Additional SPC for Additional SPC for VariablesVariables

EBB 341EBB 341

Additional SPC?Additional SPC?

Provides information on continuous and Provides information on continuous and batch processes, short runs, and gage batch processes, short runs, and gage control.control.

Continuous ProcessesContinuous Processes

The best example is paper-making The best example is paper-making process.process.

Paper-making machines:Paper-making machines:

wood chips wood pulp washedwood chips wood pulp washed

treated refined wet mat rollertreated refined wet mat roller

dryingdrying

Batch ChartBatch Chart

TTraditional SPC methods assume that raditional SPC methods assume that process data follow a normal curve process data follow a normal curve distribution. distribution.

Many real-world processes, however, don’t Many real-world processes, however, don’t obey this convenient assumption. obey this convenient assumption.

The semiconductor industry is very familiar The semiconductor industry is very familiar with non-normal, skewed distributions for with non-normal, skewed distributions for impurities and particle counts.impurities and particle counts.

Batch ChartBatch Chart

It also uses many batch processes that It also uses many batch processes that involve nested variation sources. involve nested variation sources.

For example, vacuum chambers and For example, vacuum chambers and furnaces apply thin coatings of metals or furnaces apply thin coatings of metals or insulators to batches of silicon wafers.insulators to batches of silicon wafers.

We expect the wafers in each batch or lot to We expect the wafers in each batch or lot to see the same process conditions, but these see the same process conditions, but these conditions will vary randomly from batch to conditions will vary randomly from batch to batch.batch.

Batch ChartBatch Chart

Statistician Statistician D. WheelerD. Wheeler explains the danger explains the danger of lumping data together and using its of lumping data together and using its collective collective mean and standard deviation tomean and standard deviation to set control limits.set control limits.

By using this By using this “wrong”“wrong” method can lead to method can lead to burying the signals contained in the data, burying the signals contained in the data, and the process seems to be in control. and the process seems to be in control.

Batch ChartBatch Chart Consider a heat treatment process for Consider a heat treatment process for

metal parts or plastic products for example, metal parts or plastic products for example, polymer curing. polymer curing.

A properly functioning furnace will subject A properly functioning furnace will subject all the pieces in a batch to the same all the pieces in a batch to the same tempemperature for the same time. tempemperature for the same time.

Unavoidable random temperature Unavoidable random temperature fluctuations within the furnace causes fluctuations within the furnace causes within-batch variation. within-batch variation.

Random differences between the conditions Random differences between the conditions for each batch also will occur. for each batch also will occur.

Thus there are two variance components: Thus there are two variance components: within run and between run.within run and between run.

Statistical model for a batch Statistical model for a batch processprocess

Here is the model for a batch process Here is the model for a batch process with only one level of nesting. with only one level of nesting.

TheThe ith ith batch’s mean, batch’s mean, µµii is a random is a random sample from the overall process. sample from the overall process.

Pieces from the Pieces from the ithith batch, batch, xxijij are then are then random observations from this batch.random observations from this batch.

Equation Set 1--Equation Set 1--Statistical model for a batch Statistical model for a batch process:process:

Equation Set 2--Equation Set 2-- Isolation of variance components: Isolation of variance components:

The procedure for nonconstant The procedure for nonconstant sample sizes sample sizes

MSE and MST are the mean squares for errors and MSE and MST are the mean squares for errors and treatments, respectively.treatments, respectively.

  Table 1 shows the data Table 1 shows the data

Next, use MSE (within groups) and MST Next, use MSE (within groups) and MST (between groups) to find the variance (between groups) to find the variance components:components:

Many industrial processes do not obey Many industrial processes do not obey the basic assumptions behind traditional the basic assumptions behind traditional SPC. SPC.

Practitioners should account for the Practitioners should account for the process’s nature before developing process’s nature before developing control charts. control charts.

One-sided speci. limits (e.g., for One-sided speci. limits (e.g., for impurities) are a clue that the data may impurities) are a clue that the data may be non-normal. be non-normal.

Batch operations usually have nested Batch operations usually have nested variation sources. variation sources.

Techniques exist for assessing such Techniques exist for assessing such nonideal data and setting control limits. nonideal data and setting control limits.

Selection of the right model, however, Selection of the right model, however, depends on a proper understanding of depends on a proper understanding of the manufacturing process.the manufacturing process.

Within batch variation is stable as reflected Within batch variation is stable as reflected by the R chartby the R chart

Out-of-control condition reflected in X-bar Out-of-control condition reflected in X-bar chart indicates that there is significant chart indicates that there is significant variation between batches.variation between batches.

Since charts are in control, calculate between batch Since charts are in control, calculate between batch variation.variation.

Percentage contribution to total variation:Percentage contribution to total variation:

Eliminating between batch variation would Eliminating between batch variation would leave:leave:

Assume a 6σ natural tolerance and a perfectly Assume a 6σ natural tolerance and a perfectly centered process:centered process:Lower process limit = 500-3(86.74) = 240 Lower process limit = 500-3(86.74) = 240 We are still well below the lower specification of We are still well below the lower specification of

300. 300.

Within batch variation must also be reduced.Within batch variation must also be reduced.

Short Run ChartsShort Run Charts

What is a short run?What is a short run? Short run problems:Short run problems:

Not enough parts in a single run to establish Not enough parts in a single run to establish control limits.control limits.

Process cycles so quickly that run are over Process cycles so quickly that run are over berfore data can be gathered.berfore data can be gathered.

Many different parts are made for many different Many different parts are made for many different customers.customers.

Remember: SPC is not about parts, it’s about Remember: SPC is not about parts, it’s about the process!the process!

Short Run ChartsShort Run Charts

The short run control chart, or control chart The short run control chart, or control chart for short production runs, plots observations for short production runs, plots observations of variables or attributes for multiple parts on of variables or attributes for multiple parts on the same chart. the same chart.

Short run control charts were developed to Short run control charts were developed to address the requirement that several dozen address the requirement that several dozen measurements of a process must be measurements of a process must be collected before control limits are calculated. collected before control limits are calculated.

For example:For example: A paper mill may produce only 3 or 4 rolls A paper mill may produce only 3 or 4 rolls

of a particular kind of paper and then shift of a particular kind of paper and then shift production to another kind of paper. production to another kind of paper.

If variables, such as If variables, such as paper thicknesspaper thickness, are , are monitored for several dozen rolls of paper, monitored for several dozen rolls of paper, control limits for thickness could be control limits for thickness could be calculated for the calculated for the transformedtransformed variable variable values of interest. values of interest.

These These transformationstransformations will rescale the will rescale the variable values such that they are of variable values such that they are of compatible magnitudes across the compatible magnitudes across the different short production runs (or parts). different short production runs (or parts).

For example …For example … The control limits computed for those The control limits computed for those

transformed values could then be applied transformed values could then be applied in monitoring thickness, regardless of the in monitoring thickness, regardless of the types of paper being produced. types of paper being produced.

SPC procedures could be used to SPC procedures could be used to determine if the production process is in determine if the production process is in control, to monitor continuing production, control, to monitor continuing production, and to establish procedures for and to establish procedures for continuous quality improvement. continuous quality improvement.

Short Run Charts for Variables Short Run Charts for Variables

The types of short run charts: The types of short run charts: The most basic are the The most basic are the nominalnominal short run short run

chart, and the chart, and the targettarget short run chart. short run chart. Measurements for each part are transformed Measurements for each part are transformed

by subtracting a part-specific constant. by subtracting a part-specific constant. These constants can either be the nominal These constants can either be the nominal

values for the respective parts or they can be values for the respective parts or they can be target values computed from the means for target values computed from the means for each part (each part (Target X-bar and R chartTarget X-bar and R chart). ).

Short Run Charts for VariablesShort Run Charts for Variables

For example, the diameters of piston For example, the diameters of piston bores for different engine blocks bores for different engine blocks produced in a factory can only be produced in a factory can only be meaningfully compared (for determining meaningfully compared (for determining the consistency of bore sizes) if the the consistency of bore sizes) if the mean differences between bore mean differences between bore diameters for different sized engines are diameters for different sized engines are first removed. first removed.

The nominal or target short run chart The nominal or target short run chart makes such comparisons possible. makes such comparisons possible.

Specification chartSpecification chart

Assume that the specifications call for Assume that the specifications call for 25.00 25.00 ± 0.12 mm. Then the CL = 25.00. ± 0.12 mm. Then the CL = 25.00. The USL-LSL = 0.24 mm, CThe USL-LSL = 0.24 mm, Cpp = 1.00. = 1.00.

ThusThus

CCpp = (USL-LSL)/(6 sigma) = (USL-LSL)/(6 sigma)

Sigma = (USL-LSL)/(6CSigma = (USL-LSL)/(6Cpp))

Sigma = (25.12-24.88)/6(1.00) = 0.04Sigma = (25.12-24.88)/6(1.00) = 0.04

For n = 4For n = 4

= 25.00 + 1.500(0.04) = 25.06 = 25.00 + 1.500(0.04) = 25.06

= 25.00 - 1.500(0.04) = 24.94 = 25.00 - 1.500(0.04) = 24.94

RRoo = d = d22 = (2.059)(0.04) = 0.08 = (2.059)(0.04) = 0.08

UCLUCLRR = D = D22 = (4.698)(0.04) = 0.19 = (4.698)(0.04) = 0.19

LCLLCLRR = D = D11 = (0)(0.04) = 0 = (0)(0.04) = 0

AXLSL oX

AXUSL oX

Deviation chartDeviation chart

Deviation from target:Deviation from target:– Record different between measured Record different between measured

value and target value.value and target value.