3. BITS Pilani, Hyderabad Campus
Scope
Control charts for Attributes
P Chart
NP Chart
C Chart
U Chart
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4. BITS Pilani, Hyderabad Campus
STATISTICAL PROCESS CONTROL:
CONTROLCHARTS forATTRIBUTES
• What is attribute?, refers to quality characteristics that
conform or do not conform to specifications (e.g. OK-NG,
Accept-Reject)
• Attributes control charts use pass – fail information for
charting.
• 2 types of usage:
1. Measurements not possible – for example, visually
inspected items such as color, missing parts, scratches,
and damage
2. Measurements can be made but are not made because of
time, cost, or need (e.g. use go-no-go gauge, fitting jig)
• 2 important terms to differentiate
1. Defect - items that contribute to nonconformity of a
quality characteristics
2. Defective - part/product inspected not conforming or
meeting specification (can have > 1 defects)
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5. BITS Pilani, Hyderabad Campus
Types ofAttributes control charts
The types of attributes control charts include the following:
1. p charts
- a single chart that tracks the percentage of nonconforming item in
each sample
- sample sizes are large, usually 100 pieces or more. Sample size may
vary.
2. np charts
- tracks the number of nonconforming items in each sample
- easier to use than the p chart because the percentage of defective
items does not have to be calculated, but it has one restrictions
- all the samples must be the same size
3. c charts
- graphs the total number of nonconformance found in each piece or
unit that is inspected
4. u charts
- samples are taken and the total number of nonconformance in the
sample is determined
- tracks the average number of nonconformance per unit
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P Chart
Attributes are discrete events: yes/no or pass/fail
– Use P-Charts for quality characteristics that are discrete and involve
yes/no or good/bad decisions
• Number of leaking caulking tubes in a box of 48
• Number of broken eggs in a carton
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P-ChartExample:Aproductionmanagerforatirecompanyhasinspectedthenumberofdefective
tiresinfiverandomsampleswith20tiresineachsample.Thetablebelowshowsthenumberof
defectivetiresineachsampleof20tires.Calculatethecontrollimits.
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9. BITS Pilani, Hyderabad Campus
P chart Steps
Construction of p Chart (constant subgroup size)
• General procedure same as variable control chart
1. Select quality characteristic
- determine use of control chart
- p chart can control (one quality characteristic, group of quality
characteristic, a part, an entire product, a number of products)
- performance control for operator, department, shift, etc.
2. Determine subgroup size and method size subgroup depends on p
- NOT A If p = 0.001 and n = 1000
GOOD average number nonconforming np = 1 per subgroup
CHART
many zeroes
- GOOD p = 0.15, n = 50
CHART np = 7.5
minimum n = 50, usually 1000
10. BITS Pilani, Hyderabad Campus
P Chart steps
3. Collect the data
- al least 25 subgroup
- for each subgroup p = np/n; np = number of defectives
n = number of samples
4. Calculate the trial limits
12. P Chart Steps
5. Establish revised limits
- remove data points out of control
- establish revised limits out of control situation present (discard)
limits can only be calculated until finish inspection
14. BITS Pilani, Hyderabad Campus
P chart steps
6. Achieve the objective
- the first five step are planning
- the last step involves action and leads to the achievement
of the objective
- some representative values of inspection results for the
month of June are shown in Figure above
- analysis of the June results shows that the quality
improved and also for entire month of July and August
16. P Chart
4. Determine trial limits
- first, average proportion nonconforming
- since n changes, limits calculated for each subgroup
- DO IT DIFFERENT n
17. P chart
- SINCE n is only changing simplify
- Note: as n CL are closer
n CL gets wider
18. P chart
5. Establish revised central line and control limits
- remove data points out of control
- establish revised limits out of control situation present (discard)
- DO IT CALCULATIONS for MAY 4 and MAY 5
19. P Chart minimize Steps
Two techniques to minimize effect of variable subgroup size
1. Using average subgroup size
- calculate individual limits when subgroup size not within
± 15% of nav
20. P Chart minimize Steps
2. Establish control limits for different subgroup sizes
21. 21
Number Nonconforming Chart (np):
The np chart is easier for operating
personnel to understand than the p chart.
The limitation that this chart has is that the
subgroup size needs to be constant.
The np Chart
22. 22
Number Nonconforming Chart (np):
If the fraction nonconforming po is
unknown, then it must be determined by
collecting data, calculating trial control
limits, and obtaining the best estimate of
po.
The np Chart
26. C Chart
Construction of c chart
1. Select the quality characteristics
2. Determine the subgroup size and method
For c chart n = 1
- one aeroplane
- one dozen of pencils, etc.
method – audit or on-line
3. Collect data, calculate trial limits
27. BITS Pilani, Hyderabad Campus
CONTROL CHARTS for ATTRIBUTES
4. Draw the centerline and control limits on the chart
28. CONTROL CHARTS for ATTRIBUTES
5. Interpret the chart
- point 6 is out of control and should be investigated to
determine the cause of so many nonconformities
- except for point 6, the chart is performing in a very steady
manner
6. Revising the c chart
- the reasons behind special-cause situations have been identified
and corrected, c charts can be revised using this formula:
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CONTROL CHARTS for ATTRIBUTES
Construction of u chart (count of defects per unit)
• For unit > 1
• For varying sample size
• Also if subgroup size constant
• u chart is developed same as c chart, collect 25 subgroup data,
calculate trial limits and revise limits
Data: Hose Connection Formula
31. BITS Pilani, Hyderabad Campus
U chart
• Interpret the chart
- except for point 16, the chart appears to be under statistical
control
- there are no runs or unusual patterns
- point 16 should be investigated to determine the cause of such
a large number of nonconformities per unit
• Revising the u chart
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Selection of Control Charts
• ANALYSIS STATE OF CONTROL SAME AS VARIABLE
CONTROL CHART
• Selection of Control Chart
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Control Chart : pattern analysis
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35. Possible Causes by Pattern
Pattern Description Rules Possible Causes
Large shifts from the average 1, 2 New person doing the job
Wrong setup
Measurement error
Process step skipped
Process step not completed
Power failure
Equipment breakdown
Small shifts from the average 3, 4 Raw material change
Change in work instruction
Different measurement device/calibration
Different shift
Person gains greater skills in doing the job
Change in maintenance program
Change in setup procedure
Trends 5 Tooling wear
Temperature effects (cooling, heating)
Mixtures 6 More than one process present (e.g. shifts, machines, raw
material.)
Stratifications 7 More than one process present (e.g. shifts, machines, raw
materials)
Over-control 8 Tampering by operator
Alternating raw materials
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36. 36
Process Capability
Product Specifications
– Preset product or service dimensions, tolerances: bottle fill might be 16 oz. ±.2 oz.
(15.8oz.-16.2oz.)
– Based on how product is to be used or what the customer expects
Process Capability – Cp and Cpk
– Assessing capability involves evaluating process variability relative to preset product
or service specifications
– Cp assumes that the process is centered in the specification range
– Cpk helps to address a possible lack of centering of the process
6σ
LSL
USL
width
process
width
ion
specificat
Cp
3σ
LSL
μ
,
3σ
μ
USL
min
Cpk
37. 37
Relationship between Process Variability
and Specification Width
Three possible ranges for Cp
– Cp = 1, as in Fig. (a), process
variability just meets specifications
– Cp ≤ 1, as in Fig. (b), process not capable
of producing within specifications
– Cp ≥ 1, as in Fig. (c), process
exceeds minimal specifications
One shortcoming, Cp assumes that the
process is centered on the specification
range
Cp=Cpk when process is centered
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Computing the Cp Value at Cocoa Fizz: 3 bottling machines are being evaluated for
possible use at the Fizz plant. The machines must be capable of meeting the design
specification of 15.8-16.2 oz. with at least a process capability index of 1.0 (Cp≥1)
The table below shows the information gathered
from production runs on each machine. Are
they all acceptable? Solution:
– Machine A
– Machine B
Cp=
– Machine C
Cp=
Machine σ USL-LSL 6σ
A .05 .4 .3
B .1 .4 .6
C .2 .4 1.2
1.33
6(.05)
.4
6σ
LSL
USL
Cp
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Computing the Cpk Value at Cocoa Fizz
Design specifications call for a target
value of 16.0 ±0.2 OZ.
(USL = 16.2 & LSL = 15.8)
Observed process output has now
shifted and has a µ of 15.9 and a
σ of 0.1 oz.
Cpk is less than 1, revealing that the
process is not capable
.33
.3
.1
Cpk
3(.1)
15.8
15.9
,
3(.1)
15.9
16.2
min
Cpk
