Transcript Additional SPC for Variables

Additional SPC for
Variables
EBB 341
Additional SPC?
 Provides information on continuous and
batch processes, short runs, and gage
control.
Continuous Processes
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The best example is paper-making
process.
Paper-making machines:
wood chips wood pulp washed
treated refined
wet mat roller
drying
Batch Chart
 Traditional SPC methods assume that
process data follow a normal curve
distribution.
 Many real-world processes, however, don’t
obey this convenient assumption.
 The semiconductor industry is very familiar
with non-normal, skewed distributions for
impurities and particle counts.
Batch Chart
 It also uses many batch processes that
involve nested variation sources.
 For example, vacuum chambers and
furnaces apply thin coatings of metals or
insulators to batches of silicon wafers.
 We expect the wafers in each batch or lot to
see the same process conditions, but these
conditions will vary randomly from batch to
batch.
Batch Chart
 Statistician D. Wheeler explains the danger
of lumping data together and using its
collective mean and standard deviation to
set control limits.
 By using this “wrong” method can lead to
burying the signals contained in the data,
and the process seems to be in control.
Batch Chart
 Consider a heat treatment process for metal
parts or plastic products for example, polymer
curing.
 A properly functioning furnace will subject all
the pieces in a batch to the same
tempemperature for the same time.
 Unavoidable random temperature fluctuations
within the furnace causes within-batch variation.
 Random differences between the conditions for
each batch also will occur.
 Thus there are two variance components: within
run and between run.
Statistical model for a batch
process
 Here is the model for a batch process with
only one level of nesting.
 The ith batch’s mean, µi is a random
sample from the overall process.
 Pieces from the ith batch, xij are then
random observations from this batch.
 Equation Set 1--Statistical model for a batch process:
 Equation Set 2-- Isolation of variance components:
The procedure for nonconstant
sample sizes
 MSE and MST are the mean squares for errors and
treatments, respectively.
 Table 1 shows the data
 Next, use MSE (within groups) and MST
(between groups) to find the variance
components:
 Many industrial processes do not obey the
basic assumptions behind traditional SPC.
 Practitioners should account for the process’s
nature before developing control charts.
 One-sided speci. limits (e.g., for impurities) are
a clue that the data may be non-normal.
 Batch operations usually have nested variation
sources.
 Techniques exist for assessing such nonideal
data and setting control limits.
 Selection of the right model, however, depends
on a proper understanding of the
manufacturing process.
 Within batch variation is stable as reflected
by the R chart
 Out-of-control condition reflected in X-bar
chart indicates that there is significant
variation between batches.
 Since charts are in control, calculate between batch
variation.
 Percentage contribution to total variation:
 Eliminating between batch variation would
leave:
 Assume a 6σ natural tolerance and a perfectly
centered process:
Lower process limit = 500-3(86.74) = 240
We are still well below the lower specification of
300.
 Within batch variation must also be reduced.
Short Run Charts
 What is a short run?
 Short run problems:
 Not enough parts in a single run to establish
control limits.
 Process cycles so quickly that run are over
berfore data can be gathered.
 Many different parts are made for many
different customers.
 Remember: SPC is not about parts, it’s
about the process!
Short Run Charts
 The short run control chart, or control chart
for short production runs, plots observations
of variables or attributes for multiple parts on
the same chart.
 Short run control charts were developed to
address the requirement that several dozen
measurements of a process must be
collected before control limits are calculated.
For example:
 A paper mill may produce only 3 or 4 rolls of a
particular kind of paper and then shift
production to another kind of paper.
 If variables, such as paper thickness, are
monitored for several dozen rolls of paper,
control limits for thickness could be calculated
for the transformed variable values of interest.
 These transformations will rescale the variable
values such that they are of compatible
magnitudes across the different short production
runs (or parts).
For example …
 The control limits computed for those
transformed values could then be applied in
monitoring thickness, regardless of the types of
paper being produced.
 SPC procedures could be used to determine if
the production process is in control, to monitor
continuing production, and to establish
procedures for continuous quality
improvement.
Short Run Charts for Variables
 The types of short run charts:
 The most basic are the nominal short run chart,
and the target short run chart.
 Measurements for each part are transformed by
subtracting a part-specific constant.
 These constants can either be the nominal values
for the respective parts or they can be target
values computed from the means for each part
(Target X-bar and R chart).
Short Run Charts for Variables
 For example, the diameters of piston
bores for different engine blocks
produced in a factory can only be
meaningfully compared (for determining
the consistency of bore sizes) if the mean
differences between bore diameters for
different sized engines are first removed.
 The nominal or target short run chart
makes such comparisons possible.
Specification chart
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Assume that the specifications call for 25.00
± 0.12 mm. Then the CL = 25.00. The USLLSL = 0.24 mm, Cp = 1.00.
Thus
Cp = (USL-LSL)/(6 sigma)
Sigma = (USL-LSL)/(6Cp)
 Sigma = (25.12-24.88)/6(1.00) = 0.04
For n = 4
USLX  X o  A
= 25.00 + 1.500(0.04) = 25.06
LSLX  X o  A
= 25.00 - 1.500(0.04) = 24.94
 Ro = d2 = (2.059)(0.04) = 0.08
UCLR = D2 = (4.698)(0.04) = 0.19
LCLR = D1 = (0)(0.04) = 0
Deviation chart
 Deviation from target:
– Record different between measured
value and target value.