chapter 13 statistical quality control method. statistical quality control methods statistical...
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Chapter 13 Statistical Quality Control Method
Statistical Quality Control Methods
Statistical QualityControl Methods
Acceptance SamplingStatistical Process
Control
Attributes Variables Attributes Variables
Type of Data
Statistical Quality Control Methods
Attribute Data: data which count items, such as the number of defective items on a sample
Variable Data: data which measure a particular product characteristic such as length or weight
Statistical Quality Control Methods
Sampling Error
Sample results are not representative of the actualpopulation or process
In agreement
The populationor process is actually
Good or in control Bad or out of control
In agreement
or Type II error
or Type I error
Good orin control
Bad or out of control
The samplesays that thepopulation orprocess is
Prducer’s risk
Customer’srisk
Acceptance Sampling
Designing a Sampling Plan for Attribute
Costs to justify inspection
Full or 100% inspection or not?
Cost to InspectCost incurred by passing a reject
Acceptance Sampling
Purpose of Sampling Plan
•Find its quality
•Ensure that the quality is what it is supposed to be
Acceptance Sampling
n: Number of units in the sample depended on the lot size
c: the acceptance number
Designing a Sampling Plan for Attribute
AQL (acceptable quality level): maximum percentage of defects that a company is willing to accept
LTPD (lot tolerance percent defective): minimum percentage of defects that a company is willing to reject
: producer’s risk
: consumer’s risk
Acceptance Sampling
Designing a Sampling Plan for Attribute
c LTPD/AQL nAQL
0 44.890 0.0521 10.946 0.3552 6.509 0.8183 4.890 1.3664 4.057 1.9705 3.549 2.6136 3.206 3.2867 2.957 3.9818 2.768 4.6959 2.618 5.426
=0.05=0.10
MIL-STD-105E
Operating Characteristic Curve
Operating Characteristic Curve
!
)()(
r
nperP
rnp
p np P(r c)
1% 0.99 0.97
2% 1.98 0.95
…
Acceptance Sampling
Determine a Sampling Plan for Variables
Control Limit: Points on an acceptance sampling chart that distinguish the accept and reject regions. Also, points on a process control chart that distinguish between a process being in and out of control.
nzCL
2
Acceptance Sampling
Determine a Sampling Plan for Variables
Acceptance Sampling
LCL
Statistical Process Control
Statistical process control (SPC)
Statistical method for determining whether a particularprocess is in or out of control.
Central Limit Theorem
Statistical Process Control
Statistical Process Control
Statistical Process Control
SPC Using Attribute Measurement
Attribute data are data that are counted, such as good or badunits produced by a machine.
Samples
defects
Sample size=6defects=2
Statistical Process Control
SPC Using Attribute Measurement
Center line = p = Long-run average percent defective
Standard deviation of sample = n
ppS p
)1(
n
ppzpCL
)1(2
Note: X~Bernoulli distribution E(x)=p V(x)=p(1-p)
32Z
Statistical Process Control
Variable Measurements Using X and R Charts
An X chart tracks the changes in the means of samples by plottingthe means that were taken from a process.
An R chart tracks the changes in the variability by plotting the range within each sample.
Statistical Process Control
Variable Measurements Using X and R Charts
Setup Control Chart:
1. At least 25 samples2. Setup control limits
RAXX 2Control limits for
RDR 4RDR 3
Upper control limit for
Lower control limit for
Statistical Process Control
n A2 D3 D4
2 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 1.7412 0.27 0.28 1.7213 0.25 0.31 1.69
n A2 D3 D4
14 0.24 0.33 1.6715 0.22 0.35 1.6516 0.21 0.36 1.6417 0.20 0.38 1.6218 0.19 0.39 1.6119 0.19 0.40 1.6020 0.18 0.41 1.59
Statistical Process Control
Process Capability
Process Capability
Process Capability Ratio
sC p 6
limit ranceLower tole -limit ranceUpper tole
The larger the ratio, the greater the potential for producingparts within tolerance from the specified process.
Process Capability
Capability Index
s
XUSL
s
LSLXC pk 3
,3
min
To determine whether the process mean is closer to theupper specification limit, or the lower specification limit.
Six Sigma
Quality improvement program developed by Motorola to reduceprocess variation to 50% of design tolerance
Cp=1; defect rate = 2700 per million parts Cp=2; defect rate = 3.4 per million parts