quality and statistical quality control
TRANSCRIPT
-
8/7/2019 QUALITY AND STATISTICAL QUALITY CONTROL
1/36
-
8/7/2019 QUALITY AND STATISTICAL QUALITY CONTROL
2/36
` Conformance to specifications
` Fulfilling customer needs
` Fitness for use
-
8/7/2019 QUALITY AND STATISTICAL QUALITY CONTROL
3/36
` According to Feigenbaumthe underlying principle
of total quality is that ,to provide genuine
effectiveness, control must start with the design of
the product and end only when the product hasbeen in the hands of a customer who remains
satisfied.
-
8/7/2019 QUALITY AND STATISTICAL QUALITY CONTROL
4/36
` Performance
` Features
` Reliability
` Conformance` Durability
` Serviceability
` Aesthetics
` Safety` Other perceptions
-
8/7/2019 QUALITY AND STATISTICAL QUALITY CONTROL
5/36
` system for verifying and maintaining a desired
level of quality in a product or process by careful
planning, use of proper equipment, continued
inspection, and corrective action as required
-
8/7/2019 QUALITY AND STATISTICAL QUALITY CONTROL
6/36
` The production processes are not perfect!
` Which means that the output of these processes will not be
perfect correct and deterministic.
` Successive runs of the same production process will produce
non-identical parts.
` Alternately, seemingly similar runs of the production process
will vary, by some degree, and impart the variation into the
some product characteristics.
` Because of these variations in the products, we needprobabilistic models and robust statistical techniques to
analyze quality of such products.
-
8/7/2019 QUALITY AND STATISTICAL QUALITY CONTROL
7/36
` No matter how carefully a production process is controlled,these quality measurements will vary from item to item, andthere will be a probability distribution associated with the
population of such measurements.
` If all important sources of variations are under control in aproduction process, then the slight variations among thequality measurements usually cause no serious problems.
` Such a process should produce the same distribution of qualitymeasurements no matter when it is sampled, thus this is a
stable system.
-
8/7/2019 QUALITY AND STATISTICAL QUALITY CONTROL
8/36
` Objective ofquality control is to develop a scheme forsampling a process, making a quality measurement of intereston sample items, and then making a decision as to whether ornot the process is in the stable state, or in control.
` If the sample data suggests that the process is out of control,a cause is for the abnormality is sought.
` A common method for making these decisions involves theuse ofcontrol charts.
` These are very important and widely used techniques in
industry, and everyone in the industry, even if not directlyrelated to quality control, should be aware of these.
-
8/7/2019 QUALITY AND STATISTICAL QUALITY CONTROL
9/36
Statistical process control
` Methodology formonitoring a process to identify special
causes of variation and signaling the need to take corrective
action.
` Whenspecial causes are present, the system said to be
statistically out of control.
` If the variations are due to common causes alone, the process
is said to be in statistical control.
` SPC relies heavily on control charts.
-
8/7/2019 QUALITY AND STATISTICAL QUALITY CONTROL
10/36
Control Chart Selection: Attribute DataControl Chart Selection: Attribute Data
X, R chart
Process ControlProduct Control
Variables Attributes Variables Attributes
Acceptance Sampling (Single/Double
Sampling Plan)c, p, np chart
In Process control Techniques
-
8/7/2019 QUALITY AND STATISTICAL QUALITY CONTROL
11/36
Control Charts: Recognizing Sources ofControl Charts: Recognizing Sources of
VariationVariation
Why Use a Control Chart? To monitor, control, and improveprocess performance over time by
studying variation and its source.
What Does a Control Chart Do? Focuses attention on detecting and monitoring process variation over
time;
Distinguishesspecialfrom common causes of variation, as a guide tolocal or management action;
Serves as a tool for ongoing control of a process;
Helps improve a process to perform consistently and predictably forhigher quality, lower cost, and higher effective capacity;
Provides a common language for discussing process performance.
-
8/7/2019 QUALITY AND STATISTICAL QUALITY CONTROL
12/36
Control Charts:Control Charts:
Recognizing Sources of VariationRecognizing Sources of Variation
How Do I Use Control Charts?
There are many types of control charts. The control
charts that you or your team decides to use should be
determined by the type of data that you have.
Use the following tree diagram to determine whichchart will best fit your situation. Only the most
common types of charts are addressed.
-
8/7/2019 QUALITY AND STATISTICAL QUALITY CONTROL
13/36
` Attributes A performance characteristics that is either
present or absentin the product or service under
consideration.
` Examples: Order is either complete or incomplete; an invoice
can have one, two, or more errors.
` Attributes data are discrete and tell whether the characteristics
conforms to specifications.
` Attributes measurements typically represented as proportions
or rates. e.g. rate of errors per opportunity.` Typically measured by Go-No Go gauges.
-
8/7/2019 QUALITY AND STATISTICAL QUALITY CONTROL
14/36
` Variable Continuous data that is concerned with degree ofconformance to specifications.
` Generally expressed with statistical measures such as averagesand standard deviations.
` Sophisticated instruments (caliper) used.
` In statistical sense, attributes inspection less efficient thanvariable inspection.
` Attribute data requires larger sample than variable inspectionto obtain same amount of statistical information.
` Most quality characteristics in service industry are attributes.
-
8/7/2019 QUALITY AND STATISTICAL QUALITY CONTROL
15/36
Statistical Process ControlStatistical Process Control
Statistical Process Control (SPC) can be
thought of as the application of statistical
methods for the purposes of quality controland improvement.
Quality Improvement is perhaps foremost
among all areas in business for applicationof statistical methods.
-
8/7/2019 QUALITY AND STATISTICAL QUALITY CONTROL
16/36
Control Chart ConstructionControl Chart Construction
Initiate data collection:
Run the process untouched, and gather sampled data. Record data on an appropriate Control Chart sheet or
other graph paper. Include any unusual events that occur.
Calculate the appropriate statistics and control limits:
Use the appropriate formulas.
Construct the control chart(s) and plot the data.
-
8/7/2019 QUALITY AND STATISTICAL QUALITY CONTROL
17/36
CL
U1SL
U2SWL
UCL
L1SL
L2SWL
LCL
A
B
C
C
B
A
Control Charts: Colors UsedControl Charts: Colors Used
*
** *
*
* *
**
**
*
*
*
*
-
8/7/2019 QUALITY AND STATISTICAL QUALITY CONTROL
18/36
Control Chart InterpretationControl Chart Interpretation
Center line (CL) positioned at the estimated mean
Upper and lower one standard deviation lines (U1SL and
L1SL) positioned one standard deviation above andbelow the mean.
Upper and lower two standard deviation warning lines(U2SWL and L2SWL) positioned at two standard
deviations above and below the mean.
Upper and lower control lines (UCL and LCL) positionedat three standard deviations above and below the mean.
-
8/7/2019 QUALITY AND STATISTICAL QUALITY CONTROL
19/36
Control Charts for theControl Charts for the
Process Mean and DispersionProcess Mean and Dispersion
X bar ChartTypically used to monitor process centrality (or location)
Limits depend on the measure is used to monitor process dispersion(R or S may be used).
S orStandard Deviation Chart:Used to monitor process dispersion
R orRange Chart:
Also used to monitor process dispersion
-
8/7/2019 QUALITY AND STATISTICAL QUALITY CONTROL
20/36
m = 20 to 40 initial samples of n observations each.
Xi = mean of ith sample
Si = standard deviation of ith sample
Ri = range of ith sample
Sample Summary InformationSample Summary Information
X = (X1 + X2 +... + Xm) / mR = (R1 + R2 + ... +Rm)/m
S = (S1 + S2 + ... + Sm)/m
W = R/d2 where d2 depends only on n
-
8/7/2019 QUALITY AND STATISTICAL QUALITY CONTROL
21/36
Coordinates for the XCoordinates for the X--bar Control Chart: Rbar Control Chart: R
CL= X,
UCL= X+ A2R,
UCL= X- A2R
U2SWL= X+ 2A2R/3
L2SWL= X- 2A2R/3
U1SL= X+ A2
R/3
L1SL= X- A2R/3
A2 is a constant that depends only on n.
-
8/7/2019 QUALITY AND STATISTICAL QUALITY CONTROL
22/36
Coordinates for an R Control ChartCoordinates for an R Control Chart
CL= R
UCL= D4R
LCL= D3R U2SWL= R+ 2(D4-1)R/3
L2SWL= R- 2(D4-1)R/3
U1SL= R+ (D4
-1)R/3
L1SL= R- (D4-1)R/3
where D3 and D4 depend only on n
-
8/7/2019 QUALITY AND STATISTICAL QUALITY CONTROL
23/36
Championship
Championship Card CompanyChampionship Card Company
-
8/7/2019 QUALITY AND STATISTICAL QUALITY CONTROL
24/36
Championship Card CompanyChampionship Card Company
Championship Card Company (CCC) produces collectiblesports cards of college and professional athletes.
CCCs card-front design uses a picture of the athlete, bordered
all-the-way-around with one-eighth inch gold foil. However,
the process used to center an athletes picture does not functionperfectly.
Five cards are randomly selected from each 1000 cards produced
and measured to determine the degree of off-centeredness of each
cards picture. The measurement taken represents percentageof total margin (.25) that is on the left edge of a card. Data
from 30 consecutive samples is included with your materials,
and summarized on the following slides.
-
8/7/2019 QUALITY AND STATISTICAL QUALITY CONTROL
25/36
Championship Card CompanyChampionship Card Company
Sample X-bar R Sample X-bar R Sample X-bar R
1 55.6 22 11 51.2 15 21 50.0 11
2 61.0 23 12 49.4 14 22 47.0 14
3 45.2 20 13 44.0 32 23 50.6 15
4 46.2 11 14 51.6 14 24 48.8 165 46.8 18 15 53.2 12 25 44.6 22
6 49.8 23 16 52.4 23 26 46.8 16
7 46.8 18 17 50.6 8 27 49.2 88 44.2 20 18 56.0 18 28 45.6 19
9 50.8 32 19 50.2 19 29 57.6 40
10 48.4 16 20 44.0 23 30 51.4 17
-
8/7/2019 QUALITY AND STATISTICAL QUALITY CONTROL
26/36
Championship Card CompanyChampionship Card Company
Summary InformationSummary Information
n = 5
X = 49.63S = 7.42
R = 18.63
d2 = 2.326
A2 = 0.577
A3 = 1.427
B3 = NAB4 = 2.089
D3 = NA
D4 = 2.115
W = R/d2 = 8.01
-
8/7/2019 QUALITY AND STATISTICAL QUALITY CONTROL
27/36
-
8/7/2019 QUALITY AND STATISTICAL QUALITY CONTROL
28/36
3020100
60
50
40
Sample Number
SampleMean
X Bar Chart for Sports Cards Centering Values
Samples of 5 from each 1000 Cards Printed
1
=49.63
1.0S L=53 .22
2.0S L=56 .80
3.0S L=60 .38
-1.0SL=46.05
- 2.0S L=42.47
- 3.0S L=38.89
Championship Card CompanyChampionship Card Company
Limits Based on R
-
8/7/2019 QUALITY AND STATISTICAL QUALITY CONTROL
29/36
3020100
40
30
20
10
0
Sample Number
SampleRang
e
R Chart for Sports Card Centering
Samples of 5 Cards from each 1000 Produced
R=18.63
1.0SL=25.55
2.0S L=32.48
3.0S L=39.40
- 1.0S L=11.71
- 2.0SL =4.791
- 3.0SL =0.000
Championship Card CompanyChampionship Card Company
-
8/7/2019 QUALITY AND STATISTICAL QUALITY CONTROL
30/36
Championship Card Company XChampionship Card Company X--bar & Rbar & R
Chart InterpretationChart Interpretation
Application of all eight PATs to the X-bar chart indicated aviolation of PAT 1 (one point plotting above the UCL) at sample2. Apparently, a successful process adjustment was made, as
suggested by examination of the remainder of the chart.
Application of PATs one through four to the R chart indicated aviolation of PAT 1 at sample 29. Measures would be investigatedto reduce process variation at that point. The violation was a
close call and was out of character with the remainder of thedata.
We are close to being able to apply PDCA to the process for thepurpose of achieving lasting process improvements.
-
8/7/2019 QUALITY AND STATISTICAL QUALITY CONTROL
31/36
Coordinates for the X bar Control Chart: SCoordinates for the X bar Control Chart: S
CL= X
UCL=X=A3S
LCL=X- A3S
U2SWL= X+ 2A3S/3
L2SWL= X- 2A3S/3
U1SL= X+ A3S/3
L1SL= X- A3S/3
where A3 depends only on n
-
8/7/2019 QUALITY AND STATISTICAL QUALITY CONTROL
32/36
Coordinates on an S Control ChartCoordinates on an S Control Chart
CL= S
UCL= B4S
LCL= B3S
U2SWL= S+ 2(B4-1)S/3
L2SWL= S- 2(B4-1)S/3
U1SL= S+ (B4-1)S/3 L1SL= S- (B4-1)S/3
where B3 and B4 depend only on n
-
8/7/2019 QUALITY AND STATISTICAL QUALITY CONTROL
33/36
Championship Card CompanyChampionship Card CompanyChampionship Card CompanyChampionship Card Company
Sample X-bar S Sample X-bar S Sample X-bar S
1 55.6 9.63 11 51.2 6.83 21 50.0 5.15
2 61.0 8.63 12 49.4 5.46 22 47.0 5.15
3 45.2 7.40 13 44.0 14.35 23 50.6 5.55
4 46.2 4.09 14 51.6 5.18 24 48.8 6.505 46.8 7.22 15 53.2 5.36 25 44.6 8.96
6 49.8 8.76 16 52.4 9.48 26 46.8 6.50
7 46.8 6.72 17 50.6 3.44 27 49.2 3.19
8 44.2 8.53 18 56.0 7.00 28 45.6 7.96
9 50.8 11.95 19 50.2 7.60 29 57.6 14.38
10 48.4 6.19 20 44.0 8.46 30 51.4 6.80
-
8/7/2019 QUALITY AND STATISTICAL QUALITY CONTROL
34/36
UCL
U2SWLU1SL
CL
L1SLL2SWL
LCL
X based on S S
60.22
56.6953.16
49.63
46.1142.58
39.05
15.49
12.8010.11
7.42
4.722.03
------
Championship Card CompanyChampionship Card Company
XX--bar and S Chart imitsbar and S Chart imits
-
8/7/2019 QUALITY AND STATISTICAL QUALITY CONTROL
35/36
3020100
60
50
40
Samp l mber
SampleMean
X Bar Chart for Sports Cards Centering Values
Samples of 5 from each 1000 Cards Printed
1
X=49.63
1.0S L=53 .16
2.0S L=56.69
3.0S L=60.22
- 1.0S L=46 .11
- 2.0S L=42.58
- 3.0S L=39.05
Championship Card CompanyChampionship Card Company
Limits Based on S
-
8/7/2019 QUALITY AND STATISTICAL QUALITY CONTROL
36/36
3020100
15
10
5
0
Sample Number
SampleStdev
S Chart for Sports Card Centering Values
5 Cards Sampled from each 1000 Cards Produced
S =7.416
1.0S L=10.11
2.0S L=12.80
3.0S L=15.49
- 1.0S L=4.724
- 2.0SL =2.032
- 3.0SL =0.000
Championship Card CompanyChampionship Card Company