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Quality Planning and Control

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Learning Objectives •  To understand concepts of Total Quality and Six Sigma:

–  Quality defined –  Quality control to Quality Management –  Cost of Quality –  Six Sigma Quality –  Methodology and Tools for Six Sigma Quality

•  To understand the concepts of Statistical Quality Control (SQC) : - –  Statistical Process Control (SPC)

•  Control Charts for Variables( x-Charts) and R-Charts) •  The Central Limit Theorem •  Natural and assignable causes of variation •  Process Capability •  Control Charts for Attributes (p-charts and C-charts)

–  Acceptance Sampling •  Producer’s and consumer’s risk •  Operating Characteristic (OC) Curves •  Average Outgoing Quality

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Meaning of Quality

§  Webster’s Dictionary §  degree of excellence of a thing

§  American Society for Quality §  totality of features and characteristics

that satisfy needs §  Consumer’s and producer’s

perspective

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Meaning of Quality: Consumer’s Perspective

§  Fitness for use §  how well product or

service does what it is supposed to

§  Quality of design §  designing quality

characteristics into a product or service

A Mercedes and a Ford are equally “fit for use,” but with different design dimensions

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Meaning of Quality: Producer’s Perspective

§  Quality of conformance § Making sure product or service is produced

according to design §  if new tires do not conform to specifications, y

wobble §  if a hotel room is not clean when a guest checks in,

hotel is not functioning according to specifications of its design

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Fitness for Consumer Use

Producer’s Perspective Consumer’s Perspective

Quality of Conformance

•  Conformance to specifications

•  Cost

Quality of Design

•  Quality characteristics •  Price

Marketing Production

Meaning of Quality

Meaning of Quality

Dimensions of quality

Dimension Physical product e.g. laser printer

Performance Pages per min, dpi

Features Sizing, scan, ink saving

Reliability/durability MTBF, life

Serviceability Dealer network/cost of maintenance

Aesthetics Case style, color, ergonomics

Perceived quality Ratings by customers

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Quality characteristics of goods and services

•  Functionality - how well the product or service does job for which it was intended

•  Appearance - aesthetic appeal, look, feel, sound and smell of the product or service

•  Reliability - consistency of product or services performance over time.

•  Durability - the total useful life of the product or service.

•  Recovery - the ease with which problems with the product or service can be rectified or resolved.

•  Contact - the nature of the person-to-person contacts that take place.

Quality Specifications

•  Design quality: Inherent value of the product in the marketplace

Dimensions include: Performance, Features, Reliability/Durability, Serviceability, Aesthetics, and Perceived Quality.

•  Conformance quality: Degree to which the product or service design specifications are met

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From “Quality Control” to “Quality Management”

1 Inspection –  Error detection of finished goods –  Rectification

2 Quality Control –  Statistical Methods applied to processes –  Quality standards –  Process improvement

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From “Quality Control” to “Quality Management” continued

3 Quality Assurance –  Quality Systems –  Quality Costing –  Quality Planning –  Problem solving

4 Quality Management –  Everyone involved; teamwork; staff empowerment –  Involves customers and suppliers –  Quality strategy

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Costs of Quality

External Failure Costs

Appraisal Costs

Prevention Costs

Internal Failure Costs

Costs of Quality

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Costs of Quality

•  Prevention Costs –  New product quality

planning –  Product improvement –  Process improvement –  Staff training and

development

•  Appraisal Costs –  Incoming materials

inspection –  Monitoring production

for quality issues –  Customer surveys –  Quality laboratories –  Finished goods

inspection

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Costs of Quality continued

•  Internal Failure Costs –  Scrap –  Reworking / correcting –  Downgrading –  Retest –  Plant downtime –  Investigation /

troubleshooting

•  External Failure Costs –  Warranty / guarantees –  Returned goods –  Handling complaints –  Allowances / litigation –  Loss of goodwill

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Cost of Quality Model

Quality Effort

Cos

ts

Prevention + Appraisal costs

Internal + External Failure Costs

Total Cost

Make P+A more effective

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Six Sigma Quality

•  A philosophy and set of methods companies use to eliminate defects in their products and processes

•  Seeks to reduce variation in the processes that lead to product defects

•  The name, “six sigma” refers to the variation that exists within plus or minus three standard deviations of the process outputs

•  3.4 defects per million

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Six Sigma Quality (Continued)

•  Six Sigma allows managers to readily describe process performance using a common metric: Defects Per Million Opportunities (DPMO)

DPMO =Number of defects

Number of opportunitiesfor error per unit

!

"

###

$

%

&&& x No. of units

x 1, 000, 000

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Six Sigma Quality (Continued) Example of DPMO calculation.

Suppose we observe 200 letters delivered to the wrong addresses in a small city during a single day when a total of 200,000 letters were delivered.

[ ]000,1== 1,000,000 x

200,000 x 1

200DPMO

So, for every one million letters delivered this city’s postal managers can expect to have 1,000 letters incorrectly sent to the wrong address.

Cost of Quality: What might that DPMO mean in terms of over-time employment to correct the errors?

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Six Sigma Quality: DMAIC Cycle

•  Define, Measure, Analyze, Improve, and Control (DMAIC)

•  Developed by General Electric as a means of focusing effort on quality using a methodological approach

•  Overall focus of the methodology is to understand and achieve what the customer wants

•  A 6-sigma program seeks to reduce the variation in the processes that lead to these defects

•  DMAIC consists of five steps….

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Six Sigma Quality: DMAIC Cycle (Continued)

1. Define (D)

2. Measure (M)

3. Analyze (A)

4. Improve (I)

5. Control (C)

Customers and their priorities

Process and its performance

Causes of defects

Remove causes of defects

Maintain quality

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Example to illustrate the process…

•  We are the maker of a cereal. Consumer reports has just published an article that shows that we frequently have less than 15 ounces of cereal in a box.

•  What should we do?

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Step 1 - Define •  What is the critical-to-quality

characteristic? •  The CTQ (critical-to-quality)

characteristic in this case is the weight of the cereal in the box.

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2 - Measure

•  How would we measure to evaluate the extent of the problem?

•  What are acceptable limits on this measure?

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2 – Measure (continued)

•  Let’s assume that the government says that we must be within ± 5 percent of the weight advertised on the box.

•  Upper Tolerance Limit = 16 + .05(16) = 16.8 ounces

•  Lower Tolerance Limit = 16 – .05(16) = 15.2 ounces

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2. Measure (continued)

•  We go out and buy 1,000 boxes of cereal and find that they weigh an average of 15.875 ounces with a standard deviation of .529 ounces.

•  What percentage of boxes are outside the tolerance limits?

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Upper Tolerance = 16.8

Lower Tolerance = 15.2

Process Mean = 15.875 Std. Dev. = .529

What percentage of boxes are defective (i.e. less than 15.2 oz)? Z = (x – Mean)/Std. Dev. = (15.2 – 15.875)/.529 = -1.276 NORMSDIST(Z) = NORMSDIST(-1.276) = .100978 Approximately, 10 percent of the boxes have less than 15.2 Ounces of cereal in them!

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Step 3 - Analyze - How can we improve the capability of our cereal box filling process?

– Decrease Variation – Center Process –  Increase Specifications

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Step 4 – Improve – How good is good enough? Motorola’s “Six Sigma”

– 6σ minimum from process center to nearest spec

1 23 1 02 3

12σ

6σ

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Motorola’s “Six Sigma” •  Implies 2 ppB “bad” with no process shift •  With 1.5σ shift in either direction from

center (process will move), implies 3.4 ppm “bad”.

1 23 1 02 3

12σ

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Step 5 – Control

•  Statistical Process Control (SPC) – Use data from the actual process – Estimate distributions – Look at capability - is good quality

possible – Statistically monitor the process

over time

Analytical Tools for Six Sigma and Continuous

Improvement: Flow Chart No, Continue…

Material Received

from Supplier

Inspect Material for

Defects Defects found?

Return to Supplier for Credit

Yes

Can be used to find quality problems

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Analytical Tools for Six Sigma and Continuous Improvement: Run Chart

Can be used to identify when equipment or processes are not behaving according to specifications

0.44 0.46 0.48 0.5

0.52 0.54 0.56 0.58

1 2 3 4 5 6 7 8 9 10 11 12 Time (Hours)

Dia

met

er

Analytical Tools for Six Sigma and Continuous Improvement: Pareto Analysis

Can be used to find when 80% of the problems may be attributed to 20% of the causes

Assy. Instruct.

Freq

uenc

y

Design Purch. Training

80%

Analytical Tools for Six Sigma and Continuous Improvement: Checksheet

Billing Errors

Wrong Account

Wrong Amount A/R Errors

Wrong Account

Wrong Amount

Monday

Can be used to keep track of defects or used to make sure people collect data in a correct manner

Analytical Tools for Six Sigma and Continuous Improvement: Histogram

Num

ber o

f Lot

s

Data Ranges Defects in lot

0 1 2 3 4

Can be used to identify the frequency of quality defect occurrence and display quality performance

Analytical Tools for Six Sigma and Continuous Improvement: Cause & Effect Diagram

Effect

Man Machine

Material Method

Environment

Possible causes: The results or effect

Can be used to systematically track backwards to find a possible cause of a quality problem (or effect)

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Analytical Tools for Six Sigma and Continuous Improvement: Control Charts

Can be used to monitor ongoing production process quality and quality conformance to stated standards of quality

970

980

990

1000

1010

1020

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

LCL

UCL

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Statistical Quality Control (SQC)

The application of statistical techniques to control quality. Often the term statistical process control is use interchangeably with statistical quality control, although statistical quality control includes acceptance sampling as well as statistical process control

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Statistical Quality Control

Process Control

Acceptance Sampling

Variables Charts

Attributes Charts Variables Attributes

Routes in SQC

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•  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

Attributes Variables

Quality Characteristics

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

•  May be in whole or in fractional numbers

•  Continuous random variables

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•  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)

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Process Control: Three Types of Process Outputs

Frequency

Lower control limit

Size Weight, 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.

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X

As sample size gets large enough,

sampling distribution becomes almost normal regardless of population distribution.

Central Limit Theorem

X

Theoretical Basis of Control Charts

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X

Mean

Central Limit Theorem

σσ

xxn

=µ=X

Standard deviation

X = µ

Theoretical Basis of Control Charts

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The Relationship Between Population and Sampling Distributions

Uniform

Normal

Beta Distribution of sample means

x means sample of Mean =

nx

xσ

=σ=Standard deviation of the sample means

(mean)

x2 withinfall x all of 95.5% σ±

x3 withinfall x all of 99.7% σ±

x3 x2 x x x1 x2 x3 σ+σ+σ1+σ−σ−σ−

Three population distributions

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Sampling Distribution of Means and Process Distribution

Sampling distribution of the means

Process distribution of the sample

)mean(mx =

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Process Control Charts Plot of Sample Data Over Time

010203040506070

1 5 9 13 17 21

Time

Sam

ple V

alue Sample

ValueUCL

Average

LCL

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•  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 Purposes

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Theoretical Basis of Control Charts

Properties of normal distribution

x2 withinfall x lal of 95.5%

σ± x3 withinfall x lal of 99.7%

σ±

x

µ=x

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Control Charts

R Chart

Variables Charts

Attributes Charts

X Chart

P Chart

C Chart

Continuous Numerical Data

Categorical or Discrete Numerical Data

Control Chart Types

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Produce Good Provide Service

Stop Process

Yes

No

Assign. Causes? Take Sample

Inspect Sample

Find Out Why Create Control Chart

Start

Statistical 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

X Chart

•  Std dev of sample means can be reasonably estimated with large samples

•  When data (proc std dev) is not available or sample size is small, a well-established with R

•  Random variable W=R/σ W: relative range •  Its distribution depends on ‘n’, and mean denoted

by •  Estimator of sample standard dev

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X Chart Control Limits

s = Rd2 n

d2

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X Chart Control Limits

Sample Range at Time i

# Samples

Sample Mean at Time j

Mean Factor that increases when sample size is large (Refer to table)

UCLx=x+A2R

LCLx=x−A2R

R = ∑ i=1

nRi

nx =

∑i=1

nxi

n

Conversion of D2 to A2

•  Note: A_subscript_2 is computed as 3/{d2*sqrt(n)} for plus/minus 3 sigma

•  Thus, from tables for D2 (being 1.128 for n=2), A2 becomes 1. 880

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Factors for Computing Control Chart Limits

Sample Size, n

Mean Factor, A2

Upper Range, D4

Lower Range, D3

D2

2 1.880 3.268 0 1.128 3 1.023 2.574 0 1.693 4 0.729 2.282 0 2.059 5 0.577 2.115 0 2.326 6 0.483 2.004 0 2.534 7 0.419 1.924 0.076 2.704 8 0.373 1.864 0.136 2.847 9 0.337 1.816 0.184 2.970

10 0.308 1.777 0.223 3.078 0.184

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•  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

R Chart

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Sample Range at Time i

# Samples

Range Factor (Refer to table)

R Chart Control Limits

n

R R

R D LCL

R D UCL

in

1i

3R

4R

=∑

=

=

=

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Example Plot a Mean chart and an R chart for the following tread wear data. Comment the quality level and what action should be taken.

Sample Tread Wear 1 31 38 22 2 26 36 41 3 28 33 15 4 17 27 29 5 20 38 44 6 55 20 43 7 40 29 37 8 43 26 14 9 15 28 35 10 11 15 21

Solution

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Steps to Follow When Using Control Charts

•  Collect 20 to 25 samples of n=4 or n=5 each 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.

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Steps to Follow When Using Control 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.

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Which Charts to use?

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Process Capability

The ability of a process to produce parts that conform to (engineering) specifications. Process Capability relates to the inherent variability of a process that is in a state of statistical control

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Process Capability Index Cpk

population process theof deviation standard mean process x where

Limition SpecificatLower x

or , x Limit ion SpecificatUpper of minimum

=

=

⎥⎦

⎤−

⎢⎣

⎡ −=

σ

σ3

σ3pkC

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

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Meanings of Cpk Measures

Cpk = negative number

Cpk = zero

Cpk = between 0 and 1

Cpk = 1

Cpk > 1