using control charts to keep an eye on variability of control charts see if process is “in...
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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
Definitions of Out of Control 1. 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
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. Variables Attributes: 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 i Size
z = 2 for 95.5% limits z = 3 for 99.7% limits p = avg defect rate n = avg sample size sp = sample std dev
p Chart Example You’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 =.100 2 800 90 .113 3 400 21 .053 4 350 25 .071 5 300 18 .06 6 400 12 .03 7 600 30 .05
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 Data Day Delivery Time
1 7.30 4.20 6.10 3.45 5.55 2 4.60 8.70 7.60 4.43 7.62 3 5.98 2.92 6.20 4.20 5.10 4 7.20 5.10 5.19 6.80 4.21 5 4.00 4.50 5.50 1.89 4.46 6 10.10 8.10 6.50 5.06 6.94 7 6.77 5.08 5.90 6.90 9.30
R &X Chart Hotel Data Sample
Day Delivery Time Mean Range 1 7.30 4.20 6.10 3.45 5.55 5.32
7.30 + 4.20 + 6.10 + 3.45 + 5.55 5 Sample Mean =
R &X Chart Hotel Data Sample
Day Delivery Time Mean Range 1 7.30 4.20 6.10 3.45 5.55 5.32 3.85
7.30 - 3.45 Sample Range =
Largest Smallest
R &X Chart Hotel Data Sample
Day Delivery Time Mean Range 1 7.30 4.20 6.10 3.45 5.55 5.32 3.85 2 4.60 8.70 7.60 4.43 7.62 6.59 4.27 3 5.98 2.92 6.20 4.20 5.10 4.88 3.28 4 7.20 5.10 5.19 6.80 4.21 5.70 2.99 5 4.00 4.50 5.50 1.89 4.46 4.07 3.61 6 10.10 8.10 6.50 5.06 6.94 7.34 5.04 7 6.77 5.08 5.90 6.90 9.30 6.79 4.22
R &X Chart Hotel Data Sample
Day Delivery Time Mean Range 1 7.30 4.20 6.10 3.45 5.55 5.32 3.85 2 4.60 8.70 7.60 4.43 7.62 6.59 4.27 3 5.98 2.92 6.20 4.20 5.10 4.88 3.28 4 7.20 5.10 5.19 6.80 4.21 5.70 2.99 5 4.00 4.50 5.50 1.89 4.46 4.07 3.61 6 10.10 8.10 6.50 5.06 6.94 7.34 5.04 7 6.77 5.08 5.90 6.90 9.30 6.79 4.22
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