TMAT 103

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TMAT 103

• Chapter 19
• Statistics for Process Control

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TMAT 103

• 19.1
• Graphic Presentation of Data

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19.1 Graphic Presentation of Data

• Collected data is presented graphically to
• Understand distribution of data
• Identify trends
• Current
• Future
• Draw conclusions

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19.1 Graphic Presentation of Data

• An automobile manufacturer is analyzing data
  gathered in regards to cars coming off an
  assembly line and not starting on the first try.
  In the month of April, the following data was
  collected

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19.1 Graphic Presentation of Data

• A frequency table can make the data more
  readable

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19.1 Graphic Presentation of Data

• A histogram can also be used
• Rectangles must be of equal width

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19.1 Graphic Presentation of Data

• A frequency polygon can also be used
• X coordinate is center of interval, y coordinate
  is frequency

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19.1 Graphic Presentation of Data

• Example
• Using 10 intervals containing 6 numbers each,
  construct a frequency table, histogram, and
  frequency polygon for the following situationA
  local restaurant counted the number of hamburgers
  served on 25 consecutive weekends the data is
  given below.

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TMAT 103

• 19.2
• Measures of Central Tendency

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19.2 Measures of Central Tendency

• Central Tendency
• Finding a number which describes a set of data
• 3 general methods
• Mean
• Median
• Mode

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19.2 Measures of Central Tendency

• The Mean
• The Mean of a set of n numbers, a1, a2, , an is
  given by

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19.2 Measures of Central Tendency

• Examples
• 13 students took an exam, with the following
  scores. Find the mean score.98, 92, 90, 85,
  85, 82, 77, 76, 75, 74, 74, 68, 52
• 10 people were surveyed for their salary. The
  following data was collected. Find the mean
  salary.35,000,000 59,50099,500 55,30088,300
  30,20067,200 25,40060,000 22,000

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19.2 Measures of Central Tendency

• The Median
• The Median of an ordered set of n numbers, a1,
  a2, , an is the middle number if n is odd, and
  the mean of the two middle numbers if n is even.

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19.2 Measures of Central Tendency

• Examples
• 13 students took an exam, with the following
  scores. Find the median score.98, 92, 90, 85,
  85, 82, 77, 76, 75, 74, 74, 68, 52
• 10 people were surveyed for their salary. The
  following data was collected. Find the median
  salary.35,000,000 59,50099,500 55,30088,300
  30,20067,200 25,40060,000 22,000

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19.2 Measures of Central Tendency

• The Mode
• The Mode of an set of n numbers, a1, a2, , an is
  the number which occurs most often. There may be
  more than one mode.

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19.2 Measures of Central Tendency

• Examples
• 13 students took an exam, with the following
  scores. Find the mode.98, 92, 90, 85, 85, 82,
  77, 76, 75, 74, 74, 68, 52
• 10 people were surveyed for their salary. The
  following data was collected. Find the
  mode.35,000,000 59,50099,500 55,30088,300 30
  ,20067,200 25,40060,000 22,000

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TMAT 103

• 19.3Measures of Dispersion

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19.3 Measures of Dispersion

• Terminology
• Range
• Difference between largest and smallest values
• Population
• Collection of all items being considered
• Sample
• Items selected to be in calculation
• Random
• When each item has an equal chance to be selected
• Sample Standard Deviation
• One way to measure dispersion

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19.3 Measures of Dispersion

• Sample Standard Deviation
• The sample standard deviation of a set of data
  x1, x2, , xn is given by

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19.3 Measures of Dispersion

• Example
• A furniture company manufactures 28-in. table
  legs. Acceptable lengths are between 27.9375 and
  28.0625 in. A random sample of 30 legs were
  measured each day for a week. The number of
  acceptable legs produced each day were 41, 41,
  43, 44, 46, 46, 48.Find the range and sample
  standard deviation for this set.

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TMAT 103

• 19.4
• The Normal Distribution

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19.4 The Normal Distribution

• Normal distribution
• Histogram of sample means with smooth curve drawn
  through centers of rectangles

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19.4 The Normal Distribution

• Important features of normal distribution
• Bell shaped
• Symmetric about a vertical line passing through
  the mean
• Smaller sx implies more data is closer to the
  mean
• Distribution of data is predictable

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19.4 The Normal Distribution

• Smaller sx implies more data is closer to the mean

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19.4 The Normal Distribution

• Distribution of data is predictable
• 68.2 within 1 standard deviation of mean
• 95.4 within 2 standard deviations of mean
• 99.7 within 3 standard deviations of means

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19.4 The Normal Distribution

• Examples
• Does the following set of numbers meet the
  criteria for a normal distribution in terms of
  the percent of values with one standard deviation
  (allow a 2 margin of error)?35, 36, 38, 43, 47,
  48, 48, 55, 67
• The scores from a test resulted in a mean of 72
  and standard deviation of 8.5. Mark scored 89.
  Assuming the scores were normally distributed,
  what percent of students can he estimate scored
  below him?

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TMAT 103

• 19.5Fitting Curves to Data Sets

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19.5 Fitting Curves to Data Sets

• Regression Analysis
• Finding an equation which relates to a data set
  as closely as possible
• Allows for analysis and prediction
• Advanced regression analysis uses matrix theory
  and calculus

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TMAT 103

• 19.6
• Statistical Process Control

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19.6 Statistical Process Control

• Using statistics for quality control
• Specifications
• Does it meet or exceed established specifications
• Durability
• Does the item perform as long as expected
• Reliability
• How often are repairs needed
• Service
• Is item easy to repair? Are shipping/billing
  errors rare?
• Customer needs
• Does item meet expectations and needs of customer?

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19.6 Statistical Process Control

• Terminology
• Common cause variation
• Variations always occur within a product
• Process in control
• Produced items consistently fall within common
  cause tolerance limits, and measurements fit a
  normal curve
• Limits
• UCL upper control limit
• LCL lower control limit
• UTL upper tolerance limit
• LTL Lower tolerance limit
• Capable process
• Control limits within tolerance limits (i.e.
  specifications)

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19.6 Statistical Process Control

• Process in control

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19.6 Statistical Process Control

• Capable Process
• A capable process is ALWAYS in control

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19.6 Statistical Process Control

• Process not in control, but within tolerance
  limits
• Unpredictable, and undesirable

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19.6 Statistical Process Control

• Determine which of the processes are capable
• Both processes are in control, and all
  measurements are in centimeters