using control charts to keep an eye on variability operations management dr. ron lembke
TRANSCRIPT
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Using Control Charts to Keep an Eye on Variability
Operations Management
Dr. Ron Lembke
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Goal of Control Charts See if process is “in control”
Process should show random values No trends or unlikely patterns
Visual representation much easier to interpret Tables of data – any patterns? Spot trends, unlikely patterns easily
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NFL Control Chart?
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Control Charts
UCL
LCL
avg
Values
Sample Number
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Definitions of Out of Control1. No points outside control limits
2. Same number above & below center line
3. Points seem to fall randomly above and below center line
4. Most are near the center line, only a few are close to control limits
1. 8 Consecutive pts on one side of centerline
2. 2 of 3 points in outer third
3. 4 of 5 in outer two-thirds region
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Control Charts
Normal Too Low Too high
5 above, or below Run of 5 Extreme variability
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Control Charts
UCL
LCL
avg
1σ
2σ
2σ
1σ
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Control Charts
2 out of 3 in the outer third
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Out of Control Point? Is there an “assignable cause?”
Or day-to-day variability?
If not usual variability, GET IT OUT Remove data point from data set, and recalculate
control limits
If it is regular, day-to-day variability, LEAVE IT IN Include it when calculating control limits
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Attributes vs. VariablesAttributes: Good / bad, works / doesn’t count % bad (P chart) count # defects / item (C chart)
Variables: measure length, weight, temperature (x-bar
chart) measure variability in length (R chart)
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p Chart Control Limits
# Defective Items in Sample i
# Samples
Sample iSize
z = 2 for 95.5% limits z = 3 for 99.7% limitsp = avg defect raten = avg sample sizesp = sample std dev
pp szpUCL
pp szpLCL
n ni
i1
k
k
p X i
i1
k
ni
i1
k
n
ppsp
)1(
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p Chart ExampleYou’re manager of a 1,700 room hotel. For 7 days, you collect data on the readiness of all of the rooms that someone checked out of. Is the process in control (use z = 3)?
© 1995 Corel Corp.
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p Chart Hotel Data# Rooms No. Not Proportion
Day n Ready p
1 1,300 130 130/1,300 =.1002 800 90 .1133 400 21 .0534 350 25 .0715 300 18 .066 400 12 .037 600 30 .05
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p Chart Control Limits
079.0150,4
326
150,4
30...90130
1
1
k
ii
k
ii
n
Xp
8.5927
150,4
7
600...80013001
k
nn
k
ii
068.7/)05.0...113.010.0( p
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p Chart Solution
8.592,079.0 np
111.0*3079.0CL pszp
0457.0LCL,1123.0UCL
0333.0079.0
0111.0
8.592
079.01079.01sp
n
pp
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Hotel Room Readiness P-Bar
1 2 3 4 5 6 70
0.02
0.04
0.06
0.08
0.1
0.12
UCL
Actual
LCL
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R Chart Type of variables control chart
Interval or ratio scaled numerical data
Shows sample ranges over time Difference between smallest & largest values
in inspection sample
Monitors variability in process Example: Weigh samples of coffee &
compute ranges of samples; Plot
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Why do we need 2 charts?Consistent, but the average is in the wrong place
UCL
LCL
UCL
LCL
X-Bar Chart R Chart
The average works out ok, but way too much variability between points
X-Bar Chart R Chart
UCL
LCL
UCL
LCL
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You’re manager of a 500-room hotel. You want to analyze the time it takes to deliver luggage to the room. For 7 days, you collect data on 5 deliveries per day. Is the process in control?
Hotel Example
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Hotel DataDay Delivery Time
1 7.30 4.20 6.10 3.455.552 4.60 8.70 7.60 4.437.623 5.98 2.92 6.20 4.205.104 7.20 5.10 5.19 6.804.215 4.00 4.50 5.50 1.894.466 10.10 8.10 6.50 5.066.947 6.77 5.08 5.90 6.909.30
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R &X Chart Hotel Data
SampleDay Delivery TimeMean Range
1 7.30 4.20 6.10 3.45 5.555.32 7.30 + 4.20 + 6.10 + 3.45 + 5.55
5Sample Mean =
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R &X Chart Hotel Data
SampleDay Delivery TimeMean Range
1 7.30 4.20 6.10 3.45 5.555.32 3.85
7.30 - 3.45Sample Range =
Largest Smallest
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R &X Chart Hotel Data
SampleDay Delivery TimeMean Range
1 7.30 4.20 6.10 3.45 5.555.32 3.85
2 4.60 8.70 7.60 4.43 7.626.59 4.27
3 5.98 2.92 6.20 4.20 5.104.88 3.28
4 7.20 5.10 5.19 6.80 4.215.70 2.99
5 4.00 4.50 5.50 1.89 4.464.07 3.61
6 10.10 8.10 6.50 5.06 6.947.34 5.04
7 6.77 5.08 5.90 6.90 9.306.79 4.22
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R Chart Control Limits
UCL D R
LCL D R
R
R
k
R
R
ii
k
4
3
1
Sample Range at Time i
# Samples
Table 10.3, p.433
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Control Chart Limits, p.161
n A2 D3 D4
2 1.88 0 3.278
3 1.02 0 2.57
4 0.73 0 2.28
5 0.58 0 2.11
6 0.48 0 2.00
7 0.42 0.08 1.92
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R Chart Control Limits
894.37
22.4...27.485.31
k
RR
k
ii
0894.3*0*
232.8894.3*11.2*
3
4
RDLCL
RDUCL
R
R
10.3 Table from , 43 DD
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R Chart Solution
1 2 3 4 5 6 70
1
2
3
4
5
6
7
8
9
UCLRangeLCL
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X Chart Control Limits
k
RR
k
XX
RAXUCL
k
ii
k
ii
X
11
2
Sample Range at Time i
# Samples
Sample Mean at Time i
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X Chart Control LimitsA2 from Table 10-3
k
RR
k
XX
RAXLCL
RAXUCL
k
ii
k
ii
X
X
11
2
2
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Control Chart Factors, p. 161
n A2 D3 D4
2 1.88 0 3.278
3 1.02 0 2.57
4 0.73 0 2.28
5 0.58 0 2.11
6 0.48 0 2.00
7 0.42 0.08 1.92
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R &X Chart Hotel Data
SampleDay Delivery TimeMean Range
1 7.30 4.20 6.10 3.45 5.555.32 3.85
2 4.60 8.70 7.60 4.43 7.626.59 4.27
3 5.98 2.92 6.20 4.20 5.104.88 3.28
4 7.20 5.10 5.19 6.80 4.215.70 2.99
5 4.00 4.50 5.50 1.89 4.464.07 3.61
6 10.10 8.10 6.50 5.06 6.947.34 5.04
7 6.77 5.08 5.90 6.90 9.306.79 4.22
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X Chart Control Limits
894.37
22.4...27.485.3
813.57
79.6...59.632.5
1
1
k
RR
k
XX
k
ii
k
ii
566.3894.3*58.0813.5*
060.8894.3*58.0813.5*
2
2
RAXLCL
RAXUCL
X
X
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X Chart Solution*
1 2 3 4 5 6 70
1
2
3
4
5
6
7
8
9
UCLMeanLCL
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Summary Overview of “In Control” Attribute vs Continuous Control Charts P Charts X-bar and R charts