PROCESS CAPABILITY ANDSPC
Chapter 9A
1.Explain what statistical quality control is.
2.Calculate the capability of a process.
3.Understand how processes are monitored withcontrol charts.
OBJECTIVES
9A-2
Types of Situations where SPC can beApplied
How many paint defects are there in the finish of acar?
How long does it take to execute market orders?
How well are we able to maintain the dimensionaltolerance on our ball bearing assembly?
How long do customers wait to be served from ourdrive-through window?
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Basic Forms of Variation
Assignable variation iscaused by factors thatcan be clearly identifiedand possibly managed
Common variation isinherent in theproduction process
Example: A poorly trainedemployee that createsvariation in finishedproduct output.
Example: A poorly trainedemployee that createsvariation in finishedproduct output.
Example: A moldingprocess that always leaves“burrs” or flaws on amolded item.
Example: A moldingprocess that always leaves“burrs” or flaws on amolded item.
9A-4
Testing examples
Taguchi’s View of Variation
Traditional view is that quality within the range isgood and that the cost of quality outside this rangeis constant
Taguchi views costs as increasing as variabilityincreases, so seek to achieve zero defects and thatwill truly minimize quality costs
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Process Capability
Taguchi argues that tolerance is not a yes/nodecision, but a continuous function
Other experts argue that the process should be sogood the probability of generating a defect shouldbe very low
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Types of Statistical Sampling
Attribute (Go or no-go information)
Defectives refers to the acceptability ofproduct across a range of characteristics.
Defects refers to the number of defects perunit which may be higher than the numberof defectives.
p-chart application
Variable (Continuous)
Usually measured by the mean and thestandard deviation.
X-bar and R chart applications
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Statistical
Process
Control
(SPC) Charts
UCL
LCL
Samplesover time
1 2 3 4 5 6
UCL
LCL
Samplesover time
1 2 3 4 5 6
UCL
LCL
Samplesover time
1 2 3 4 5 6
Normal Behavior
Normal Behavior
Possible problem, investigate
Possible problem, investigate
Possible problem, investigate
Possible problem, investigate
9A-9
Control Limits are based on the Normal Curve
x
0
1
2
3
-3
-2
-1
z
Standarddeviationunits or “z”units.
Standarddeviationunits or “z”units.
9A-10
Control Limits
We establish the Upper Control Limits (UCL)and the Lower Control Limits (LCL) with plusor minus 3 standard deviations from some x-bar or mean value. Based on this we canexpect 99.7% of our sample observations tofall within these limits.
x
LCL
UCL
99.7%
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Process Control with AttributeMeasurement: Using ρ Charts
Created for good/bad attributes
Use simple statistics to create the controllimits
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Example of Constructing a p-Chart:Required Data
Sample
No.
No. of
Samples
Number ofdefects foundin each sample
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1. Calculate thesample proportions,p (these are whatcan be plotted on thep-chart) for eachsample
1. Calculate thesample proportions,p (these are whatcan be plotted on thep-chart) for eachsample
Example of Constructing a p-chart: Step 1
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2. Calculate the average of the sample proportions
2. Calculate the average of the sample proportions
3. Calculate the standard deviation of thesample proportion
3. Calculate the standard deviation of thesample proportion
Example of Constructing a p-chart: Steps 2&3
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4. Calculate the control limits
4. Calculate the control limits
UCL = 0.0924
LCL = -0.0204 (or 0)
UCL = 0.0924
LCL = -0.0204 (or 0)
Example of Constructing a p-chart: Step 4
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Example of Constructing a p-Chart: Step 5
5. Plot the individual sample proportions, the average
of the proportions, and the control limits
5. Plot the individual sample proportions, the average
of the proportions, and the control limits
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How to Construct x and R Charts
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Example of x-bar and R Charts:Required Data
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Example of x-bar and R charts: Step 1. Calculate sample means, sample ranges,mean of means, and mean of ranges.
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Example of x-bar and R charts: Step 2. Determine Control Limit Formulas andNecessary Tabled Values
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Example of x-bar and R charts: Steps 3&4. Calculate x-bar Chart and Plot Values
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Then plot both graphs: Means tothe Mean chart and Ranges to theRange chart.Then plot both graphs: Means tothe Mean chart and Ranges to theRange chart.
ANY QUESTIONS?
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