Quality Part 2

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Statistical Control of Product Quality 2 possible approaches:

1.statistical process control (SPC) 2.acceptance sampling (inspection)

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SPC is preferable to acceptance sampling where possible:

1.Prevention, rather than detection 2. More timely feedback 3.Inspection is a non-value-adding activity, but it costs a firm time and money

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acceptance sampling

applies statistical sampling techniques to the decision whether to 1.“accept” a production lot (and pass it on to the customer) or 2.to “reject” a production lot (and either scrap the lot or sort the lot and rework the defective parts)

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random sampling

every unit in the population (production lot) has an equal chance of being included in the sample

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any time we rely on sample information to make a decision about an entire lot, there is

some margin for error

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two possible types of errors in acceptance sampling

1.accept a “bad” lot (consumer’s risk,Beta symbol) 2. Reject a “good” lot (producer’s risk,alpha symbol)

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Statistical Process Control Basic idea:

control process parameters and the product will take care of itself

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Statistical Process Control Primary tools:

1. process control charts 2.developed by Shewhart 3.signal the operator when “special cause” variation is present (i.e., the process is out of control)

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sources of “special cause” variation:

1.equipment – tool wear, machine vibrations, electrical fluctuations 2. material – thickness, moisture content 3. environment – temperature, light, humidity 4.operator – physical and emotional well-being, lack of understanding

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Statistical Process Control Types of control charts:

1.variables data – a precise measurement of some physical dimension is taken 2.attributes data – the number or proportion of units with some characteristic is tracked

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variables data – kinds of charts

1. X and R charts 2. X and s charts

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attributes data – kinds of charts

1. p chart 2. c chart

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Steps 1-4 Constructing X and R Charts

1.Choose sampling plan 2.Calculate the range (R) and the mean (X) for each sample 3.Calculate the average range (R) and the grand mean (X) for all samples 4.Calculate the average range (R) and the grand mean (X) for all samples

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Step 1 - considerations for choosing the sampling plan

1.at least 25-30 samples (more is better) 2.sample typically includes 4-5 units of product 3.critical for process to be “in control” when the data is collected for charts 4.Outliers for which the cause is known are thrown out

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constructing X and R Charts - use the Control Chart Factors Table

table will lead to control limits approximately three standard deviations from the centerline values

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See slides 11-16 for Constructing X and R Charts: An Example

example

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See slides 17-20 for Control Chart Factors Table, Control Limit Calculations. Set up Control Charts and Track process as production occurs

example

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statistical process control - sp.c.v. means special cause variation

1.control charts monitor output of process so we know if sp.c.var. is present 2.sp.c. var. suspected when non-randomness in data 3.if sp.c.var. present, identify & eliminate the cause of variation-prevent recurrence of the problem-process improvement

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non-randomness in the data:

1.“runs” of values steadily above or below the center line 2.upward or downward trend 3.periodicity 4.any points outside the control limits

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tolerance limits

tell us whether a particular item is acceptable or defective (e.g., 3.000”  0.002”)

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control limits

control limits – allow us to track process mean and variation over time; no individual item measurements are recorded

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tolerance limits and control limits

1. are not the same 2.so, a process could be in control but have low capability (i.e., producing too many defects) or could be out of control and producing no defects

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Controlling Process Variation - 5 things to consider

1.some level of variation in all processes 2.How much process variation is too much? 3.How do we measure amount of process variation? 4.determine if process is highly capable 5. higher process capability, consistently high quality products

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Controlling Process Variation some level of variation is inherent in all processes – really, no such thing as two “identical” products How much process variation is too much?

1.it depends on how much the critical dimensions of the product are allowed to vary without affecting product performance – a design issue 2.EX.: product specifications or tolerance limits for ruler length 12.000” ± 0.002”

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How do we measure the amount of process variation?

for a stable process, we can measure the standard deviation of the critical dimensions of the output (product) A higher process capability will lead to more consistently high quality products

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high process capability A higher process capability will lead to more consistently high quality products

if the amount of variation inherent in the process is small relative to the allowable variation in the product

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formula for process capability

process capability equals acceptable variation divided by actual variation

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some level of variation in all processes

no two identical products

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Process Capability Example (See slide 25) and HANDOUT from 11.06

check it out

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