Transcript PRODUCTIONS/OPERATIONS MANAGEMENT

Quality Control
McGraw-Hill/Irwin
Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.
 You should be able to:
1.
List and briefly explain the elements in the control process
2. Explain how control charts are used to monitor a process, and
the concepts that underlie their use
3. Use and interpret control charts
4. Perform run tests to check for nonrandomness in process output
5. Assess process capability
Instructor Slides
10-2
 Quality Control
 A process that evaluates output relative to a standard
and takes corrective action when output doesn’t meet
standards
 If results are acceptable no further action is required
 Unacceptable results call for correction action
Instructor Slides
10-3
Instructor Slides
10-4
 Inspection
 An appraisal activity that compares goods or services to
a standard
 Inspection issues:
1.
2.
3.
4.
Instructor Slides
How much to inspect and how often
At what points in the process to inspect
Whether to inspect in a centralized or on-site location
Whether to inspect attributes or variables
10-5
Figure 10.2
 How Much/How Often
 Where/When
 Centralized vs. On-site
Inputs
Acceptance
sampling
Transformation
Outputs
Acceptance
sampling
Process
control
10-6
Instructor Slides
10-7
 University:
 Is each student achieving acceptable performance?
 Chemistry:
 Does each product contain the correct amount of
chemical?
 Automobile:
 Does the automobile performs as intended?
 Bank:
 Are the transaction completed with precision?
10-8
 There are two general approaches to quality
management.
 The inspection approach (inspects the quality of
input and the finished product)
 The detection approach (focuses on the production
process, and detects when it starts going out of
control)
10-9
 There are two general approaches to quality
management.
 The inspection approach (inspects the quality of
input and the finished product)
 The detection approach (focuses on the production
process, and detects when it starts going out of
control)
10-10
 Typical Inspection Points:
 Raw materials and purchased parts
 Finished products
 Before a costly operation
 Before an irreversible process
 Before a covering process
Instructor Slides
10-11
 Effects on cost and level of disruption are a major
issue in selecting centralized vs. on-site inspection
 Centralized
 Specialized tests that may best be completed in a lab
 More specialized testing equipment
 More favorable testing environment
 On-Site
 Quicker decisions are rendered
 Avoid introduction of extraneous factors
 Quality at the source
Instructor Slides
10-12
Table 10.1
Type of
business
Fast Food
Inspection
points
Cashier
Counter area
Eating area
Building
Kitchen
Hotel/motel Parking lot
Accounting
Building
Main desk
Supermarket Cashiers
Deliveries
Characteristics
Accuracy
Appearance, productivity
Cleanliness
Appearance
Health regulations
Safe, well lighted
Accuracy, timeliness
Appearance, safety
Waiting times
Accuracy, courtesy
Quality,10-13
quantity
10-14
 Quality control seeks
 Quality of Conformance
 A product or service conforms to specifications
 A tool used to help in this process:
 SPC
 Statistical evaluation of the output of a process
 Helps us to decide if a process is “in control” or if corrective action is
needed
 Statistical Process Control (SPC) is a form of hypothesis testing
employed in industry.
 Its objective is to monitor the quality of a firm’s products and
services
Instructor Slides
10-15
 Two basic questions: concerning
variability:
1.
Issue of Process Control

Are the variations random? If nonrandom variation
is present, the process is said to be unstable.
2. Issue of Process Capability
 Given a stable process, is the inherent variability of
the process within a range that conforms to
performance criteria?
Instructor Slides
10-16
 Variation

Random (common cause) variation:


Natural variation in the output of a process, created by
countless minor factors
Assignable (special cause) variation:


A variation whose cause can be identified.
A nonrandom variation
Instructor Slides
10-17
 SPC involves periodically taking samples of process
output and computing sample statistics:
 Sample means
 The number of occurrences of some outcome
 Sample statistics are used to judge the randomness of
process variation
Instructor Slides
10-18
 Sampling Distribution
 A theoretical distribution that describes the random variability of
sample statistics
 The normal distribution is commonly used for this purpose
 Central Limit Theorem
 The distribution of sample averages tends to be normal regardless
of the shape of the process distribution
Instructor Slides
10-19
Instructor Slides
10-20
 Sampling and corrective action are only a part of the
control process
 Steps required for effective control:
 Define: What is to be controlled?
 Measure: How will measurement be accomplished?
 Compare: There must be a standard of comparison
 Evaluate: Establish a definition of out of control
 Correct: Uncover the cause of nonrandom variability and fix it
 Monitor: Verify that the problem has been eliminated
Instructor Slides
10-21
 Control Chart
 A time ordered plot of representative sample statistics
obtained from an ongoing process (e.g. sample means), used
to distinguish between random and nonrandom variability
 Control limits
 The dividing lines between random and nonrandom deviations
from the mean of the distribution
 Upper and lower control limits define the range of acceptable
variation
Instructor Slides
10-22
Each point on the control chart represents a sample of n
observations
Instructor Slides
10-23
 The essence of statistical process control is to
assure that the output of a process is random so
that future output will be random.
10-24
UCL
CL
LCL
0 1 2 3 4 5 6 7 8 9 101112131415161718192021222324252627
Sample
10-25
 Variations and Control


Random variation: Natural variations in the output of
a process, created by countless minor factors
Assignable variation: A variation whose source can be
identified
10-26
 All products exhibit some degree of variation.
 There are two sources of variation


Random or chance variation: Natural variations in the
output of process, created by countless minor factors
that cannot be eliminated without changing the
process
Assignable variation: A variation whose source can be
identified and eliminated
10-27
Figure 10.5
μ = E(X)
Sampling
distribution
s = σ/√n
Process
distribution
Mean
10-28
Figure 10.6
Standard deviation



Mean
95.44%
99.74%
10-29

Figure 10.7
Sampling
distribution
Process
distribution
Mean
Lower
control
limit
Upper
control
limit
10-30
 Type I error
 Concluding a process is not in control when it actually is.
 The probability of rejecting the null hypothesis when the null
hypothesis is true.
 Manufacturer’s Risk
 Type II error
 Concluding a process is in control when it is not.
 The probability of failing to reject the null hypothesis when the null
hypothesis is false.
 Consumer’s Risk
Instructor Slides
10-31
Table 10.2
In control
Out of control
In control
No Error
Out of
control
Type II Error
(consumers risk)
Type I error
(producers risk)
No error
10-32
Instructor Slides
10-33
Instructor Slides
10-34
 Variables generate data that are measured
 Mean control charts
 Used to monitor the central tendency of a process.
 “x- bar” charts
 Range control charts
 Used to monitor the process dispersion
 R charts
Instructor Slides
10-35
UCL
CL
LCL
0 1 2 3 4 5 6 7 8 9 101112131415161718192021222324252627
Sample
10-36
k
k
x
 xi
i 1
R
R
i 1
k
where
i
k
where
x  Average of sample means
R  Average of sample ranges
x i  mean of sample i
Ri  Range of sample i
k  number of samples
Instructor Slides
10-37
 The x chart
 This chart is employed to determine whether the
distribution mean has changed.
Upper control limit
x
Lower control limit
Start with k samples when the process is under control.
Average the k sample averages.
Average the k sample ranges.
10-38
X
UCL =
LCL =
x  za

2
x  za 2
n

n
10-39
 Given the following samples which have been
collected from the length of time to process loan
application:
Sample
1
Observation
Mean
Range
2
3
4
5
1
12.11
12.15
12.09
12.12
12.09
2
12.10
12.12
12.09
12.10
12.14
3
12.11
12.10
12.11
12.08
12.13
4
12.08
12.11
12.15
12.10
12.12
12.10
12.12
12.11
12.10
12.12
0.03
0.05
0.06
0.04
0.05
10-40
 Q1: If the standard deviation of the process is
σ = .02, find the three-sigma (z = 3) control
limits.
 Grand Mean =
 (12.10 + 12.12 + 12.11 + 12.10 + 12.12)/5
 = 12.11
 UCL = 12.11 + (3)(.02 / 2) = 12.14
 LCL = 12.11 - (3)(.02 /2) = 12.08
X
10-41
 Used to monitor the central tendency of a process
x  chart Control Limits
UCLx  x  A2 R
LCLx  x  A2 R
where
A2  a control chart factor based on sample size, n
Instructor Slides
10-42
 Q2: Find the mean control limits assuming
that the standard deviation is not known:
 R = (.03+.05+.06+.04+.05) / 5 = .046
 UCL = 12.11 + (.73)(.046) = 12.14358
 LCL = 12.11 – (.73)(.046) = 12.07642
10-43
 Used to monitor process dispersion
R Chart Control Limits
UCLR  D4 R
LCLR  D3 R
where
D3  a control chart factor based on sample size, n
D4  a control chart factor based on sample size, n
Instructor Slides
10-44
 Range chart
 UCL = (2.28)(.046) = .10488
 LCL =(0)(.046) = 0
10-45
Instructor Slides
10-46
Figure 10.10B
Sampling
Distribution
(process variability is increasing)
UCL
Does not
reveal increase
x-Chart
LCL
UCL
R-chart
Reveals increase
LCL
10-47
 To determine initial control limits:
 Obtain 20 to 25 samples
 Compute appropriate sample statistics
 Establish preliminary control limits
 Determine if any points fall outside of the control limits
 If you find no out-of-control signals, assume the process is in control
 If you find an out-of-control signal, search for and correct the
assignable cause of variation
 Resume the process and collect another set of observations on
which to base control limits
 Plot the data on the control chart and check for out-of-control
signals
Instructor Slides
10-48
 Attributes generate data that are counted.
 p-Chart
 Control chart used to monitor the proportion of defectives
in a process
 c-Chart
 Control chart used to monitor the number of defects per
unit
Instructor Slides
10-49
 When observations can be placed into two
categories.

Good or bad

Pass or fail

Operate or don’t operate
 When the data consists of multiple samples of
several observations each
Instructor Slides
10-50
Total number of defectives
p
Total number of observatio ns
p (1  p )
ˆ p 
n
UCL p  p  z (ˆ p )
LCL p  p  z (ˆ p )
Instructor Slides
10-51
 Using 4 samples of 100
credit card statements Sample #
each, an auditor found
1
the following:
2
Total
# with Error
4
3
3
5
4
8
20
10-52
 The fraction defective estimate is:
= 20 / (4 x 100) = .05
 Q: What is the probability distribution for this
experiment?
 The standard deviation of fraction defective
with sample size n = 100 is:

P
 σp =
p (1  p )
n
10-53
 σp =
(.05)(.95) / 100
 σp = .02179
 Note that n = 100 is the sample size and not the
number of samples
10-54
 Control limits are computed using the following





formulas:
UCL = P + Z σp
LCL = P - Z σp
For example Z =3 results in the following control
limits:
UCL = .05 + (3)(.02179) = .11537
LCL = .05 – (3)(.02179) = .01537
10-55
Sample # with Fraction
#
Error Defective
1
4
.04
In control?
Yes
2
3
.03
Yes
3
5
.05
Yes
4
8
.08
Yes
10-56
 For Z= 3, the type I error for example 2 is
calculated from the Normal probability table:
 α = 1 –(.4987 x 2) = .0026
10-57
 Use only when the number of occurrences per unit of
measure can be counted; non-occurrences cannot be
counted.





Scratches, chips, dents, or errors per item
Cracks or faults per unit of distance
Breaks or Tears per unit of area
Bacteria or pollutants per unit of volume
Calls, complaints, failures per unit of time
UCL c  c  z c
LCL c  c  z c
Instructor Slides
10-58
 The following table
displays the number
of scratches in the
exterior paint of 4
samples of ten
automobiles each:
Sample #
Total
Number
1
35
2
42
3
28
4
45
150
10-59
 The average number of defects is:

c = 150 / (4 x 10) = 3.75
 Q: What is the probability distribution for this
experiment?
 The standard deviation is:
 σc =
c
 σc = 1.9365
10-60
 Control limits are computed using the following
formulas:
 UCL =
c
c
+Z
c
c
 LCL =
-Z

 For example Z =3 results in the following control
limits:
 UCL = 3.75 + (3)(1.9365) = 9.5595
 LCL = 3.75 – (3)(1.9365) = -2.0595 or 0
10-61
 At what points in the process to use control charts
 What size samples to take
 What type of control chart to use
 Variables
 Attributes
Instructor Slides
10-62
 Even if a process appears to be in control, the data may
still not reflect a random process
 Analysts often supplement control charts with a run
test
 Run test
 A test for patterns in a sequence
 Run
 Sequence of observations with a certain characteristic
Instructor Slides
10-63
Instructor Slides
10-64
 Run test – a test for randomness
 Any sort of pattern in the data would suggest a
non-random process
 All points are within the control limits - the
process may not be random
10-65
 Trend
 Cycles
 Bias
 Mean shift
 Too much dispersion
10-66
Counting Runs
Figure 10.12
Counting Above/Below Median Runs
B A
Figure 10.13
A
B
A
B
B
B A
Counting Up/Down Runs
U
U
D
U
(7 runs)
A
B
(8 runs)
D
U
D U
10-67
U D
 Statistical process control is based on repetitive
sampling procedures and hypotheses tests.
 Therefore, we can run tests to detect an out of
control state based on patterns developed by the
repeated measurements.
 We may conclude that a process is out of control
when certain patterns of the process behavior are
detected, even if no observation falls outside
the control limits.
10-68
 Above/Below Median
runs:
 E(r)med = N/2 + 1
 med
N 1

4
u/d
16 N  29

90
 Up/Down runs:
 E(r)u/d = (2N – 1) /3
10-69
 Text example 6, pages 468-469
10-70
 Once a process has been determined to be stable, it is
necessary to determine if the process is capable of
producing output that is within an acceptable range
 Tolerances or specifications
 Range of acceptable values established by engineering design or
customer requirements
 Process variability
 Natural or inherent variability in a process
 Process capability
 The inherent variability of process output (process width) relative
to the variation allowed by the design specification (specification
width)
Instructor Slides
10-71
Lower
Upper
Specification Specification
Process variability (width)
exceeds specifications
Lower
Specification
Lower
Specification
Upper
Specification
Process variability (width)
matches specifications width
Upper
Specification
Process variability (width) is less
than the specification width
Instructor Slides
10-72
UTL - LTL
Cp 
6
where
UTL  upper tole rance (specifica tion) limit
LTL  lower tole rance(spec ification) limit
Instructor Slides
10-73
 Used when a process is not centered at its target, or
nominal, value
C pk  min C pu , C pl 
 UTL  x x  LTL 
 min 
,

3 
 3
Instructor Slides
10-74
 The control chart is divided into 6 horizontal
zones.
Example: Zones for the X control chart.
Upper control limit
A
B
C
C
B
A
lower control limit
x  3S / n
x  2S / n
x  S/ n
x
x S/ n
x  2S / n
x  3S / n
– Several pattern-tests can be applied to these zones.
Each one represents a rare event, which if it occurs indicates
10-75
an out of control state.
A
B
C
C
B
A
One point beyond
zone A.
A
A
B
B
C
C
9
2 4
8
C
C
6
B 1
B
3 5 7
A
A
Nine points in a row
in zone C or beyond
(on same side of CL).
5
1 2
3
4
Six increasing
(decreasing) points
in a row.
6
A
B
C
C
B
A
Fourteen points in a
row alternating
up and down.
A
B
C
C
B
A
A
B
C
C
B
A
A
B
C
C
B
A
A
B
C
C
B
A
2 out of 3 points in
a row in zone A or
beyond (same side
of CL).
4 out of 5 points in
a row in zone B or
beyond.
15 points in a row
in zone C (on both
sides of CL). 10-76
8 points in a row
beyond zone C (on
both sides of CL).
 The proportion of defectives in a computer
disks production line has to be monitored.
 The experiment
 Every hour a random sample of 200 disks is taken.
 Each disk is tested to determine if it is defective.
 Based on the first 40 samples, draw a p
chart and determine whether the process
was out of control.
10-77
 Solution
 Sample Defective Proportion
1
2
3
19
5
16
.095
.025
.080
Mean sample proportion =
p = (.095+..25+.080+…)/40
=.05762
..……………………………...
Centerline  p  .05762
Lower control lim it  p  3
p (1  p )
.05762(1  .05762)
 .05762  3
 .0088188
n
200
p (1  p )
.05762(1  .05762)
Upper control lim it  p  3
 .05762  3
 .1071
n
200
An estimate of the s tan dard deviation 
p(1  p )
 .01648
n
10-78
The zones
P-Chart
.05762+3(.01648)
=.1071
.05762+2(.01648)
=.09057
.05762+(.01648)
=.0741
0.12
0.1
Zone A
0.08
Zone B
0.06
Zone C
Zone C
0.04
Zone B
0.02
Zone A
0
0 1 2 3 4 5 6 7 8 9101112131415161718192021222324252627282930313233343536373839404142
There is no evidence to infer that the process was out of control
10-79
 Managers should have response plans to
investigate cause
 May be false alarm (Type I error)
 May be assignable variation
10-80
 Simplify
 Standardize
 Mistake-proof
 Upgrade equipment
 Automate
Instructor Slides
10-81
 Quality is a primary consideration for nearly all
customers
 Achieving and maintaining quality standards is of
strategic importance to all business organizations
 Product and service design
 Increase capability in order to move from extensive use of
control charts and inspection to achieve desired quality
outcomes
Instructor Slides
10-82