4. Basic Statistics
Descriptive Statistics
A straightforward presentation of facts. A
survey or summary of a population in
which all data are known.
Inferential Statistics
Drawing conclusions about a population
from a random sample
Saturday, 17
February 2024
5. Inferential Statistics
Inferential statistics is a valuable tool because it allows us to look at a
small sample size and make statements on the whole population.
Samples must be pulled RANDOMLY from a population so that the
sample truly represents the population. Every unit in a population
must have a equal chance of being selected for the sample to be truly
random.
The distribution or shape of the data is important to know for analytical
purposes.
The most common distribution is the bell shaped or normal distribution.
Parameters can be estimated from sample statistics. Two of the most
common parameters are the mean and standard deviation.
The mean (or average, denoted by μ) measures central tendency
This is estimated by the sample mean or xbar.
The standard deviation (σ ) measures the spread of the data and is
estimated by the sample standard deviation
Saturday, 17
February 2024
7. Three SQC Categories
Statistical quality control (SQC) is the term used to describe
the set of statistical tools used by quality professionals
SQC encompasses three broad categories of;
Descriptive statistics
e.g. the mean, standard deviation, and range
Statistical process control (SPC)
Involves inspecting the output from a process
Quality characteristics are measured and charted
Helpful in identifying in-process variation
Acceptance sampling used to randomly inspect a batch of goods to
determine acceptance/rejection
Does not help to catch in-process problems
Saturday, 17
February 2024
8. Sources of Variation
Variation exists in all processes.
Variation can be categorized as either;
Common or Random causes of variation, or
Random causes that we cannot identify
Unavoidable
e.g. slight differences in process variables like diameter, weight, service
time, temperature
Assignable causes of variation
Causes can be identified and eliminated
e.g. poor employee training, worn tool, machine needing repair
Saturday, 17
February 2024
9. Traditional Statistical Tools
Descriptive Statistics
include
The Mean- measure of central
tendency
The Range- difference
between largest/smallest
observations in a set of data
Standard Deviation
measures the amount of data
dispersion around mean
Distribution of Data shape
Normal or bell shaped or
Skewed
n
x
x
n
1
i
i
1
n
X
x
σ
n
1
i
2
i
Saturday, 17
February 2024
10. Distribution of Data
Normal distributions Skewed distribution
Saturday, 17
February 2024
12. Objective
Present an overview of Seven Quality Tools
Address purpose and applications
Highlight benefits
Saturday, 17
February 2024
13. The Deming Chain
Improve Quality
Decrease Costs
Improve Productivity
Decrease Price
Increase Market
Stay in Business
Provide More Jobs
Return on Investment
Why Do This?
Saturday, 17
February 2024
14. Six Problem Solving Steps
Identify
recognize the symptoms
Define
Agree on the problem and set boundaries
Investigate
Collect data
Analyze
Use quality tools to aid
Solve
Develop the solution and implement
Confirm
Follow up to ensure that the solution is effective
Saturday, 17
February 2024
15. Seven Quality Tools
Checksheets
Cause and Effect Diagrams
Flow Charts
Histograms
Pareto Charts
Scatter Diagrams
Control Charts
Saturday, 17
February 2024
16. Quality Tool
Brainstorming
Rules
• Diverse group
• Go around room and get input from all – one idea
per turn
• Continue until ideas are exhausted
• No criticism
• Group ideas that go together
• Look for answers
Saturday, 17
February 2024
18. Checksheets
Purpose:
Tool for collecting and
organizing measured or
counted data
Data collected can be used
as input data for other
quality tools
Benefits:
Collect data in a systematic
and organized manner
To determine source of
problem
To facilitate classification of
data (stratification)
Saturday, 17
February 2024
20. Fishbone Diagram
Purpose: Graphical representation
of the trail leading to the root cause of
a problem
How is it done?
• Decide which quality characteristic,
outcome or effect you want to
examine (may use Pareto chart)
• Backbone –draw straight line
• Ribs – categories
• Medium size bones –secondary
causes
• Small bones – root causes
Saturday, 17
February 2024
21. Cause & Effect Diagrams
Benefits:
Breaks problems down into bite-size pieces to find root
cause
Fosters team work
Common understanding of factors causing the problem
Road map to verify picture of the process
Follows brainstorming relationship
Saturday, 17
February 2024
22. Cause & Effect Diagrams
Sample
Incorrect
shipping
documents
Manpowe
r
Materials
Methods Machine
Environmen
t Keyboard sticks
Wrong source info
Wrong purchase order
Typos
Source info incorrect
Dyslexic
Transposition
Didn’t follow proc.
Glare on
display
Temp.
No procedure
No communications
No training
Software problem
Corrupt
data
Saturday, 17
February 2024
24. Flow Charts
Purpose:
Visual illustration of the sequence of operations required to
complete a task
Schematic drawing of the process to measure or improve.
Starting point for process improvement
Potential weakness in the process are made visual.
Picture of process as it should be.
Benefits:
Identify process improvements
Understand the process
Shows duplicated effort and other non-value-added steps
Clarify working relationships between people and
organizations
Target specific steps in the process for improvement.
Saturday, 17
February 2024
25. Flow Charts
Top Down
Benefits
• Simplest of all
flowcharts
• Used for planning new
processes or examining
existing one
• Keep people focused on
the whole process
How is it done?
• List major steps
• Write them across top of
the chart
• List sub-steps under each
in order they occur
Problem report
Hardware return
Failure analysis
Measure
Customer input
Stress analysis
Heat transfer
analysis
Life analysis
Substantiation
Analyze
Hardware
procurement
Customer
coordination
Compliance
verification
Documentation
FAA approval
Improve
Fleet leader
reports
Service reports
Operational
statistics
Control
Saturday, 17
February 2024
26. Flow charts
Linear
Benefits
Show what actually happens
at each step in the process
Show what happens when
non-standard events occur
Graphically display processes
to identify redundancies and
other wasted effort
How is it done?
Write the process step inside
each symbol
Connect the Symbols with
arrows showing the direction
of flow
Toolbox
Saturday, 17
February 2024
27. Quality Tool
Sample Linear Flow
1- Fleet Analysis
utilizes data
warehouse reports to
create and distribute
a selection matrix.
2 - Other Groups
compile data as
determined by FRB.
3 - FRB meets to
analyze data.
4 - FRB selects
candidate problems
for additional
investigation.
5 - Action Assignee
performs detail
analysis of failure.
Requests failure
analysis as needed.
6 - Action Assignee
documents
investigation
findings.
7 - Action Assignee
reports investigation
results to FRB.
8 - Fleet Analysis
monitors failed item
to ensure failure has
been corrected.
Still
failing?
9 - FRB Categorize
Failure: Workmanship,
component, material,
maintenance, or
design. Also fleet
wide or RSU.
10 - FRB determines
required corrective
action - i.e. QAM or
supplier corrective
action.
11 - Fleet Analysis
monitors failure to
ensure corrective
action is effective.
Still
failing?
No
Yes
Yes
END
No
Start
Saturday, 17
February 2024
29. Histograms
Purpose:
To determine the spread or variation
of a set of data points in a
graphical form
How is it done?:
Collect data, 50-100 data point
Determine the range of the data
Calculate the size of the class
interval
Divide data points into classes
Determine the class boundary
Count # of data points in each
class
Draw the histogram
Stable process, exhibiting bell shape
Saturday, 17
February 2024
30. Histograms
Benefits:
• Allows you to understand at a glance the variation that exists in a
process
• The shape of the histogram will show process behavior
• Often, it will tell you to dig deeper for otherwise unseen causes of
variation.
• The shape and size of the dispersion will help identify otherwise hidden
sources of variation
• Used to determine the capability of a process
• Starting point for the improvement process
Saturday, 17
February 2024
32. Pareto Charts
Purpose:
Prioritize problems.
How is it done?
Create a preliminary list of
problem classifications.
Tally the occurrences in each
problem classification.
Arrange each classification in
order from highest to lowest
Construct the bar chart
Saturday, 17
February 2024
33. Pareto Charts
Benefits:
Pareto analysis helps
graphically display
results so the
significant few
problems emerge
from the general
background
It tells you what to
work on first
0
20
40
60
80
100
120
Quantity
Defects 104 42 20 14 10 6 4
Dent Scratch Hole Others Crack Stain Gap
Saturday, 17
February 2024
34. Pareto Charts
Weighted Pareto
Weighted Pareto charts use
the quantity of defects
multiplied by their cost to
determine the order.
0
100
200
300
400
500
600
700
800
900
Weighted
Cost
Weighted cost 800 208 100 80 42 14 6
Gap Dent Hole Crack Scratch Others Stain
Defect Total Cost
Weighted
cost
Gap 4 200 800
Dent 104 2 208
Hole 20 5 100
Crack 10 8 80
Scratch 42 1 42
Others 14 1 14
Stain 6 1 6
Pareto Charts
Saturday, 17
February 2024
36. Scatter Diagrams
Purpose:
To identify the correlations that might
exist between a quality characteristic
and a factor that might be driving it
A scatter diagram shows the
correlation between two variables in
a process.
These variables could be a
Critical To Quality (CTQ)
characteristic and a factor
affecting it two factors affecting a
CTQ or two related quality
characteristics.
Dots representing data points are
scattered on the diagram.
The extent to which the dots
cluster together in a line across
the diagram shows the strength
with which the two factors are
Saturday, 17
February 2024
37. Scatter Diagrams
How is it done?:
• Decide which paired factors you want to examine. Both
factors must be measurable on some incremental linear
scale.
• Collect 30 to 100 paired data points.
• Find the highest and lowest value for both variables.
• Draw the vertical (y) and horizontal (x) axes of a graph.
• Plot the data
• Title the diagram
The shape that the cluster of dots takes will tell you something
about the relationship between the two variables that you tested.
Saturday, 17
February 2024
38. Scatter Diagrams
• If the variables are correlated,
when one changes the other
probably also changes.
• Dots that look like they are
trying to form a line are strongly
correlated.
• Sometimes the scatter plot may
show little correlation when all
the data are considered at once.
Stratifying the data, that is,
breaking it into two or
more groups based on
some difference such as
the equipment used, the
time of day, some
variation in materials or
differences in the people
involved, may show
surprising results
Saturday, 17
February 2024
39. Scatter Diagrams
• You may occasionally get scatter
diagrams that look boomerang- or
banana-shaped.
To analyze the strength of the
correlation, divide the scatter plot into
two sections.
Treat each half separately in your
analysis
Benefits:
• Helps identify and test probable causes.
• By knowing which elements of your
process are related and how they are
related, you will know what to control or
what to vary to affect a quality
characteristic.
Saturday, 17
February 2024
41. Control Charts
Purpose:
The primary purpose of a control chart is to
predict expected product outcome.
Benefits:
Predict process out of control and out of
specification limits
Distinguish between specific, identifiable
causes of variation
Can be used for statistical process control
Saturday, 17
February 2024
42. Control Charts
Strategy for eliminating assignable-cause
variation:
Get timely data so that you see the effect of the
assignable cause soon after it occurs.
As soon as you see something that indicates that an
assignable cause of variation has happened, search
for the cause.
Change tools to compensate for the assignable cause.
Strategy for reducing common-cause variation:
Do not attempt to explain the difference between any
of the values or data points produced by a stable
system in control.
Reducing common-cause variation usually requires
making fundamental changes in your process
Saturday, 17
February 2024
43. Control Charts
Control Chart Decision Tree
Determine Sample size (n)
Variable or Attribute Data
Variable is measured on a continuous scale
Attribute is occurrences in n observations
Determine if sample size is constant or changing
Saturday, 17
February 2024
44. Control Charts
Start
X bar , R
X bar, S
IX, Moving Range
p (fraction defective) or
np (number def. Per
sample
p
c (defects per sample
or
u defects per unit
u
Control Chart Decision Tree
Saturday, 17
February 2024
45. Control Charts
What does it look like?
o Adding the element of time
will help clarify your
understanding of the causes
of variation in the processes.
o A run chart is a line graph of
data points organized in time
sequence and centered on the
median data value.
Saturday, 17
February 2024
46. Control Charts
Individual X charts
How is it done?
The data must have a normal distribution (bell curve).
Have 20 or more data points. Fifteen is the absolute
minimum.
List the data points in time order. Determine the range
between each of the consecutive data points.
Find the mean or average of the data point values.
Calculate the control limits (three standard deviations)
Set up the scales for your control chart.
Draw a solid line representing the data mean.
Draw the upper and lower control limits.
Plot the data points in time sequence.
Saturday, 17
February 2024
47. Control Charts
Next, look at the upper and
lower control limits. If your
process is in control, 99.73%
of all the data points will be
inside those lines.
The upper and lower control
limits represent three standard
deviations on either side of the
mean.
Divide the distance between
the centerline and the upper
control limit into three equal
zones representing three
standard deviations.
Saturday, 17
February 2024
48. Control Charts
Search for trends:
Two out of three
consecutive points are in
zone “C”
Four out of five
consecutive points on the
same side of the center
line are on zone “B” or “C”
Only one of 10
consecutive points is in
zone “A”
Saturday, 17
February 2024
49. Control Charts
Basic Control Charts
interpretation rules:
Specials are any points above
the UCL or below the LCL
A Run violation is seven or
more consecutive points above
or below the center (20-25 plot
points)
A trend violation is any upward
or downward movement of
five or more consecutive points
or drifts of seven or more
points (10-20 plot points)
A 1-in-20 violation is more than
one point in twenty consecutive
points close to the center line
Saturday, 17
February 2024
50. SPC Methods-Control Charts
Control Charts show sample data plotted on a graph with CL,
UCL, and LCL
Control chart for variables are used to monitor characteristics
that can be measured, e.g. length, weight, diameter, time
Control charts for attributes are used to monitor characteristics
that have discrete values and can be counted, e.g. % defective,
number of flaws in a shirt, number of broken eggs in a box
Saturday, 17
February 2024
51. Analysis of Patterns on Control Charts
When do you have a problem with your process?
One or more points outside of the control limits
A run of at least seven points (up, down or above or
below center line)
Two or three consecutive points outside the 2-sigma
warning limits, but still inside the control limits
Four or five consecutive points beyond the 1-sigma
limits
An unusual or nonrandom pattern in the data
From Douglas C. Montgomery “Introduction to Statistical Quality Control”
Saturday, 17
February 2024
52. Setting Control Limits
Percentage of values
under normal curve
Control limits balance
risks like Type I error
Saturday, 17
February 2024
53. Hypothesis Tests
Results of hypothesis tests fall into one of
four scenarios:
Type I Error OK
OK Type II Error
Saturday, 17
February 2024
54. Type I and Type II Error
ART and BAF
Type I - ART (Alpha, Reject Ho
when true)
Type II - BAF (Beta, Accept Ho
when false)
Saturday, 17
February 2024
55. Jury Trial vs. Hypothesis Test
Defendant is
Innocent
Jury Trial Hypothesis
Test
Assumption
Standard of Proof
Evidence
Decision
Beyond a
reasonable doubt
Null hypothesis
is true
Facts presented
at trial
Fail to reject
assumption
(not guilty)
or
reject (guilty)
Determined by
Summary
statistics
Fail to reject H0
or
Reject H0 in favor
of Ha
Saturday, 17
February 2024
56. Context?
What does it mean to make a type I error here?
Convict an innocent person of a crime.
What does it mean to make a type II error?
Fail to convict a guilty person.
What do we usually say about type I and type II
error rates in this context?
Saturday, 17
February 2024
57. Control Charts for Variables
Use x-bar and R-bar
charts together
Used to monitor
different variables
X-bar & R-bar Charts
reveal different
problems
In statistical control on
one chart, out of control
on the other chart? OK?
Saturday, 17
February 2024
58. Control Charts for Variables
Use x-bar charts to monitor the
changes in the mean of a process
(central tendencies)
Use R-bar charts to monitor the
dispersion or variability of the process
System can show acceptable central
tendencies but unacceptable variability or
System can show acceptable variability
but unacceptable central tendencies
Saturday, 17
February 2024
59. Graphical Analysis
“A picture is worth a thousand words.”
Graphical analysis is the first step in
analyzing your data. Examples:
Distribution (histogram, dotplot,
boxplot)
Time Series plot for trending
I-chart (for Individual data points)
Normality
Cpk (when applicable) graph (Minitab)
Saturday, 17
February 2024
60. Dotplot of Tensile Test Data
80
75
70
65
60
55
50
CONTROL
Dotplot of CONTROL
Saturday, 17
February 2024
64. Cpk Graph (Minitab)
84
78
72
66
60
54
LSL USL
LSL 65
Target *
USL 85
Sample Mean 71.7151
Sample N 73
StDev(Within) 3.67538
StDev(Overall) 6.4853
Process Data
Cp 0.91
CPL 0.61
CPU 1.20
Cpk 0.61
Pp 0.51
PPL 0.35
PPU 0.68
Ppk 0.35
Cpm *
Overall Capability
Potential (Within) Capability
PPM < LSL 123287.67
PPM > USL 0.00
PPM Total 123287.67
Observed Performance
PPM < LSL 33846.99
PPM > USL 150.42
PPM Total 33997.41
Exp. Within Performance
PPM < LSL 150234.16
PPM > USL 20257.02
PPM Total 170491.18
Exp. Overall Performance
Within
Overall
Process Capability of CONTROL
Saturday, 17
February 2024
65. 65
Process control
( Standardization )
Evaluation of result
Implementation
Develop
Improvement
method
( Solution )
Detecting causes of
problem
Record of facts
Defining the
problem
Identification of
problem
Control
Chart
Scatter
Diagram
Histogra
m
Cause &
Effect
Diagram
Pareto
Diagra
m
Stratifi
cation
Check
sheet
Graphs
Application of QC tools in Problem Solving
Relation :-
Strong Normal
66. Confidence Statements
A confidence statement is used to state the level of
quality of manufactured product. Whether it is
dimensional or pass/fail data, confidence statements
can help to state the quality level achieved by a
process in relation to the specification.
When the true means and standard deviations are
not known, estimates of these parameters such as
sample standard deviations and sample means are
used to make confidence statements based on
tolerance limits using either binomial probabilities or
k-factors.
There are three types of confidence statements that
are primarily used.
Saturday, 17
February 2024
67. Confidence Statements
1. Attribute data confidence statements are used to
state the quality level when data is of a pass/fail
type. A binomial probability is used to calculate a
95% confidence statement that at least x% of the
population will pass the required specification.
2. Two sided confidence statements are used to
describe the quality level of data that has an upper
and lower specification limit. The data is assumed to
come from a normally distributed population. A two
sided tolerance limit table is used for determining
probability levels for percent of population. This
probability is stated as a 95% confidence that at
least x% of the population will be within the
specification.
Saturday, 17
February 2024
68. Confidence Statements
3. One sided confidence statements are used to
describe the quality level of data that has either a
maximum or minimum specification limit. As with the
two sided confidence statement the data is assumed
to be from a normally distributed population. A one
sided tolerance limit table is used for the probability
levels for percent of population in this case. This
probability is stated as a 95% confidence that at
least x% of the population will be either above the
minimum specification or below the maximum
specification.
Saturday, 17
February 2024
69. Confidence Statements
For confidence that data is greater than min spec
Sample mean – K*(sample sd) = min spec
xbar- Ks = min
- Ks = min - xbar
K = (xbar - min)/s
For confidence that data is less than max spec
Sample mean + K*(sample sd) = max spec
xbar + Ks = max
Ks = max - xbar
K = (max - xbar)/s
For two sided tolerance limit both calculations should be made and lowest k-factor
compared with table value.
Saturday, 17
February 2024
71. Confidence Statements
In the case of attribute data sample size will determine the level that is
reached with a confidence statement. The higher the sample size used
(with zero or minimal failures), the higher the percent of population is
when stating the confidence.
Below is a chart showing how sample sizes can effect the 95%
confidence statements:
Percent of Population Defects Sample Size
90 0 30
95 0 60
99 0 300
99.9 0 3,000
99.99 0 30,000
99.999 0 300,000
Saturday, 17
February 2024
72. Sample Size
The following simple formula may be used to estimate sample
size (for any distribution) to determine a sample mean, or
average, when estimates of the standard deviation are known.
2
2
2
B
s
z
n
n represents the sample size to be calculated
z represents the table value for the specified confidence desired
(i.e., z %)
90
( = 1.65, z %)
95
( = 1.96, z %)
99
( = 2.58)
s represents the estimated standard deviation
B represents the bound of the error of estimation, or ½ of the
desired range of accuracy, e.g., if you desire accuracy of x ± 3 psi,
then B = 3 psi.
Saturday, 17
February 2024
73. Sample Size
The following simple formula may be used to estimate sample
size to determine a proportion (fraction) defective.
n= p (1-p) (z / B)
Where:
n represents the sample size to be calculated.
p represents the estimate of the population fraction defective. If no
estimate of p is available, assume worst case of p = 0.5.
z represents the table value for the specified confidence desired
(i.e., z %)
90
( ) = 1.65, z %)
95
( = 1.96, z %)
99
( - 2.58).
B represents the bound of the error of estimation, or ½ of the
desired range of accuracy, e.g., if you desire accuracy of p ± 0.002.
Saturday, 17
February 2024
74. Sample Size
Example: An engineer wants to estimate a sample size to determine the
proportion of unacceptable attributes that may be present in a
manufacturing process, e.g., the number of molded components with
flash present on the parting line.
If a known history of scrap is already present in a similar product, then
that proportion can be used.
If the expected proportion is unknown, then you should use the worst
case, or 0.5 as your estimated proportion.
Let’s say the engineer does not know the proportion and uses 0.5 as the
estimate.
He/she wants to know at 95% confidence what the sample size should
be and is willing to be accurate within ± 0.1.
n = 0.5 (0.5) (1.96/0.1) = 96.04 or rounded up, 97
Saturday, 17
February 2024
75. Process Capability
Process Capability Study is an approach to determine the
inherent variability of each process, sub-process, and piece of
equipment.
This study provides a method to compare the relationship
between the variability of the process and the tolerance range
to assure that the process is capable of achieving the
tolerance window.
Typically process capability studies occur in five stages;
(1) process characterization,
(2) metrology characterization,
(3) capability determination,
(4) optimization or reduction of variability, and
(5) preventive control.
The two standard methods for measuring process capability are Cp
and CpK.
Saturday, 17
February 2024
76. Process Capability
Cp: Process Cp is a numeric index that represents the inherent
capability of a process to meet the requirements of the
tolerance range without respect to centeredness. It represents
precision, and is calculated as follows:
6
LSL
USL
Cp
Where:
USL= The Upper Specification Limit
LSL = The Lower Specification Limit
σ = The population standard deviation
Saturday, 17
February 2024
77. Process Capability
Cp represents the precision, but not the
accuracy of the process in respect to the
tolerance window.
High Accuracy but low
precision
High Precision but low
Accuracy
Saturday, 17
February 2024
78. Process Capability
The 6 is estimated from the process, and is
more accurate as the sample size gets larger.
Decisions about process capability may not be
valid with data from a single run, and when
possible, should be based on data from 2 or
more runs.
Cp is only valid when the distribution of the
data is statistically normal.
Outliers, bimodal tendencies and skewness may
lower the Cp value.
Saturday, 17
February 2024
79. Process Capability
CpK: Process Cpk is a numeric index that represents the ability
of the process to manufacture parts that are within
specification. It represents accuracy. Cpk provides a numeric
index that focuses on the centeredness of the process on the
tolerance window. Cpk is the smallest resulting ratio of the
following two (2) equations:
S
LSL
x
Cpk
3
S
x
USL
Cpk
3
USL = The upper specification limit
LSL = The lower specification limit
= The product related process mean.
s = The product related standard deviation
x
x
x
x
Saturday, 17
February 2024
80. Process Capability
A machine or process is sometimes referred to as being
capable when its Cpk has a minimum value of one (1.00) and
when process stability has been proven.
A Cpk equal to one (1.00) implies that 99.73% of the product
is within specification limits, provided that the process is
stable. However, it should be noted that if the machine
capability is only 1.0, it will be impossible to maintain a Cpk of
1.0 or higher.
The goal should be a Cp as high as possible.
It is possible for a process to have a high Cp, but a low Cpk, if
the process is not centered in the tolerance window. A Cpk of
1.33 or higher should be targeted.
Saturday, 17
February 2024
81. CpK
A CpK of 1.33 means that the difference between the
mean and specification limit is 4σ (since 1.33 is 4/3).
With a CpK of 1.33, 99.994% of the product is
within the within specification.
Similarly a CpK of 2.0 is 6σ between the mean and
specification limit (since 2.0 is 6/3).
With a CpK of 2.0 99.9999998% of the product is
within specification.
Saturday, 17
February 2024
82. Acceptance Sampling
Definition: the third branch of SQC refers to the
process of randomly inspecting a certain number of
items from a lot or batch in order to decide whether to
accept or reject the entire batch
Different from SPC because acceptance sampling is
performed either before or after the process rather
than during
Sampling before typically is done to supplier material
Sampling after involves sampling finished items before shipment
or finished components prior to assembly
Used where inspection is expensive, volume is high, or
inspection is destructive
Saturday, 17
February 2024
83. Acceptance Sampling Plans
Goal of Acceptance Sampling plans is to determine the criteria
for acceptance or rejection based on:
Size of the lot (N)
Size of the sample (n)
Number of defects above which a lot will be rejected (c)
Level of confidence we wish to attain
There are single, double, and multiple sampling plans
Which one to use is based on cost involved, time consumed, and cost of
passing on a defective item
Can be used on either variable or attribute measures, but more
commonly used for attributes
Saturday, 17
February 2024
84. Acceptance Sampling Plans
ANSI/ASQC Z1.4 (Attribute or P/F Data)
ANSI/ASQC Z1.9 (Variable Data)
C=0 (Attribute, reject on 1)
MIL STD 1235C (Continuous
Production)
Saturday, 17
February 2024
89. Acceptance Sampling Plans
• As mentioned acceptance sampling can reject “good” lots and accept “bad”
lots. More formally:
Producers risk refers to the probability of rejecting a good lot. In order to
calculate this probability there must be a numerical definition as to what
constitutes “good”
– AQL (Acceptable Quality Limit) - the numerical definition of a good lot. The
ANSI/ASQC standard describes AQL as “the maximum percentage or proportion
of nonconforming items or number of nonconformities in a batch that can be
considered satisfactory as a process average”
• Consumers Risk refers to the probability of accepting a bad lot where:
– LTPD (Lot Tolerance Percent Defective) - the numerical definition of a bad lot
described by the ANSI/ASQC standard as “the percentage or proportion of
nonconforming items or noncomformities in a batch for which the customer
wishes the probability of acceptance to be a specified low value.
Saturday, 17
February 2024
91. Implications for Managers
How much and how often to inspect?
Consider product cost and product volume
Consider process stability
Consider lot size
Where to inspect?
Inbound materials
Finished products
Prior to costly processing
Which tools to use?
Control charts are best used for in-process production
Acceptance sampling is best used for inbound/outbound
Saturday, 17
February 2024
92. SQC Across the Organization
SQC requires input from other organizational
functions, influences their success, and are actually
used in designing and evaluating their tasks
Marketing – provides information on current and future
quality standards
Finance – responsible for placing financial values on SQC
efforts
Human resources – the role of workers change with SQC
implementation. Requires workers with right skills
Information systems – makes SQC information accessible for
all.
Saturday, 17
February 2024
