Quality at Source
Manufacturing Systems Analysis
Professor: Nour El Kadri
e-mail: nelkadri@ site.uottawa.ca
What is Quality?

Quality: The ability of a product or service
to consistently meet or exceed customer
expectations.
– Not something tacked on, but an integral part
of the product/service.
– Comes from the fundamental process, not
from material or from inspection
What does a customer perceive
as quality
– Performance
– Aesthetics
– Features
– Conformance
– Reliability
– Durability
– Perceived quality (eg: reputation)
– Serviceability
Expectations
– Customer’s perceptions and expectations shift
and evolve:
 With product life cycle:
 Features & functionality are critical in a leadingedge hi-tech product
 Reliability, durability, serviceability are critical in a
mature product
 With an evolving industry, market or technology
(cf: “Quality & the Ford Model T”)
Why is Quality Important?

Quality is:
– A critical basis of competition (ie: A critical
differentiator)
– Critical to SC effectiveness (Partners demand
objective evidence of quality measures,
programs)
– A measure of efficiency & cost saving
(“Quality does not cost anything”)
– NB: Quality as one key identifier of a HighPerformance company
Cost of Quality
– Prevention Costs: All training, planning, customer
assessment, process control, and quality
improvement costs required to prevent defects from
occurring
– Appraisal Costs: Costs of activities designed to
ensure quality or uncover defects
– Failure Costs: Costs incurred by defective
parts/products or faulty services.
 Internal Failure Costs: Costs incurred to fix problems that
are detected before the product/service is delivered to
the customer.
 External Failure Costs: Costs incurred to fix problems that
are detected after the product/service is delivered to the
customer.
Consequences of Poor Quality
– Liability
– Loss of productivity
– Loss of business:
 Dissatisfied customers will switch
 You usually won’t know why (<5% of dissatisfied
customers complain)
 He will cost you add’l business (Average
dissatisfied customer will complain to 19 others)
The Evolution of Quality
Management
Craft production: Strict craftsman concern
for quality
 Industrial revolution: Specialization,
division of labour. Little control of or
identification with overall product quality

SPC (Statistical Process Control)
Sample mean
value
0.13%
Upper control limit
99.74%
Normal
tolerance
of
process
Process mean
Lower control limit
0.13%
0
1
2
3
4
5
6
Sample number
7
8
Quality Control Charts
Definitions




Variables Measurements on a continuous scale, such as
length or weight
Attributes Integer counts of quality characteristics, such
as # of good or bad
Defect
A single non-conforming quality characteristic,
such as a blemish
Defective A physical unit that contains one or more
defects
Types of Control Charts
Data monitored




Mean, range of sample variables
Individual variables
% of defective units in a sample
Number of defects per unit
Chart name
MR-CHART
I-CHART
P-CHART
C/U-CHART
Sample size
2 to 5 units
1 unit
at least 100 units
1 or more units
Control Factors
n
2
3
4
5

A
2.121
1.732
1.500
1.342
A2
1.880
1.023
0.729
0.577
D3
0
0
0
0
D4
3.267
2.574
2.282
2.114
d2
1.128
1.693
2.059
2.316
d3
0.853
0.888
0.880
0.864
Control factors are used to convert the mean of sample ranges
( R ) to:
(1) standard deviation estimates for individual observations,
and
(2) standard error estimates for means and ranges of samples
For example, an estimate of the population standard deviation
of individual observations (σx) is:
σx = R / d2
Control Factors (cont.)

Note that control factors depend on the sample size n.

Relationships amongst control factors:
A2 = 3 / (d2 x n1/2)
D4 = 1 + 3 x d3/d2
D3 = 1 – 3 x d3/d2, unless the result is negative, then D3 = 0
A = 3 / n1/2
D2 = d2 + 3d3
D1 = d2 – 3d3, unless the result is negative, then D1 = 0
Mean-Range control chart
MR-CHART
1. Compute the mean of sample means ( X ).
2. Compute the mean of sample ranges ( R ).
3. Set 3-std.-dev. control limits for the sample means:
UCL = X + A2R
LCL = X – A2R
4. Set 3-std.-dev. control limits for the sample ranges:
UCL = D4R
LCL = D3R
Control chart for percentage defective
in a sample — P-CHART
1. Compute the mean percentage defective ( P ) for all samples:
P = Total nbr. of units defective / Total nbr. of units sampled
2. Compute an individual standard error (SP ) for each sample:
SP = [( P (1-P ))/n]1/2
Note: n is the sample size, not the total units sampled.
If n is constant, each sample has the same standard error.
3. Set 3-std.-dev. control limits:
UCL = P + 3SP
LCL = P – 3SP
Control chart for individual
observations — I-CHART
1. Compute the mean observation value ( X )
X = Sum of observation values / N
where N is the number of observations
2. Compute moving range absolute values, starting at obs. nbr. 2:
Moving range for obs. 2 = obs. 2 – obs. 1
Moving range for obs. 3 = obs. 3 – obs. 2
…
Moving range for obs. N = obs. N – obs. N – 1
3. Compute the mean of the moving ranges ( R ):
R = Sum of the moving ranges / N – 1
Control chart for individual
observations — I-CHART (cont.)
4. Estimate the population standard deviation (σX):
σX = R / d2
Note: Sample size is always 2, so d2 = 1.128.
5. Set 3-std.-dev. control limits:
UCL = X + 3σX
LCL = X – 3σX
Control chart for number of defects
per unit — C/U-CHART
1. Compute the mean nbr. of defects per unit ( C ) for all samples:
C = Total nbr. of defects observed / Total nbr. of units sampled
2. Compute an individual standard error for each sample:
SC = ( C / n)1/2
Note: n is the sample size, not the total units sampled.
If n is constant, each sample has the same standard error.
3. Set 3-std.-dev. control limits:
UCL = C + 3SC
LCL = C – 3SC
Notes:
● If the sample size is constant, the chart is a C-CHART.
● If the sample size varies, the chart is a U-CHART.
● Computations are the same in either case.
SPC & Cost of Quality
– Deming (Promoted SPC in Japan):
 The cause of poor quality is the system, not the
employee
 Mgmt is responsible to correct poor quality
– Juran (“Cost of Quality”: Emphasized need for
accurate and complete identification of the
costs of quality) :
 Quality means fitness for use
 Quality begins in knowing what customers want,
planning processes which are capable of producing
the required level of quality
From Quality to Quality Assurance
Changing emphasis from “Quality” to “Quality
Assurance”(Prevent defects rather than finding
them after they occur)
New techniques for Quality Improvement (eg:
TQM, Six Sigma):
 New quality programs (Provide objective
measures of quality for use of customers, SC
partners, etc.)

– Baldridge Award
– ISO 9000/14000 Certification
– Industry-specific programs (eg: TL9000(Telecom))
Correlation:
Strong positive
Positive
x Negative
* Strong negative
Competitive
evaluation
x = Us
A = Comp. A
B = Comp. B
(5 is best)
1 2 3 4 5
x
AB
x AB
x AB
A xB
x A
B
x
x
x
Reduce energy
to 7.5 ft/lb
Acoustic trans.,
window
6
Energy needed
to open door
6
9
2
3
B xA
BA
x
7
5
3
3
2
Importance weighting
10
Target values
Technical evaluation
(5 is best)
Check force on
level ground
Easy to close
Stays open on a hill
Easy to open
Doesn’t leak in rain
No road noise
Reduce force
to 9 lb.
Customer
requirements
Door seal
resistance
Engineering
characteristics
x
Maintain
current level
x
5
4
3
2
1
B
A
x
BA
x
B
A
x
B
x
A
Relationships:
Strong = 9
Medium = 3
Small = 1
Source: Based on John R. Hauser
and Don Clausing, “The House of
Quality,” Harvard Business Review,
May-June 1988.
Taguchi analysis
Loss function
L(x) = k(x-T)2
where
x = any individual value of the quality characteristic
T = target quality value
k = constant = L(x) / (x-T)2
Average or expected loss, variance known
E[L(x)] = k(σ2 + D2)
where
σ2 = Variance of quality characteristic
D2 = ( x – T)2
Note: x is the mean quality characteristic. D2 is zero if the mean
equals the target.
Taguchi analysis (cont.)
Average or expected loss, variance unkown
E[L(x)] = k[Σ ( x – T)2 / n]
When smaller is better (e.g., percent of impurities)
L(x) = kx2
When larger is better (e.g., product life)
L(x) = k (1/x2)
TQM

Total Quality Management: A philosophy that
involves everyone in an organization in a
continual effort to improve quality and achieve
customer satisfaction.
– The TQM Approach:
 Find out what the customer wants
 Design a product or service that meets or exceeds
customer wants
 Design processes that facilitates doing the job right the
first time
 Keep track of results
 Extend quality initiatives to include suppliers &
distributors.
Elements of TQM
 Continual improvement
 Competitive benchmarking
 Employee empowerment (eg: Quality circles, etc.)
 Team approach
 Decisions based on facts
 Knowledge of tools
 Supplier quality
 Identify and use quality champion
 Develop quality at the source
 Include suppliers
Criticism of TQM
– Criticisms of TQM include:
 Blind pursuit of TQM programs
 Programs may not be linked to strategies
 Quality-related decisions may not be tied to
market performance
 Failure to carefully plan the program
Obstacles to Implementing TQM
 Poor inter-organizational communication
 View of quality as a “quick fix”
 Emphasis on short-term financial results
 Internal political and “turf” wars
 Lack of:
–
–
–
–
–
–
–
Company-wide definition of quality
Strategic plan for change
Customer focus
Real employee empowerment
Strong motivation
Time to devote to quality initiatives
Leadership
Six Sigma

Six Sigma (eg: Jack Welch @ GE):
– Statistically: Having no more than 3.4 defects
per million
– Conceptually: A program designed to reduce
defects
Six Sigma programs
 Improve quality, save time & cut costs
 Are employed in a wide variety of areas (Design,
Production, Service, Inventory , Management,
Delivery)
 Focus on management as well as on the technical
component
 Requires specific tools & techniques
 Require commitment & active participation by sr
management to:
 Provide strong leadership
 Define performance metrics
 Select projects likely to succeed
Six Sigma Programs
Select and train appropriate people
 The team includes top management & program
champions as well as master “black belts”, “Black
belts” & “Green belts”
 A methodical, five- step process: Define, Measure,
Analyze, Improve, Control (DMAIC)
Process Capability Analysis
1. Compute the mean of sample means ( X ).
2. Compute the mean of sample ranges ( R ).
3. Estimate the population standard deviation (σx):
σx = R / d2
4. Estimate the natural tolerance of the process:
Natural tolerance = 6σx
5. Determine the specification limits:
USL = Upper specification limit
LSL = Lower specification limit
Process capability analysis (cont.)
6. Compute capability indices:
Process capability potential
Cp = (USL – LSL) / 6σx
Upper capability index
CpU = (USL – X ) / 3σx
Lower capability index
CpL = ( X – LSL) / 3σx
Process capability index
Cpk = Minimum (CpU, CpL)
Multiplicative seasonality
The seasonal index is the expected ratio of actual data
to the average for the year.
Actual data / Index = Seasonally adjusted data
Seasonally adjusted data x Index = Actual data
Multiplicative seasonal adjustment
1.
Compute moving average based on length of seasonality (4
quarters or 12 months).
2.
Divide actual data by corresponding moving average.
3.
Average ratios to eliminate randomness.
4.
Compute normalization factor to adjust mean ratios so they
sum to 4 (quarterly data) or 12 (monthly data).
5.
Multiply mean ratios by normalization factor to get final
seasonal indexes.
6.
Deseasonalize data by dividing by the seasonal index.
7.
Forecast deseasonalized data.
8.
Seasonalize forecasts from step 7 to get final forecasts.
Additive seasonality
The seasonal index is the expected difference
between actual data and the average for the year.
Actual data - Index = Seasonally adjusted data
Seasonally adjusted data + Index = Actual data
Additive seasonal adjustment
1.
Compute moving average based on length of seasonality
(4 quarters or 12 months).
2.
Compute differences: Actual data - moving average.
3.
Average differences to eliminate randomness.
4.
Compute normalization factor to adjust mean differences so
they sum to zero.
5.
Compute final indexes: Mean difference – normalization
factor.
6.
Deseasonalize data: Actual data – seasonal index.
7.
Forecast deseasonalized data.
8.
Seasonalize forecasts from step 7 to get final forecasts.
How to start up a control chart system
1.
Identify quality characteristics.
2.
Choose a quality indicator.
3.
Choose the type of chart.
4.
Decide when to sample.
5.
Choose a sample size.
6.
Collect representative data.
7.
If data are seasonal, perform seasonal adjustment.
8.
Graph the data and adjust for outliers.
How to start up a control chart system
(cont.)
9. Compute control limits
10. Investigate and adjust special-cause variation.
11. Divide data into two samples and test stability of limits.
12. If data are variables, perform a process capability study:
a. Estimate the population standard deviation.
b. Estimate natural tolerance.
c. Compute process capability indices.
d. Check individual observations against specifications.
13. Return to step 1.
Quick reference to quality formulas

Control factors
n
2
3
4
5

A
2.121
1.732
1.500
1.342
A2
1.880
1.023
0.729
0.577
D3
0
0
0
0
D4
3.267
2.574
2.282
2.114
d2
1.128
1.693
2.059
2.316
d3
0.853
0.888
0.880
0.864
Process capability analysis
σx = R / d2
Cp = (USL – LSL) / 6σx
CpL = ( X – LSL) / 3σx
CpU = (USL – X ) / 3σx
Cpk = Minimum (CpU, CpL)
Quick reference to quality formulas
(cont.)

Means and ranges
UCL = X + A2R
LCL = X – A2R

Percentage defective in a sample
SP = [( P (1-P ))/n]1/2

UCL = P + 3SP
LCL = P – 3SP
Individual quality observations
σx = R / d2

UCL = D4R
LCL = D3R
UCL = X + 3σX
LCL = X – 3σX
Number of defects per unit
SC = ( C / n)1/2
UCL = C + 3SC
LCL = C – 3SC