Egekwu-211 2 Statistical Quality Control/Statistical Process Control u Acceptance Sampling –...
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Transcript of Egekwu-211 2 Statistical Quality Control/Statistical Process Control u Acceptance Sampling –...
Egekwu-2112
Statistical Quality Control/Statistical Process Control
Acceptance Sampling– Operating Characteristic Curve
Process Control Procedures– Variable data– Attribute or Characteristic data
Process Capability
Egekwu-2113
Basic Forms of Statistical Sampling for Quality Control
Sampling to accept or reject the immediate lot of product at hand (Acceptance Sampling).
Sampling to determine if the process is within acceptable limits (Statistical Process Control)
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Acceptance Sampling Purposes
– Determine quality level– Ensure quality is within predetermined level
Advantages– Economy– Less handling damage– Fewer inspectors– Upgrading of the inspection job– Applicability to destructive testing– Entire lot rejection (motivation for improvement)
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Acceptance Sampling
Disadvantages– Risks of accepting “bad” lots and rejecting “good”
lots– Added planning and documentation– Sample provides less information than 100-percent
inspection
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Statistical Sampling--Data
Attribute (Go no-go information)– Defectives--refers to the acceptability of product
across a range of characteristics.– Defects--refers to the number of unacceptable
conditions per unit--may be higher than the number of defectives.
Variable (Continuous)– Usually measured by the mean and the standard
deviation.
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Acceptance Sampling--Single Sampling Plan
A simple goal
Determine (1) how many units, n, to sample from a lot, and
(2) the maximum number of defective items, c, that can be found in the sample before the lot is rejected.
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Risk
Acceptable Quality Level (AQL)– Max. acceptable percentage of defectives defined by
producer. (Producer’s risk)
– The probability of rejecting a good lot. Lot Tolerance Percent Defective (LTPD)
– Percentage of defectives that defines consumer’s rejection point.
(Consumer’s risk)– The probability of accepting a bad lot.
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Example: Acceptance Sampling
Zypercom, a manufacturer of video interfaces, purchases printed wiring boards from an outside vender, Procard. Procard has set an acceptable quality level of 1% and accepts a 5% risk of rejecting lots at or below this level. Zypercom considers lots with 3% defectives to be unacceptable and will assume a 10% risk of accepting a defective lot.
Develop a sampling plan for Zypercom and determine a rule to be followed by the receiving inspection personnel.
Egekwu-21112
Example: Continued
LTPD
AQL =
.03
.01 = 3 n (AQL) = 3.286
c LTPD/AQL n AQL c LTPD/AQL n AQL0 44.890 0.052 5 3.549 2.6131 10.946 0.355 6 3.206 3.2862 6.509 0.818 7 2.957 3.9813 4.890 1.366 8 2.768 4.6954 4.057 1.970 9 2.618 5.426
How can we determine the value of n?What is our sampling procedure?
Exhibit TN 7.10
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Example: Continued
c = 6, from Table; c is also called acceptance numbern (AQL) = 3.286, from TableAQL = .01, given in problem
n(AQL/AQL) = 3.286/.01 = 328.6, or 329 (always round up)
Sampling Procedure:Take a random sample of 329 units from a lot. Reject the lot if more than 6 units are defective.
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Operating Characteristic Curve
n = 99c = 4
AQL LTPD
00.10.20.30.40.50.60.70.80.9
1
1 2 3 4 5 6 7 8 9 10 11 12
Percent defective
Pro
bab
ilit
y of
acc
epta
nce
=.10(consumer’s risk)
= .05 (producer’s risk)
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Chance Versus Assignable Variation
Chance variation is variability built into the system.
Assignable variation occurs because some element of the system or some operating conditions are out of control.
Quality control seeks to identify when assignable variation is present so that corrective action can be taken.
Egekwu-211
Control Based on Attributes and Variables
Inspection for Variables: measuring a variable that can be scaled such as weight, length, temperature, and diameter.
Inspection of Attributes: determining the existence of a characteristic such as acceptable-defective, timely-late, and right-wrong.
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Control Charts: Assumptions
Developed in 1920s to distinguish between chance variation in a system and variation caused by the system’s being out of control - assignable variation.
Egekwu-211
Control Charts - Assumptions continued
Repetitive operation will not produce exactly the same outputs.
Pattern of variability often described by normal distribution.
Random samples that fully represent the population being checked are taken.
Sample data plotted on control charts to determine if the process is still under control.
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Control Limits
If we establish control limits at +/- 3 standard deviations, then
we would expect 99.7% of our observations to fall within these limits
xLCL UCL
UCL
LCL
UCL
LCL
UCL
LCL
What other evidence(s) might prompt investigation?
StatisticalProcessControl
©The McGraw-Hill Companies, Inc., 1998
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Attribute Data: Constructing a p-Chart
Sample n Defectives1 100 42 50 23 100 54 100 35 75 66 100 47 100 38 50 89 100 1
10 100 211 100 312 100 213 100 214 100 815 100 3
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Statistical Process Control--Attribute Measurements (P-Charts)
p =Total Number of Defectives
Total Number of Observations
= p (1- p)
npS
UCL = p + Z
LCL = p - Z p
p
s
s
(Std Deviation)
= [ p ]
1. Calculate the sample proportion, p, for each
sample.Sample n Defectives p
1 100 4 0.042 50 2 0.043 100 5 0.054 100 3 0.035 75 6 0.086 100 4 0.047 100 3 0.038 50 7 0.149 100 1 0.01
10 100 2 0.0211 100 3 0.0312 100 2 0.0213 100 2 0.0214 100 8 0.0815 100 3 0.03
19©The McGraw-Hill Companies, Inc., 1998Irwin/McGraw-Hill
2. Calculate the average of the sample proportions.
0.04=1375
55 = p
3. Calculate the standard deviation of the sample proportion
.020467= 91.6667
.04)-.04(1=
n
)p-(1 p = ps
20©The McGraw-Hill Companies, Inc., 1998
Irwin/McGraw-Hill
4. Calculate the control limits.
3(.020467) .04
UCL = 0.1014
LCL = -0.0214 (or 0)
UCL = p + Z
LCL = p - Z p
p
s
s
21©The McGraw-Hill Companies, Inc., 1998
Irwin/McGraw-Hill
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p-Chart (Continued)
5. Plot the individual sample proportions, the average
of the proportions, and the control limits
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Observation
p
UCL
LCL
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Variable Data Example: x-Bar and R Charts
Sample Obs 1 Obs 2 Obs 3 Obs 4 Obs 51 10.68 10.689 10.776 10.798 10.7142 10.79 10.86 10.601 10.746 10.7793 10.78 10.667 10.838 10.785 10.7234 10.59 10.727 10.812 10.775 10.735 10.69 10.708 10.79 10.758 10.6716 10.75 10.714 10.738 10.719 10.6067 10.79 10.713 10.689 10.877 10.6038 10.74 10.779 10.11 10.737 10.759 10.77 10.773 10.641 10.644 10.72510 10.72 10.671 10.708 10.85 10.71211 10.79 10.821 10.764 10.658 10.70812 10.62 10.802 10.818 10.872 10.72713 10.66 10.822 10.893 10.544 10.7514 10.81 10.749 10.859 10.801 10.70115 10.66 10.681 10.644 10.747 10.728
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Calculate sample means, sample ranges, mean of means, and mean of ranges.
Sample Obs 1 Obs 2 Obs 3 Obs 4 Obs 5 Avg Range1 10.68 10.689 10.776 10.798 10.714 10.732 0.1162 10.79 10.86 10.601 10.746 10.779 10.755 0.2593 10.78 10.667 10.838 10.785 10.723 10.759 0.1714 10.59 10.727 10.812 10.775 10.73 10.727 0.2215 10.69 10.708 10.79 10.758 10.671 10.724 0.1196 10.75 10.714 10.738 10.719 10.606 10.705 0.1437 10.79 10.713 10.689 10.877 10.603 10.735 0.2748 10.74 10.779 10.11 10.737 10.75 10.624 0.6699 10.77 10.773 10.641 10.644 10.725 10.710 0.13210 10.72 10.671 10.708 10.85 10.712 10.732 0.17911 10.79 10.821 10.764 10.658 10.708 10.748 0.16312 10.62 10.802 10.818 10.872 10.727 10.768 0.25013 10.66 10.822 10.893 10.544 10.75 10.733 0.34914 10.81 10.749 10.859 10.801 10.701 10.783 0.15815 10.66 10.681 10.644 10.747 10.728 10.692 0.103
Averages 10.728 0.220400
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Control Limit Formulas & Factor Table
x Chart Control Limits
UCL = x + A R
LCL = x - A R
2
2
R Chart Control Limits
UCL = D R
LCL = D R
4
3
n A2 D3 D42 1.88 0 3.273 1.02 0 2.574 0.73 0 2.285 0.58 0 2.116 0.48 0 2.007 0.42 0.08 1.928 0.37 0.14 1.869 0.34 0.18 1.8210 0.31 0.22 1.7811 0.29 0.26 1.74
Exhibit TN 7.7
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x-Bar Chart
10.601
10.856
=).58(0.2204-10.728RA - x = LCL
=).58(0.2204-10.728RA + x = UCL
2
2
10.550
10.600
10.650
10.700
10.750
10.800
10.850
10.900
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Sample
Mea
ns
UCL
LCL
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R-Chart
0
0.46504
)2204.0)(0(R D= LCL
)2204.0)(11.2(R D= UCL
3
4
UCL
LCL0.000
0.100
0.200
0.300
0.400
0.500
0.600
0.700
0.800
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Sample
R
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Process Capability
Process limits - determined from manufacturing process data.
Tolerance limits - specified in engineering design drawing
How do the limits relate to one another?
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Process Capability
TQM’s emphasis on “making it right the first time” has resulted in organizations emphasizing the ability of a production system to meet design specifications rather than evaluating the quality of outputs after the fact with acceptance sampling.
Process Capability measures the extent to which an organization’s production system can meet design specifications.
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Process Capability Depends On:
Location of the process mean. Natural variability inherent in the process. Stability of the process. Product’s design requirements.
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Natural Variation Versus Product Design Specifications
(Mean out ofsync.)
(Look for moreeconomical means of production)
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Process Capability Ratio (Text calls it Index)
6
LSL - USL
system production theof deviations standard 6
rangeion specificatdesign sproduct'pC
Cp < 1: process not capable of meeting design specs
Cp > 1: process capable of meeting design specs
As rule of thumb, many organizations desire a Cp ratio of at least 1.5.
Six sigma quality (fewer than 3.4 defective parts per million) corresponds to a Cp (index/ratio) of 2.