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Chapter 3: Attribute Measurement Systems Analysis (Optional)

3.1 Introduction to Attribute Measurement Systems Analysis

3.2 Conducting an Attribute MSA

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Chapter 3: Attribute Measurement Systems Analysis (Optional)

3.1 Introduction to Attribute Measurement Systems 3.1 Introduction to Attribute Measurement Systems AnalysisAnalysis

3.2 Conducting an Attribute MSA

Objectives Introduce the basic concepts of an attribute

measurement systems analysis (MSA). Understand operational definitions for inspection

and evaluation. Define attribute MSA terms.

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What Is an MSA? A measurement systems analysis is an evaluation of

the efficacy of a measurement system. It is applicable to both continuous and attribute data. An attribute MSA evaluates whether a classification

system correctly sorts items. Companies make decisions each day based on

classifications; it is necessary to evaluate the efficacy of such classifications.

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Operational DefinitionsIn order for a rater to decide if a product is defective or not, he must have a clear description, or an operational definition, of what constitutes a defect. Such a definition might include the following: photographs physical specimens descriptions specifications.

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EffectivenessThe effectiveness of an inspection process is the percentage of time that a rater, or other

measurement tool, is correct in its classification of quality

is often significantly low before any attempts at improvement are instigated

should be at least 95%.

Effectiveness = number of correct evaluations

number of total opportunities

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3.01 Multiple Choice PollSuppose 100 windshields are inspected, and 10 are defective and 90 are non-defective. If an inspector decides that 6 non-defectives are defective, and 1 defective is non-defective, what is his effectiveness?

a. .67

b. .067

c. .1

d. .93

e. None of the above

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3.01 Multiple Choice Poll – Correct AnswerSuppose 100 windshields are inspected, and 10 are defective and 90 are non-defective. If an inspector decides that 6 non-defectives are defective, and 1 defective is non-defective, what is his effectiveness?

a. .67

b. .067

c. .1

d. .93

e. None of the above

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False AlarmsA false alarm is a non-defective item that is classified as defective.

The probability of a false alarm, also known as Type I error or producer’s risk, is given by:

P(False Alarm) = number of false alarms

number of non-defective items

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3.02 Multiple Choice PollSuppose 100 windshields are inspected, and 10 are defective and 90 are non-defective. If an inspector decides that 6 non-defectives are defective, and 1 defective is non-defective, what is the probability of a false alarm?

a. .67

b. .067

c. .1

d. .93

e. None of the above

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3.02 Multiple Choice Poll – Correct AnswerSuppose 100 windshields are inspected, and 10 are defective and 90 are non-defective. If an inspector decides that 6 non-defectives are defective, and 1 defective is non-defective, what is the probability of a false alarm?

a. .67

b. .067

c. .1

d. .93

e. None of the above

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MissesA miss is a defective item that is classified as non-defective.

The probability of a miss, also known as Type II error or consumer’s risk, is given by:

P(Miss) = number of misses

number of defective items

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3.03 Multiple Choice PollSuppose 100 windshields are inspected, and 10 are defective and 90 are non-defective. If an inspector decides that 6 non-defectives are defective, and 1 defective is non-defective, what is the probability of a miss?

a. .67

b. .067

c. .1

d. .93

e. None of the above

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3.03 Multiple Choice Poll – Correct AnswerSuppose 100 windshields are inspected, and 10 are defective and 90 are non-defective. If an inspector decides that 6 non-defectives are defective, and 1 defective is non-defective, what is the probability of a miss?

a. .67

b. .067

c. .1

d. .93

e. None of the above

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Escape RateAn escape rate gives the percentage of time a customer is likely to see a defective item.

Escape Rate = P(Miss) × P(Defect)

where P(Defect) = number of defects

number of items inspected.

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Bias Bias is the tendency of an inspector to classify items

either as defective or as non-defective. Bias is defined as P(False Alarm)/P(Miss). Bias =1 implies there is no bias. Bias < 1 implies a bias towards accepting bad items. Bias > 1 implies a bias towards rejecting good items.

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3.04 Multiple Choice PollThe bias is given by the probability of a false alarm divided by the probability of a miss. In the windshield example, the bias is given by .067/.1 = .67. What is the interpretation of this value?

a. There is no bias.

b. There is a bias towards accepting bad items.

c. There is a bias towards rejecting good items.

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3.04 Multiple Choice Poll – Correct AnswerThe bias is given by the probability of a false alarm divided by the probability of a miss. In the windshield example, the bias is given by .067/.1 = .67. What is the interpretation of this value?

a. There is no bias.

b. There is a bias towards accepting bad items.

c. There is a bias towards rejecting good items.

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Rater AgreementRater agreement is a measure of how well raters agree with each other is not an indication of correctness

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Kappa StatisticThe Kappa statistic is used to measure between-rater variability, or how

often two or more raters agree in their interpretations is a measure and not a test is given by:

kappa = po – pe

1 – pe

where po is the sum of observed proportions in diagonal cells of the contingency table and pe is the sum of expected proportions in diagonal cells of the contingency table.

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Chapter 3: Attribute Measurement Systems Analysis (Optional)

3.1 Introduction to Attribute Measurement Systems Analysis

3.2 Conducting an Attribute MSA3.2 Conducting an Attribute MSA

Objectives Examine the requirements for an attribute MSA. Perform an attribute MSA in JMP.

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Sample SizeTo conduct an attribute MSA, the minimum recommended sample sizes are given as follows:

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Number of

Raters

Minimum Number of Parts

Number of Evaluations

1 40 3

2 30 3

3+ 25 3

Attribute MSA Example Suppose three inspectors, Henry, Matt, and Tom, are

independently going to classify each of 30 parts as defective or non-defective in a random order. They will evaluate each part three different times. Of the 30 parts, 13 are defective and 17 are non-defective.

The classification will be based on a predetermined operational definition of defective and non-defective.

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This demonstration illustrates the concepts discussed previously.

Attribute MSA

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Exercise

This exercise reinforces the concepts discussed previously.