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Sampling Techniques
by
Variables
Assoc. Prof. Ir. Dr. Cheong Kuan Yew
School of Materials & Mineral Resources Engineering
Engineering Campus
Universiti Sains Malaysia
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Topic Outcome: At the end of this topic, students will be able to:
Discuss the advantages and disadvantages of
variable sampling.
Describe the Shainin Lot Plot Plan.
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Outline:
An Introduction.
Types of Sampling Plan.
- Shainin Lot Plot Plan.
- ANSI/ASQ Z1.9
Variability Unknown
Standard Deviation Method
Range Method
Variability known
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An Introduction When a quality characteristic is measurable on a
continuous scale, and is know to have a distribution of aspecific type (e.g. normal distribution); it is possible to use
a sampling based on sample measurements such as:
Mean and
Standard Deviation.
Variables Sampling Plans.
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Population
Sample
LSL USL
LSL USL
Compare
Compare to required Quality LevelACCEPT REJECT
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Percent nonconforming below and above specifications.
LSL USL
pu
+g-gpL
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Advantages of Variable Sampling Plan:
Same protection with smaller sample size.
Feedback of data on Process.
Extent of conformity given weightage.
Errors in measurement more likely detected.
Disadvantages of Variable Sampling Plan: Applicable to only one quality characteristic at a time.
Higher inspection cost Measurement.
Higher clerical cost Calculation.
Possibility of no nonconformity in a rejected lot.
Dependence on assumption of distribution shape.
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Types of Variable Sampling Plan
Variable Sampling Plan
Percent nonconforming Process Parameter
To determine the
proportion of product that
is outside specification
To control the averageand standard deviation of
the distribution of the
product to specified level
E.g.:Shainin lot plot
ANSI/ASQ Z1.9-1993
E.g.:Shainin lot plot
ANSI/ASQ Z1.9-1993
E.g.:Acceptance control chart
Sequential sampling for variable
Hypothesis testing
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Shainin Lot Plot Plan
Developed by Dorian Shainin (Hamilton Standard Division
of United Aircraft Corporation, 1950).
The plan uses a plotted frequency distribution
(histogram) to evaluate a sample for decisions
(accept/reject a lot).
It is a practical plan forin-house inspection & receiving
inspection.
Advantages:
Applicable to both normal and non-normal frequency
distributions.
Simple to use.
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The method for obtaining the lot plots is as follows: A random sample of 10 subgroups (g) of 5 each for a
total of 50 items is obtained from the lot.
The average, X-bar and range, R, are calculated for
each subgroup.
A histogram is constructed (number of cell: 7-16).
Calculate the average of averages, X-double bar, and
average of ranges, R-bar. Calculate the upper and lower lot limits (ULL & LLL)
Lot Plotting Method
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Q&A
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9.957.973
5.99326.2
)37.1)(3(
7.97
3
326.2
)37.1)(3(
2
2
!!!
!!!
d
RXLLL
d
R
XULL
37.110
7.13
7.9710
8.976
!!
!
!!
!
g
RR
g
XX
Chart for Ranges:
Factor for Central Line d2
3Wcontrol
limits
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Fig 10-14: Lot plot histogram
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Decision is based on a comparison of the lot plot with 11
different types of lot plots.
Lot Plot Evaluation
Type Distribution Comments
1
normal
-within spec.limits
- accepted without calculate lot limits.
2-lot limits within spec. limits.
-accept.3 -lot limits outside spec. limits.
-percentage of product beyond spec is obtained.
-Review board determines the final disposition of the stock.4
5nonnormal
skrewed
6 Lot was screened & sorted
7 Bimodal condition
8nonnormal Lot was screened & sorted
9
10 Bimodal condition
11 Stray values
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Once learned, the lot plot procedure is relatively simple and
has resulted in improved quality and lower inspectioncost.
Unacceptable lots are returned to the producer, and this
action will cause a subsequent improvement in quality.
Inspectors can accept lots; however, disposition of
unsatisfactory lots is left to a material-review board.
Many users of the lot plot method have modified the Shainin
method for their own situation.
The majorcriticism of the plan is that the shape of the plot
does not always give an accurate indication of the truedistribution. Shainin states that the plot is close enough to
have no practical effect on the final decision, or if there are
any errors, they are in a safe direction.
Summary
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End