1. STATISTICAL PROCESS CONTROL: CONTROL CHARTS for ATTRIBUTES
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)

2. CONTROL CHARTS for ATTRIBUTES
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
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

3. CONTROL CHARTS for ATTRIBUTES

4. CONTROL CHARTS for ATTRIBUTES

5. CONTROL CHARTS for ATTRIBUTES
Control Charts for Nonconforming Units
Control charts for Fraction Defective for nonconforming units based on Binomial Distribution
- p Chart (proportion nonconforming in sample or subgroup)
- np Chart (number nonconforming)
Objectives
- Determine the average quality level – this information provides
the process capability in terms of attributes
- Bring to the attention of management any changes in the average –
once the average quality is known, changes, become significant
- Improve the product quality – p chart can motivate operating and
management personnel to initiate ideas for quality improvement
- Evaluate the quality performance of operating and management
personnel – supervisors of activities and especially the CEO should
be evaluated by a chart for nonconforming units
- Determine acceptance criteria of a product before shipment to the
customer – knowledge of the proportion nonconforming provides
management with information on whether or not to release an order

6. CONTROL CHARTS for ATTRIBUTES
p Chart
Used for data consists of proportion of number of occurrences to total number of occurrences
Reports fraction nonconforming in a product, quality characteristics, or group of quality characteristics
Fraction nonconforming:
Fraction nonconforming usually quite small i.e. about 0.15 or less
If > 0.15 problem, need take drastic action
Since p is small n must be big to produce meaningful chart
e.g. 450 books inspected from a production if books at the end of inspections 5 book found defectives
notice n large
The subgroup sizes of the p chart can be either:
(a) constant size (same through out)
(b) variable size (changes)

7. CONTROL CHARTS for ATTRIBUTES
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 = 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

8. CONTROL CHARTS for ATTRIBUTES
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

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10. CONTROL CHARTS for ATTRIBUTES
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

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12. CONTROL CHARTS for ATTRIBUTES
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

13. CONTROL CHARTS for ATTRIBUTES
Construction of p Chart (variable subgroup size)
There are situations when you cannot obtain constant subgroup size
- e.g. using 100% inspection results with output quantity
varying day to day
It is undesirable, but it exists – how to handle?
- construction step 1 and 2 is same
- step 3 – collect data
Additional columns needed:
Each day fraction defective calculated by inspector using np/n

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15. CONTROL CHARTS for ATTRIBUTES
4. Determine trial limits
- first, average proportion nonconforming
- since n changes, limits calculated for each subgroup
- DO IT DIFFERENT n

16. CONTROL CHARTS for ATTRIBUTES
- SINCE n is only changing simplify
- Note: as n CL are closer
n CL gets wider

17. CONTROL CHARTS for ATTRIBUTES
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

18. CONTROL CHARTS for ATTRIBUTES
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

19. CONTROL CHARTS for ATTRIBUTES
2. Establish control limits for different subgroup sizes

20. CONTROL CHARTS for ATTRIBUTES
Control Charts for Count of Nonconformities
Nonconformities (defects) chart controls the count of nonconformities
within product
2 types of chart:
- c chart – count of nonconformities
- u chart – count of nonconformities per unit
2 conditions must be met (due to Poisson distribution)
1) average count of nonconformities must be far less than total
possible count of nonconformities if everything went wrong
2) occurrences are independent – opportunity for defects same
Examples
- imperfections in a large roll paper
- appearance on rubber mat
- imperfect soldering in a PCB
- rust spots on sheets/rolls of steel
- mould marks
- short mould of rubber seal
Same as nonconforming control chart, the CL ± from centerline

21. CONTROL CHARTS for ATTRIBUTES
Objective
- Determine the average quality level as a benchmark or starting
point – gives the initial process capability
- Bring to the attention of management any changes in the average
- Improve the product quality – charts can motivate operating and
management personnel to initiate ideas for quality improvement
- Evaluate the quality performance of operating and management
personnel.
- Provide information concerning the acceptability of the product
prior to shipment
Because of the limitations of the charts for count of nonconformities, many organizations do not have occasion for their use

22. CONTROL CHARTS for ATTRIBUTES
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

23. CONTROL CHARTS for ATTRIBUTES
4. Draw the centerline and control limits on the chart

24. 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:

25. 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

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27. CONTROL CHARTS for ATTRIBUTES
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

28. CONTROL CHARTS for ATTRIBUTES
ANALYSIS STATE OF CONTROL SAME AS VARIABLE CONTROL CHART
Selection of Control Chart