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5/12/2018 Lecture4 Control Charts - slidepdf.com
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STATISTICAL QUALITY CONTROL
AND IMPROVEMENT
Lecture 4 – Control Charts
Shashikant Sathaye
Polytechnic Institute of NYU
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Variable Control ChartsHow to Use the Process Control Charts
• A process is said to be in control when the performance of the process
falls within the statistically calculated control limits and exhibits only
random variation due to chance causes
• Process under control does not mean that the process meets designspecifications
• Identifying Patterns:
– Trends are changes in levels; for e.g the center line might be driftingdownwards
– Change or jump in level can be detected if a consecutive set of observationsare consistently above(below) the center line.
Statistical Quality Control and
ImprovementPolytechnic Institute of NYU Lecture 4 – MN611 2
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Variable Control ChartsExample: Printer Assembly –
• An assembly area has been experiencing serious delays in the
manufacture of computer printers. As a quality assurance manager you
are asked to investigate and determine the cause of delays and fix theproblems. Given the limited time, you get together with the
representatives from all the departments and develop an cause andeffect diagram
• Set the qualitycharacteristicto measured –
length of a shaft
Statistical Quality Control and
ImprovementPolytechnic Institute of NYU Lecture 4 – MN611 3
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Variable Control ChartsExample: Printer Assembly –
• Choose a rational sub-group to sample –
needs to be homogeneous
– Sub-group should be at least 4.
– Normally use range R for estimating std dev.If sub-group size is more than 10, then use‘s’.
• Collect the data
• Determine the trial central line for the X
chart.
X =
where X = average of the subgroup
averagesXi = average of the ith groupm = number of subgroups
Statistical Quality Control and
ImprovementPolytechnic Institute of NYU Lecture 4 – MN611 4
ΣXi
m
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Variable Control Charts• Determine the Trial Control Limits for the Xbar Chart
UCLx = X + 3 σx
LCLx = X - 3 σx
Since the std deviation, σ is not known and we have a small sample sizefor each subgroup (4), we use the range R as a proxy for the std deviationand a factor A2 as the multiplier for the 99% confidence limit. A2 dependson the sample size.
Thus
UCLx = X + A2RLCLx = X – A2R
So for our example: X = (11.99+12.00,…+12.00)/21= 11.99
and R = (.08+.07_.04+….+.04)/21 = 0.05
UCLx = X + A2R = 11.99 + .577(.05) = 12.02LCLx = X – A2R = 11.99 - .577(.05) = 11.96
Statistical Quality Control and
ImprovementPolytechnic Institute of NYU Lecture 4 – MN611 5
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Variable Control Charts• Determine the Trial Control Limits for the R Chart
R = = .05
The upper and lower control limits are determined using another set ofmultiplier D3 and D4; for a sample of n=5, D3 and D4 are 0 and 2.114.
Thus
UCLR = D4R = 2.114(.05) = 0.11LCLR = D3R = 0(.05) = 0
Statistical Quality Control and
ImprovementPolytechnic Institute of NYU Lecture 4 – MN611 6
ΣRi
m
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Variable Control Charts
Statistical Quality Control and
ImprovementPolytechnic Institute of NYU Lecture 4 – MN611 7
11.88 11.90 11.92 11.94 11.96 11.98 12.00 12.02 12.04
‐
0.02
0.04
0.06
0.08
0.10
0.12
LCLr
UCLr
CL
X
bar
CH
ART
R
C
HART
UCLr
LCLr
CLine
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Variable Control Charts• Examine the process: Control Chart Interpretation
– Avoid misinterpretations
Blaming people for problems they cannot control
Spending time and money on process adjustments that are not necessary Asking for workers to improve when it the equipment that needs fixing
– State of Process Control – Process is under control when the performancefalls within the statistically calculated control and exhibits only chance orrandom causes.
– +/-3σ limits 99.73% of the measurements will be within the limits. – Based upon the normal curve
Statistical Quality Control and
ImprovementPolytechnic Institute of NYU Lecture 4 – MN611 8
Region A = 68.3%Region B = 27.2%
Region C = 4.2%
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Variable Control Charts• Examine the process: Control Chart Interpretation
Thus the basic guidelines for a process under control are: – Two thirds of the points are close to center
– A few points on or near the center line
– Points equally spread around the center
– No points outside the control limits
– No patterns or trends on the chart
• The range chart reveals the amount of variation in the process; so lookfor amount of variation in addition to the rules listed above.
• Types of patterns (non random variations)
– Trends (upward or downward)
– Change or shift in level
– Runs – Recurring cycles
– Non homogenous data
Statistical Quality Control and
ImprovementPolytechnic Institute of NYU Lecture 4 – MN611 9
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Variable Control Charts• Revising the charts
– R chart should be under control (it appear so)
– Isolate the cause of out of control and fix the problem
Statistical Quality Control and
ImprovementPolytechnic Institute of NYU Lecture 4 – MN611 10
11.88 11.90 11.92 11.94 11.96 11.98 12.00 12.02 12.04
‐
0.02
0.04
0.06
0.08
0.10
0.12
LCLr
UCLr
CL
Xba
r
CHART
R
CHART
UCLr
LCLr
CLine
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Variable Control Charts• Revise the charts
– Eliminate the out of control points from both the charts and re-calculate thecenter line and control limits
Eliminate the three points –
Xnew = = (251.77-11.94-11.95-11.95)/(21-3) = 12 = Xo
and
Rnew = = (1.06-.04-.05-.6)(21-3) = .05
New Control Limits
σo = Rnew /d2 = .05/2.326 = 0.02
UCLx = Xo + A σo = 12 + 1.342(.02) = 12.03
LCLx = Xo - A σo = 12 - 1.342(.02) = 11.97
Statistical Quality Control and
ImprovementPolytechnic Institute of NYU Lecture 4 – MN611 11
ΣXi - Xd
m - md
ΣRi - Rd
m - md
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Variable Control Charts
Statistical Quality Control and
ImprovementPolytechnic Institute of NYU Lecture 4 – MN6113 - 12
Revising the control charts
11.88
11.90
11.92
11.94
11.96
11.98
12.00
12.02
12.04
UCLo
LCLo
Center Lineo
LCLx
UCLx
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Variable Control Charts
• X and s charts
– s chart is more precise than R charts but require larger sample subgroup size (> 10)
– The control limits are calculated in a similar manner as X and R charts except that the
control limits are based upon s.
s = = (.03+.029+…..+.011)/21 = 0.414/21 = .02
UCLx = X +A3s
= 11.99
+ 1.427(.02)
= 12.02
LCLx = X ‐A3s = 11.99 – 1.427(.02) = 11.96
UCLs = B4s = 2.089(.02) = .04
LCLs = B3s = 0(.02) = 0
Statistical Quality Control and
ImprovementPolytechnic Institute of NYU Lecture 4 – MN6113 - 13
Σsi
m
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Variable Control Charts (Xbar and s charts)
Statistical Quality Control and
ImprovementPolytechnic Institute of NYU Lecture 4 – MN611 14
11.88 11.90 11.92 11.94 11.96 11.98 12.00 12.02 12.04
X
bar
CH
ART
S
C
HART
UCLr
LCLr
CLine
‐
0.01
0.01
0.02
0.02
0.03
0.03
0.04
0.04
0.05
LCLs
UCLs
CL
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Variable Control Charts
Statistical Quality Control and
ImprovementPolytechnic Institute of NYU Lecture 4 – MN611 15