Continuous Process Improvement: The Lessons of History BADM 701 Dr. Ron Lembke.
Using Control Charts to Keep an Eye on Variability Operations Management Dr. Ron Lembke.
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Transcript of Using Control Charts to Keep an Eye on Variability Operations Management Dr. Ron Lembke.
Using Control Charts to Keep an Eye on Variability
Operations Management
Dr. Ron Lembke
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
NFL Control Chart?
Control Charts
UCL
LCL
avg
Values
Sample Number
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
Control Charts
Normal Too Low Too high
5 above, or below Run of 5 Extreme variability
Control Charts
UCL
LCL
avg
1σ
2σ
2σ
1σ
Control Charts
2 out of 3 in the outer third
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
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)
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(
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.
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
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
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
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
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
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
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
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
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 =
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
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
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
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
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
R Chart Solution
1 2 3 4 5 6 70
1
2
3
4
5
6
7
8
9
UCLRangeLCL
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
X Chart Control LimitsA2 from Table 10-3
k
RR
k
XX
RAXLCL
RAXUCL
k
ii
k
ii
X
X
11
2
2
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
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
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
X Chart Solution*
1 2 3 4 5 6 70
1
2
3
4
5
6
7
8
9
UCLMeanLCL
Summary Overview of “In Control” Attribute vs Continuous Control Charts P Charts X-bar and R charts