Misc.

Causes, by percent total defects

Freq

uenc

y (N

umbe

r)

0%

20%

40%

60%

80%

100%

Cum

ulat

ive

Perc

ent

72% 16% 5% 4% 3%

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Measures performance of a process Uses mathematics (i.e., statistics) Involves collecting, organizing, & interpreting

data Objective: provide statistical when assignable

causes of variation are present Used to

Control the process as products are produced Inspect samples of finished products

Statistical Quality Control (SPC)Statistical Quality Control (SPC)

S6-33

Figure S6.1Figure S6.1

S6-34

StatisticalQuality Control

ProcessControl

AcceptanceSampling

VariablesCharts

AttributesCharts

Variables Attributes

Types ofTypes of Statistical Quality Control Statistical Quality Control

S6-35

Characteristics for which you focus on defects

Classify products as either ‘good’ or ‘bad’, or count # defects e.g., radio works or not

Categorical or discrete random variables

AttributesAttributesVariablesVariables

Quality CharacteristicsQuality Characteristics

Characteristics that you measure, e.g., weight, length

May be in whole or in fractional numbers

Continuous random variables

S6-36

Statistical technique used to ensure process is making product to standard

All process are subject to variability Natural causes: Random variations Assignable causes: Correctable problems

Machine wear, unskilled workers, poor material

Objective: Identify assignable causes Uses process control charts

Statistical Process Control (SPC)Statistical Process Control (SPC)

S6-37

Process Control:Process Control: Three Types of Process Outputs Three Types of Process Outputs

Frequency

Lower control limit

SizeWeight, length, speed, etc.

Upper control limit

(b) In statistical control, but not capable of producing within control limits. A process in control (only natural causes of variation are present) but not capable of producing within the specified control limits; and

(c) Out of control. A process out of control having assignable causes of variation.

(a) In statistical control and capable of producing within control limits. A process with only natural causes of variation and capable of producing within the specified control limits.

S6-38

The Relationship Between Population The Relationship Between Population and Sampling Distributionsand Sampling Distributions

Uniform

Normal

BetaDistribution of sample means

x means sample of Mean

n

xx

Standard deviation of

the sample means

(mean)

x2 withinfall x all of 95.5%

x3 withinfall x all of 99.7%

x3 x2 x x x1 x2 x3

Three population distributions

S6-39

Sampling Distribution of Means, Sampling Distribution of Means, and Process Distribution and Process Distribution

Sampling distribution of the means

Process distribution of the sample

)mean(

mx

S6-40

Process Control ChartsProcess Control Charts

Plot of Sample Data Over Time

0

20

40

60

80

1 5 9 13 17 21

Time

Sam

ple

Val

ue

SampleValueUCL

Average

LCL

S6-41

Show changes in data pattern e.g., trends

Make corrections before process is out of control

Show causes of changes in data Assignable causes

Data outside control limits or trend in data

Natural causes Random variations around average

Control Chart PurposesControl Chart Purposes

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X

As sample size gets large enough,

sampling distribution becomes almost normal regardless of population distribution.

Central Limit Theorem

XX

Theoretical BasisTheoretical Basis of Control Charts of Control Charts

S6-43

X

Mean

Central Limit Theorem

x

x

n

xx

nX X

Standard deviation

X X

Theoretical BasisTheoretical Basis of Control Charts of Control Charts

S6-45

ControlCharts

RChart

VariablesCharts

AttributesCharts

XChart

PChart

CChart

Continuous Numerical Data

Categorical or Discrete Numerical Data

Control Chart TypesControl Chart Types

S6-46

Produce GoodProvide Service

Stop Process

Yes

No

Assign.Causes?Take Sample

Inspect Sample

Find Out WhyCreate

Control Chart

Start

Statistical Process Control StepsStatistical Process Control Steps

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Type of variables control chart Interval or ratio scaled numerical data

Shows sample means over time Monitors process average Example: Weigh samples of coffee & compute

means of samples; Plot

XX Chart Chart

S6-48

X Chart Control Limits

Sample Range at Time i

# Samples

Sample Mean at Time i

From Table S6.1

RAxxLCL

RAxxUCL

n

R R

i

n

1i

n

xi

n

ix

S6-49

Factors for Computing Control Factors for Computing Control Chart LimitsChart Limits

SampleSize, n

MeanFactor, A2

UpperRange, D4

LowerRange, D3

2 1.880 3.268 0

3 1.023 2.574 0

4 0.729 2.282 0

5 0.577 2.115 0

6 0.483 2.004 0

7 0.419 1.924 0.076

8 0.373 1.864 0.136

9 0.337 1.816 0.184

10 0.308 1.777 0.2230.184

S6-50

Type of variables control chart Interval or ratio scaled numerical data

Shows sample ranges over time Difference between smallest & largest values in

inspection sample

Monitors variability in process Example: Weigh samples of coffee & compute

ranges of samples; Plot

RR Chart Chart

S6-51

Sample Range at Time i

# Samples

From Table S6.1

RR Chart Chart Control LimitsControl Limits

n

R R

R D LCL

R D UCL

i

n

1i

3R

4R

S6-52

Steps to Follow When Using Steps to Follow When Using Control ChartsControl Charts

Collect 20 to 25 samples of n=4 or n=5 from a stable process and compute the mean.

Compute the overall means, set approximate control limits,and calculate the preliminary upper and lower control limits.If the process is not currently stable, use the desired mean instead of the overall mean to calculate limits.

Graph the sample means and ranges on their respective control charts and determine whether they fall outside the acceptable limits.

S6-53

Steps to Follow When Using Steps to Follow When Using Control Charts - continuedControl Charts - continued

Investigate points or patterns that indicate the process is out of control. Assign causes for the variations.

Collect additional samples and revalidate the control limits.

S6-54


S6-55

Type of attributes control chart Nominally scaled categorical data

e.g., good-bad

Shows % of nonconforming items Example: Count # defective chairs & divide by

total chairs inspected; Plot Chair is either defective or not defective

pp Chart Chart

S6-56

pp Chart Chart Control LimitsControl Limits

# Defective Items in Sample i

Size of sample i

z = 2 for 95.5% limits; z = 3 for 99.7% limits

i

k

1i

i

k

1ii

k

i

p

p

n

xp and

k

nn

n

)p(pzpLCL

n

)p(pzpUCL

S6-57

Type of attributes control chart Discrete quantitative data

Shows number of nonconformities (defects) in a unit Unit may be chair, steel sheet, car etc. Size of unit must be constant

Example: Count # defects (scratches, chips etc.) in each chair of a sample of 100 chairs; Plot

cc Chart Chart

S6-58

cc Chart Chart Control LimitsControl Limits

# Defects in Unit i

# Units Sampled

Use 3 for 99.7% limits

k

c c

i

k

1i

ccLCL

ccUCL

c

c

S6-59


S6-60

Process Capability CProcess Capability Cpkpk

population process theof deviation standard

mean process x where

Limition SpecificatLower x

or , x Limit ion SpecificatUpper

of minimum

pkC

Assumes that the process is:•under control•normally distributed

S6-61

Meanings of CMeanings of Cpkpk Measures Measures

Cpk = negative number

Cpk = zero

Cpk = between 0 and 1

Cpk = 1

Cpk > 1

S6-62

Form of quality testing used for incoming materials or finished goods e.g., purchased material & components

Procedure Take one or more samples at random from a lot

(shipment) of items Inspect each of the items in the sample Decide whether to reject the whole lot based on the

inspection results

What Is What Is Acceptance Sampling?Acceptance Sampling?

S6-63

Set of procedures for inspecting incoming materials or finished goods

Identifies Type of sample Sample size (n) Criteria (c) used to reject or accept a lot

Producer (supplier) & consumer (buyer) must negotiate

What Is an What Is an Acceptance Plan?Acceptance Plan?

S6-64

Shows how well a sampling plan discriminates between good & bad lots (shipments)

Shows the relationship between the probability of accepting a lot & its quality

Operating Characteristics CurveOperating Characteristics Curve

S6-65% Defective in Lot

P(Accept Whole Shipment)

100%

0%

Cut-Off1 2 3 4 5 6 7 8 9 100

Return whole shipment

Keep whole shipment

OC CurveOC Curve100% Inspection100% Inspection

S6-66

OC Curve with Less than 100% OC Curve with Less than 100% SamplingSampling


100%

0%

% Defective in LotCut-Off

1 2 3 4 5 6 7 8 9 100

Return whole shipment

Keep whole shipment

Probability is not 100%: Risk of keeping bad shipment or returning good one.

S6-67

Acceptable quality level (AQL) Quality level of a good lot Producer (supplier) does not want lots with fewer

defects than AQL rejected

Lot tolerance percent defective (LTPD) Quality level of a bad lot Consumer (buyer) does not want lots with more

defects than LTPD accepted

AQL & LTPDAQL & LTPD

S6-68

Producer's risk () Probability of rejecting a good lot Probability of rejecting a lot when fraction

defective is AQL

Consumer's risk (ß) Probability of accepting a bad lot Probability of accepting a lot when fraction

defective is LTPD

Producer’s & Consumer’s RiskProducer’s & Consumer’s Risk

S6-69

An Operating Characteristic (OC) An Operating Characteristic (OC) Curve Showing Risks Curve Showing Risks

= 0.05 producer’s risk for AQL

= 0.10

Consumer’s risk for LTPD

Probability of Acceptance

Percent Defective

Bad lotsIndifference zoneGood lots

LTPDAQL

0 1 2 3 4 5 6 7 8

10095

75

50

25

10

0

S6-70

OC Curves for Different Sampling OC Curves for Different Sampling PlansPlans

1 2 3 4 5 6 7 8 9 100

% Defective in Lot


100%

0%

LTPDAQL

n = 50, c = 1

n = 100, c = 2

S6-71

Negotiate between producer (supplier) and consumer (buyer)

Both parties attempt to minimize risk Affects sample size & cut-off criterion

Methods MIL-STD-105D Tables Dodge-Romig Tables Statistical Formulas

Developing a Sample PlanDeveloping a Sample Plan

S6-72

Statistical Process Control - Identify Statistical Process Control - Identify and Reduce Process Variabilityand Reduce Process Variability

Lower specification

limit

Upper specification

limit

(a) Acceptance sampling

(b) Statistical process control

(c) cpk >1

s6-1 outline statistical process control (spc) control charts for variables the central limit...

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