Irwin/McGraw-Hill 1 TN7: Basic Forms of Statistical Sampling for Quality Control Acceptance Sampling: Sampling to accept or reject the immediate lot of product at hand. Statistical Process Control (SPC): Sampling to determine if the process is within acceptable limits.
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Irwin/McGraw-Hill 1 TN7: Basic Forms of Statistical Sampling for Quality Control Acceptance Sampling: Sampling to accept or reject the immediate lot of.
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Irwin/McGraw-Hill1
TN7: Basic Forms of Statistical Sampling for Quality Control
Acceptance Sampling: Sampling to accept or reject the immediate lot of product at hand.
Statistical Process Control (SPC): Sampling to determine if the process is within acceptable limits.
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Acceptance Sampling Purposes
Determine quality level Ensure quality is within predetermined level
Lot received for inspection
Sample selected and analyzed
Results compared with acceptance criteria
Accept the lot
Send to production or to customer
Reject the lot
Decide on disposition
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Basic Forms of Variation - SPC
Assignable variation is caused by factors that can be clearly identified and possibly managed.
Common variation is inherent in the production process.
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Control Limits are based on the Normal Curve
x
0 1 2 3-3 -2 -1z
Standard deviation units or “z” units.
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Control LimitsIf we establish control limits at +/- 3 standard deviations, then
we would expect 99.7% of our observations to fall within these limits
xLCL UCL
See Exhibit S6.3 for other evidence prompting investigation
StatisticalProcessControl
UCL
LCL
UCL
LCL
UCL
LCL
UCL
LCL
Samples over time
1 2 3 4 5 6
UCL
LCL
Samples over time
1 2 3 4 5 6
UCL
LCL
Samples over time
1 2 3 4 5 6
Normal Behavior
Possible problem, investigate
Possible problem, investigate
Statistical Process Control (SPC) Charts
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Statistical Sampling--Data
Attribute (Go no-go information) Defectives Defects Typically use sample size of 50-100
Variable (Continuous) Usually measured by the mean and the
standard deviation Typically use sample size of 2 to 10
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Statistical Process Control:Attribute Measurements (P-Charts)
p =Total Number of Defectives
Total Number of Observations
nS
)p-(1 p = p
UCL = p + Z
LCL = p - Z p
p
s
s
Where Z is equal to the number of Standard Deviations
1. Calculate the sample proportion, p, for each sample.
If you treat special causes like common causes, you lose an opportunity to track down and eliminate something specific that is increasing variation in your process.If you treat common causes like special causes, you will most likely end up increasing variation (called “tampering”).Taking the wrong action not only doesn’t improve the situation, it usually makes it worse.
Matching Action to the Type of Variation
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Quarterly Audit Scores
1 2 3 4 5
···
··
Score
Quarter
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Quarterly Audit Scores
1 2 3 4 5
···
··
Score
Quarter
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Quarterly Audit Scores
1 2 3 4 5
···
·Score
··
··
···· ·· ·
· · ·
·O
O
O
O
O · ·····
···
·
·
···
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Process Capability Process limits (The “Voice of the Process” or The
“Voice of the Data”) - based on natural (common cause) variation
Tolerance limits (The “Voice of the Customer”) – customer requirements
Process Capability – A measure of how “capable” the process is to meet customer requirements; compares process limits to tolerance limits
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Process Capability
natural variation
specification
(a)
specification
natural variation
(b)
specification
natural variation
(c)
specification
natural variation
(d)
Evans and Lindsay The Management and Control of Quality, Southwestern Books.
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Process Capability Index, Cpk
3
X-UTLor
3
LTLXmin=Cpk
Capability Index - shows how well parts being produced fit into design limit specifications.
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Interpreting the Cpk
Cpk < 1 Not Capable
Cpk = 1 Capable at 3
Cpk = 1.33 Capable at 4
Cpk = 1.67 Capable at 5
Cpk = 2 Capable at 6
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Process Capability Index, Cpk
Find the Cpk for the following:
A process has a mean of 50.50 and a variance of 2.25. The product has a specification of 50.00 ± 4.00.
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Is 99% Good Enough?
22,000 checks will be deducted from the wrong bank accounts in the next 60 minutes.
20,000 incorrect drug prescriptions will be written in the next 12 months.
12 babies will be given to the wrong parents each day.