Transcript Chapter 9A - Management

Chapter 9A
Process Capability and
SPC
McGraw-Hill/Irwin
©2011 The McGraw-Hill Companies, All Rights Reserved
Learning Objectives
 Explain what statistical quality control
is.
 Calculate the capability of a process.
 Understand how processes are
monitored with control charts.
 Recognize acceptance sampling
concepts.
9A-2
Types of Situations where
SPC can be Applied
 How many paint defects are there in the
finish of a car?
 How long does it take to execute
market orders?
 How well are we able to maintain the
dimensional tolerance on our ball
bearing assembly?
 How long do customers wait to be
served from our drive-through window?
LO 1
9A-3
What Is Quality?
 How do you define quality?



Durability, reliability, long warrantee
Fitness for use, degree of conformance
Maintainability
 Measures of quality



Grade—measurable characteristics, finish
Consistency—good or bad, predictability
Conformance—degree product meets
specifications

Consistency versus conformance
9A-4
Basic Forms of Variation
 Assignable variation: caused by
factors that can be clearly identified
and possibly managed

Example: a poorly trained employee that
creates variation in finished product output
 Common variation: variation that is
inherent in the production process

Example: a molding process that always
leaves “burrs” or flaws on a molded item
LO 1
9A-5
Variations Around Us
 When variation is reduced, quality is
improved
 However, it is impossible to have zero
variation


Engineers assign acceptable limits for
variation
The limits are know as the upper and lower
specification limits

Also known as upper and lower tolerance limits
LO 1
9A-6
Taguchi’s View of Variation
 Traditional view is that quality within the range is good
and that the cost of quality outside this range is constant
 Taguchi views costs as increasing as variability
increases, so seek to achieve zero defects and that will
truly minimize quality costs




Society loses (pays) for poor quality
Design products/processes impervious to variations
Use experimental/robust design
Shoot for target not conformance to specifications
LO 1
9A-7
Process Capability
 Taguchi argues that tolerance is not a
yes/no decision, but a continuous
function
 Other experts argue that the process
should be so good the probability of
generating a defect should be very low
LO 2
9A-8
Process Capability
 Process (control) limits




Calculated from data gathered from the process
It is natural tolerance limits
Defined by ±3σ (standard deviation)
Used to determine if process is in statistical
control
 Tolerance (specification) limits


Often determined externally, e.g., by customer
Process may be in control but not within
specification
 How do the limits relate to one another?
9A-9
Process Capability
LO 2
9A-10
Process Capability
 USL  LSL 
Cp  

6


 Case 1: Cp > 1




USL-LSL > 6 sigma
Process quality higher than customer’s
Situation desired
Defacto standard is 1.33+
LSL
USL
LNTL
UNTL

6
9A-11
 USL  LSL 
Cp  

6



Process Capability
 Case 2: Cp = 1



USL-LSL = 6 sigma
Approximately 0.27% defectives will be
made
Process is unstable
LSL
LNTL
USL
UNTL

6
9A-12
Process Capability
 USL  LSL 
Cp  

6


 Case 3: Cp < 1




USL-LSL < 6 sigma
Situation undesirable
Process is yield sensitive
Could produce large number of defectives
LNTL
UNTL
USL
LSL

6
9A-13
Process
Capability Index, C pk
 Most widely used capability measure
 Measures design versus specification
relative to the nominal value
 Based on worst case situation
 Defacto value is 1 and processes with
this score is capable
 Scores > 1 indicates 6-sigma
subsumed by the inspection limits
 Scores less than 1 will result in an
incapable process
9A-14
Capability Index (Cpk)
 Capability index (Cpk) shows how well
parts being produced fit into design
limit specifications
 X  LT L UT L- X 

C pk = min
or

3

3



 Also useful to calculate probabilities
Z LTL 
LTL  X

ZUTL 
UTL  X

LO 2
9A-15
Example: Capability
 Data

Designed for an average of 60 psi


Lower limit of 55 psi, upper limit of 65 psi
Sample mean of 61 psi, standard deviation
of 2 psi
 Calculate Cpk
C pk
LO 2
 x  LSL USL  x 
 min
,

3
 3

 61 55 65  61
 min
,
32  
 32 
 min1, 0.6667  0.6667
9A-16
What does a Cpk of
0.6667 mean?
 An index that shows how well the
units being produced fit within the
specification limits.
 This is a process that will produce a
relatively high number of defects.
 Many companies look for a Cpk of 1.3
or better… 6-Sigma companies want
2.0!
9A-17
Example: Probabilities
Less than 55 psi
X X
55  61
Z

 3

2
P( Z  3)  0.00135
More than 65 psi
X X
65  61
Z

2

2
P( Z  2)  0.02275
LO 2
P( Z  3 or Z  2)  0.00135 0.02275 0.02410
9A-18
Process Control
Procedures
 Attribute (Go or no-go information)



Defectives refers to the acceptability of
product across a range of characteristics.
Defects refers to the number of defects per
unit which may be higher than the number
of defectives.
p-chart application
 Variable (Continuous)
LO 3
 Usually measured by the mean and the
standard deviation.
 X-bar and R chart applications
9A-19
Control Chart Evidence for
Investigation
LO 3
9A-20
Process Control with Attribute
Measurement: Using ρ Charts
 Created for good/bad attributes
 Use simple statistics to create the
control limits
T ot alnumber of defect sfromall samples
p
Number of samples Sample size
sp 

p 1 p
n

UCL  p  zs p
LCL  p  zs p
LO 3
9A-21
Example: Control Chart
Design
LO 3
9A-22
Example: Calculations
p
sp 
T otalnumber of defectsfromall samples
91

 0.03033
Number of samples x Sample size
3,000


p 1 p
0.030331  0.03033

 0.00990
n
300
UCL  p  3s p  0.03033 30.00990  0.06003
LCL  p  3s p  0.03033 30.00990  0.00063
LO 3
9A-23
Process Control with Attribute
Measurements: Using c Charts
 With ρ charts, each item was either
good or bad
 With a c chart, each item can have
multiple defects
c  Averagenumber of defect sper unit
sp  c
UCL  c  z c
LO 3
LCL  c  z c
9A-24
Example: Lumber Yard
 Lumber yard expects four knotholes
per eight foot board
c4
sp  c  4  2
UCL  c  z  s p  4  32  10
LCL  c  z  s p  4  32  2  0
LO 3
9A-25
Process Control with Variable
Measurements: Using x and R
Charts
 In variable sampling, we measure
actual values rather than sampling
attributes
 Generally want small sample size
 Quicker
 Cheaper
 Samples of 4-5 are typical
 Want 25 or so samples to set up chart
LO 3
9A-26
How to Construct x Charts if
Standard Deviation Known
UCLX  X  zs X
LCLX  X  zs X
where
s  s
X
 St andard deviationof samplemeans
n
s  St andard deviationof theprocessdist ribution
n  Sample size
X  Averageof samplemeansor a target value set for theprocess
z  Number of standarddeviationsfor a specificconfidencelevel
LO 3
9A-27
How to Construct x and R
Charts
X Chart
UCLX  X  A2 R
LCLX  X  A2 R
R Chart
UCLR  D4 R
LCLR  D3 R
LO 3
9A-28
Example: The Data
LO 3
9A-29
Example: Calculations and
Chart
LO 3
9A-30
Acceptance Sampling
 Acceptance sampling is sampling to
accept or reject the immediate lot of
product at hand


Does not always “Determine quality level”
Results subject to sampling error
 Purposes


Make decision about (sentence) a product
Otherwise, ensures quality is within
predetermined level
LO 4
9A-31
Acceptance Sampling
 Advantages

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

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
Economy
Less handling damage
Fewer inspectors
Upgrading of the inspection job
Applicability to destructive testing
Entire lot rejection (motivation for improvement)
 Disadvantages



Risks of accepting “bad” lots (consumer’s risk) and
rejecting “good” lots (producer’s risk)
Added planning and documentation
Sample provides less information than 100-percent
inspection
9A-32
Single Sampling Plan
 Defined by n and c


n is sample size—how many to sample at a time
c is the acceptance number—the maximum
number of defective items that can be found in
the sample before the lot is rejected
 Values for n and c are determined by the
interaction of four factors
LO 4

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

AQL or acceptable quality level
α
LTPD or lot tolerance percent defective
β
9A-33
Risk
 Acceptable quality level (AQL)

Maximum acceptable percentage of
defectives defined by producer
 The  (producer’s risk)

The probability of rejecting a good lot
 Lot tolerance percent defective (LTPD)

Percentage of defectives that defines
consumer’s rejection point
 The  (consumer’s risk)
LO 4

The probability of accepting a bad lot
9A-34
Standard Table of
Sampling Plans
 MIL-STD-105D


For attribute sampling plans
Needs to know:




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The lot size N
The inspection level (I, II, III)
The AQL
Type of sampling (single, double, multiple)
Type of inspection (normal, tightened, reduced)
 Find a code letter then read plan from
Table
9A-35
Standard Table of Sampling Plans:
Single Sampling Plan
Example: If N=2000 and AQL=0.65% find the normal,
tightened, and reduced single sampling plan using
inspection level II.
Example: If N=20,000 and AQL=1.5% find the normal,
tightened, and reduced double sampling plan using
inspection level I.
9A-36