Quality Control

Control Chart for Attribute1Learning OutcomesAfter completing this module, you will be able to:Understand the concept of attributeApply control chart for attribute

TMA@20082Module 5: Control Chart forAttribute2IntroductionTMA@2008Module 5: Control Chart forAttribute3Many quality characteristics cannot be represented numericallyThe item is clasified as conforming and no-conforming; or other two classification (yes-no; good-bad)

3TMA@2008Module 5: Control Chart forAttribute4

Stiches in a leather bag

Eveness of leather colour4Attribute DataQuality characteristics classified as conforming and non conformingAlso in the form of the count of defects.TMA@2008Module 5: Control Chart forAttribute5

..stitches never less than 6 stitches per inch. Quality is just that. QUALITY.5Control Chart for Fraction Non ConformingFraction nonconforming is the ratio of the number of nonconforming items in a population to the total number of items in that population.Control charts for fraction nonconforming are based on the binomial distribution.

TMA@2008Module 5: Control Chart forAttribute66Notation:n = number of units of product selected at random.D = number of nonconforming units from the sample

The sample fraction nonconforming is given as:

where is a random variable with mean and variance

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7If a standard value of p is given (or a specified value), then the control limits for the fraction nonconforming are

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8If no standard value of p is given, then the control limits for the fraction nonconforming are:

where:

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9Trial Control LimitsControl limits that are based on a preliminary set of data can often be referred to as trial control limits. The quality characteristic is plotted against the trial limits, if any points plot out of control, assignable causes should be investigated and points removed. With removal of the points, the limits are then recalculated. Note: if the control chart is based on known or specified value then the trial is unnecessary

TMA@2008Module 5: Control Chart forAttribute1010ExampleA process that produces bearing housings is investigated. Ten samples of size 100 are selected.

Is this process operating in statistical control?

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11TMA@2008Module 5: Control Chart forAttribute12n = 100, m = 10

Control Limits are:

12TMA@2008Module 5: Control Chart forAttribute131098765432100.100.050.00Sample NumberProportionP Chart for C1P=0.038003.0SL=0.09536-3.0SL=0.00013Design of Control Chart for Fraction Non ConformingIf p is very small then we should choose large sampleIf is the magnitude of a process shift; L is the distance from the center line then the sample size n can be determined as:TMA@2008Module 5: Control Chart forAttribute14

14The sample size n, can be chosen so that the lower control limit would be nonzero:

and:

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15np Control ChartThe control chart can be based on the actual number of nonconforming rather than the fraction of nonconformingLet n = sample size, p = proportion of nonconforming; the control limits are:

If p is not known or given use TMA@2008Module 5: Control Chart forAttribute16

16Control Chart for Non Conformities (defects)A non-conforming item is a unit of product that does not satsify specificationDepend on the condition in one product may have several non-conformitiesIf the number of non-conformities large enough, it might caused the product rejectedTMA@2008Module 5: Control Chart forAttribute1717TMA@2008Module 5: Control Chart forAttribute18Textile inspection: one-two loose thread is ok but more than certain number is defect

PCB: one defect in solder may be repairable but if it is reach certain number the PCB is rejectedC ChartTMA@2008Module 5: Control Chart forAttribute19Standard Given:

No Standard Given:

ExampleA manufacturer of computer circuit boards tested 10 after they were manufactured. The number of defects obtained per circuit board were: 5, 3, 4, 0, 2, 2, 1, 4, 3, and 2. Construct the appropriate control limits.

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Selecting control chartDetermine which process characteristics to control.Determine where the charts should be implemented in the process.Choose the proper type of control chart.Take action to improve processes as the result of SPC/control chart analysis.Select data-collection systems and computer software.

TMA@2008Module 5: Control Chart forAttribute21Sample #12345678910

# Nonconf.5238412634

Sample #12345678910

# Nonconf.5238412634

Fraction

Nonconf.0.05

0.020.030.080.040.010.020.060.030.04