Unformatted text preview: AGENDA
• FINISH UP XBAR AND R CHART
• PROCESS CAPABILITY Mean and Range Charts
(a)
(Sampling mean is
(Sampling
shifting upward but
range is consistent)
range These
These
sampling
distributions
result in the
charts below
charts
UCL xchart
LCL
UCL Rchart
LCL
Figure S6.5 (xchart detects
(xchart
shift in central
tendency)
tendency) (Rchart does not
(Rchart
detect change in
mean)
mean) Mean and Range Charts
(b)
These
These
sampling
distributions
result in the
charts below
charts (Sampling mean
(Sampling
is constant but
dispersion is
increasing)
increasing)
UCL xchart
LCL
UCL Rchart
LCL
Figure S6.5 (xchart does not
(xchart
detect the increase
in dispersion)
in (Rchart detects
(Rchart
increase in
dispersion)
dispersion) Control Charts for Attributes For variables that are categorical Good/bad, yes/no,
Good/bad,
acceptable/unacceptable
acceptable/unacceptable Measurement is typically counting
Measurement
defectives
defectives Charts may measure Percent defective (pchart) Number of defects (cchart) Control Limits for pCharts
Population will be a binomial distribution,
Population
but applying the Central Limit Theorem
allows us to assume a normal distribution
for the sample statistics
for
^
UCLp = p + zσ p σp =
^ ^
LCLp = p  zσ p p =
=
=
= p(1  p)
n mean fraction defective in the sample
number of standard deviations
^
standard deviation of the sampling distribution
sample size Control Limits for cCharts
Population will be a Poisson distribution,
Population
but applying the Central Limit Theorem
allows us to assume a normal distribution
for the sample statistics
for
UCLc = c + 3 c
c = LCLc = c  3 c mean number defective in the sample Which Control Chart to Use
Variables Data Using an xchart and Rchart: Observations are variables Collect 20  25 samples of n = 4, or n =
Collect 20
or
5, or more, each from a stable process
or
and compute the mean for the xchart
and range for the Rchart
and Track samples of n observations each Which Control Chart to Use
Attribute Data Using the pchart: Observations are attributes that can
Observations
be categorized in two states We deal with fraction, proportion, or
We
percent defectives
percent Have several samples, each with
Have
many observations
many Which Control Chart to Use
Attribute Data Using a cChart: Observations are attributes whose
Observations
defects per unit of output can be
counted
counted The number counted is a small part of
The
the possible occurrences
the Defects such as number of blemishes
Defects
on a desk, number of typos in a page
of text, flaws in a bolt of cloth
of Patterns in Control Charts
Upper control limit Target Lower control limit
Figure S6.7 Normal behavior.
Normal
Process is “in control.”
Process Patterns in Control Charts
Upper control limit
Upper Target Lower control limit
Figure S6.7 One plot out above (or
One
below). Investigate for
cause. Process is “out
of control.”
of Patterns in Control Charts
Upper control limit
Upper Target Lower control limit
Figure S6.7 Trends in either
Trends
direction, 5 plots.
Investigate for cause of
progressive change.
progressive Patterns in Control Charts
Upper control limit
Upper Target Lower control limit
Figure S6.7 Two plots very near
Two
lower (or upper)
control. Investigate for
cause.
cause. Patterns in Control Charts
Upper control limit
Upper Target Lower control limit
Figure S6.7
Figure Run of 5 above (or
Run
below) central line.
Investigate for cause. Patterns in Control Charts
Upper control limit
Upper Target Lower control limit
Erratic behavior.
Erratic
Investigate.
Investigate.
Figure S6.7 Process Capability The natural variation of a process
The
should be small enough to produce
products that meet the standards
required
required A process in statistical control does not
process
necessarily meet the design
specifications
specifications Process capability is a measure of the
Process
relationship between the natural
variation of the process and the design
specifications
specifications Process Capability Ratio
Upper Specification  Lower Specification
Upper
Cp =
6σ A capable process must have a Cp of at
capable
least 1.0
1.0 Does not look at how well the process
Does
is centered in the specification range Often a target value of Cp = 1.33 is used
Often
to allow for offcenter processes
to Six Sigma quality requires a Cp = 2.0 Process Capability Ratio
Insurance claims process
Process mean x = 210.0 minutes
Process
210.0
Process standard deviation σ = .516 minutes
Process
Design specification = 210 ± 3 minutes
Design
210
Upper Specification  Lower Specification
Upper
Cp =
6σ Process Capability Ratio
Insurance claims process
Process mean x = 210.0 minutes
Process
210.0
Process standard deviation σ = .516 minutes
Process
Design specification = 210 ± 3 minutes
Design
210
Upper Specification  Lower Specification
Upper
Cp =
6σ
213  207
=
= 1.938
6(.516) Process Capability Ratio
Insurance claims process
Process mean x = 210.0 minutes
Process
210.0
Process standard deviation σ = .516 minutes
Process
Design specification = 210 ± 3 minutes
Design
210
Upper Specification  Lower Specification
Upper
Cp =
6σ
213  207
Process is
=
= 1.938
6(.516)
capable Process Capability Index
Upper
Lower
Cpk = minimum of Specification  x , x  Specification
Limit
Limit
3σ
3σ A capable process must have a Cpk of at
capable
least 1.0
1.0 A capable process is not necessarily in the
capable
center of the specification, but it falls within
the specification limit at both extremes
the Process Capability Index
New Cutting Machine
New process mean x = .250 inches
New
.250
Process standard deviation σ = .0005 inches
Process
Upper Specification Limit = .251 inches
Upper
.251
Lower Specification Limit = .249 inches Process Capability Index
New Cutting Machine
New process mean x = .250 inches
New
.250
Process standard deviation σ = .0005 inches
Process
Upper Specification Limit = .251 inches
Upper
.251
Lower Specification Limit = .249 inches
Cpk = minimum of (.251)  .250
,
(3).0005 Process Capability Index
New Cutting Machine
New process mean x = .250 inches
New
.250
Process standard deviation σ = .0005 inches
Process
Upper Specification Limit = .251 inches
Upper
.251
Lower Specification Limit = .249 inches
Cpk = minimum of (.251)  .250
.250  (.249)
,
(3).0005
(3).0005 Both calculations result in
Cpk = .001
= 0.67
.0015 New machine is
NOT capable Interpreting Cpk
Cpk = negative number
Cpk = zero
Cpk = between 0 and 1
Cpk = 1
Cpk > 1
Figure S6.8 SPC and Process Variability
Lower
Lower
specification
limit
limit Upper
Upper
specification
limit
limit (a) Acceptance
Acceptance
sampling (Some
bad units accepted)
bad
(b) Statistical process
Statistical
control (Keep the
process in control)
process
(c) Cpk >1 (Design
a process that
is in control)
is Process mean, µ
Process Figure S6.10 ...
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 Spring '11
 Bilbrey
 Normal Distribution, Standard Deviation, Control Chart, Process capability, LCL

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