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Measure Phase Six Sigma Statistics

Measure Phase Six Sigma Statistics. Welcome to Measure. Process Discovery. Six Sigma Statistics. Basic Statistics. Descriptive Statistics. Normal Distribution. Assessing Normality. Special Cause / Common Cause. Graphing Techniques. Measurement System Analysis. Process Capability.

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Measure Phase Six Sigma Statistics

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  1. Measure PhaseSix Sigma Statistics

  2. Welcome to Measure Process Discovery Six Sigma Statistics Basic Statistics Descriptive Statistics Normal Distribution Assessing Normality Special Cause / Common Cause Graphing Techniques Measurement System Analysis Process Capability Wrap Up & Action Items Six Sigma Statistics

  3. The purpose of Basic Statistics is to: Provide a numerical summary of the data being analyzed. Data (n) Factual information organized for analysis. Numerical or other information represented in a form suitable for processing by computer Values from scientific experiments. Provide the basis for making inferences about the future. Provide the foundation for assessing process capability. Provide a common language to be used throughout an organization to describe processes. Purpose of Basic Statistics Relax….it won’t be that bad!

  4. Summation An individual value, an observation A particular (1st) individual value The Standard Deviation of sample data For each, all, individual values The Standard Deviation of population data The variance of sample data The mean, average of sample data The variance of population data The grand mean, grand average The range of data The mean of population data The average range of data A proportion of sample data Multi-purpose notation, i.e. # of subgroups, # of classes A proportion of population data The absolute value of some term Sample size Greater than, less than Population size Greater than or equal to, less than or equal to Statistical Notation – Cheat Sheet

  5. Population Parameters: Arithmetic descriptions of a population µ, , P, 2, N Population Sample Sample Sample Parameters vs. Statistics Population: All the items that have the “property of interest” under study. Frame: An identifiable subset of the population. Sample: A significantly smaller subset of the population used to make an inference. • Sample Statistics: • Arithmetic descriptions of asample • X-bar , s, p, s2, n

  6. Attribute Data (Qualitative) Is always binary, there are only two possible values (0, 1) Yes, No Go, No go Pass/Fail Variable Data (Quantitative) Discrete (Count) Data Can be categorized in a classification and is based on counts. Number of defects Number of defective units Number of customer returns Continuous Data Can be measured on a continuum, it has decimal subdivisions that are meaningful Time, Pressure, Conveyor Speed, Material feed rate Money Pressure Conveyor Speed Material feed rate Types of Data

  7. Discrete Variables

  8. Continuous Variables

  9. Understanding the nature of data and how to represent it can affect the types of statistical tests possible. Nominal Scale – data consists of names, labels, or categories. Cannot be arranged in an ordering scheme. No arithmetic operations are performed for nominal data. Ordinal Scale – data is arranged in some order, but differences between data values either cannot be determined or are meaningless. Interval Scale – data can be arranged in some order and for which differences in data values are meaningful. The data can be arranged in an ordering scheme and differences can be interpreted. Ratio Scale – data that can be ranked and for which all arithmetic operations including division can be performed. (division by zero is of course excluded) Ratio level data has an absolute zero and a value of zero indicates a complete absence of the characteristic of interest. Definitions of Scaled Data

  10. Nominal Scale Time to weigh in!

  11. Ordinal Scale

  12. Interval Scale

  13. Ratio Scale

  14. Continuous Data is always more desirable In many cases Attribute Data can be converted to Continuous Which is more useful? 15 scratches or Total scratch length of 9.25” 22 foreign materials or 2.5 fm/square inch 200 defects or 25 defects/hour Converting Attribute Data to Continuous Data

  15. Measures of Location (central tendency) Mean Median Mode Measures of Variation (dispersion) Range Interquartile Range Standard deviation Variance Descriptive Statistics

  16. Open the MINITAB™ Project “Measure Data Sets.mpj” and select the worksheet “basicstatistics.mtw” Descriptive Statistics

  17. Mean is: Commonly referred to as the average. The arithmetic balance point of a distribution of data. Measures of Location Stat>Basic Statistics>Display Descriptive Statistics…>Graphs…>Histogram of data, with normal curve Population Sample Descriptive Statistics: Data Variable N N* Mean SE Mean StDev Minimum Q1 Median Q3 Data 200 0 4.9999 0.000712 0.0101 4.9700 4.9900 5.0000 5.0100 Variable Maximum Data 5.0200

  18. Median is: The mid-point, or 50th percentile, of a distribution of data. Arrange the data from low to high, or high to low. It is the single middle value in the ordered list if there is an odd number of observations It is the average of the two middle values in the ordered list if there are an even number of observations Measures of Location Descriptive Statistics: Data Variable N N* Mean SE Mean StDev Minimum Q1 Median Q3 Data 200 0 4.9999 0.000712 0.0101 4.9700 4.9900 5.0000 5.0100 Variable Maximum Data 5.0200

  19. Trimmed Mean is a: Compromise between the Mean and Median. The Trimmed Mean is calculated by eliminating a specified percentage of the smallest and largest observations from the data set and then calculating the average of the remaining observations Useful for data with potential extreme values. Measures of Location Stat>Basic Statistics>Display Descriptive Statistics…>Statistics…> Trimmed Mean Descriptive Statistics: Data Variable N N* Mean SE Mean TrMean StDev Minimum Q1 Median Data 200 0 4.9999 0.000712 4.9999 0.0101 4.9700 4.9900 5.0000 Variable Q3 Maximum Data 5.0100 5.0200

  20. Mode is: The most frequently occurring value in a distribution of data. Measures of Location Mode = 5

  21. Range is the: Difference between the largest observation and the smallest observation in the data set. A small range would indicate a small amount of variability and a large range a large amount of variability. Interquartile Range is the: Difference between the 75th percentile and the 25th percentile. Measures of Variation Descriptive Statistics: Data Variable N N* Mean SE Mean StDev Minimum Q1 Median Q3 Data 200 0 4.9999 0.000712 0.0101 4.9700 4.9900 5.0000 5.0100 Variable Maximum Data 5.0200 Use Range or Interquartile Range when the data distribution is Skewed.

  22. Standard Deviation is: Equivalent of the average deviation of values from the Mean for a distribution of data. A “unit of measure” for distances from the Mean. Use when data are symmetrical. Measures of Variation Population Sample Descriptive Statistics: Data Variable N N* Mean SE Mean StDev Minimum Q1 Median Q3 Data 200 0 4.9999 0.000712 0.0101 4.9700 4.9900 5.0000 5.0100 Variable Maximum Data 5.0200 Cannot calculate population Standard Deviation because this is sample data.

  23. Variance is the: Average squared deviation of each individual data point from the Mean. Measures of Variation Sample Population

  24. The Normal Distribution is the most recognized distribution in statistics. What are the characteristics of a Normal Distribution? Only random error is present Process free of assignable cause Process free of drifts and shifts So what is present when the data is Non-normal? Normal Distribution

  25. The normal curve is a smooth, symmetrical, bell-shaped curve, generated by the density function. It is the most useful continuous probability model as many naturally occurring measurements such as heights, weights, etc. are approximately Normally Distributed. The Normal Curve

  26. Each combination of Mean and Standard Deviation generates a unique normal curve: “Standard” Normal Distribution Has a μ = 0, and σ = 1 Data from any Normal Distribution can be made to fit the standard Normal by converting raw scores to standard scores. Z-scores measure how many Standard Deviations from the mean a particular data-value lies. Normal Distribution

  27. The area under the curve between any 2 points represents the proportion of the distribution between those points. Convert any raw score to a Z-score using the formula: Refer to a set of Standard Normal Tables to find the proportion between μ and x. Normal Distribution The area between the Mean and any other point depends upon the Standard Deviation. m x

  28. The Empirical Rule… -6 +6 -5 -4 -3 -2 +1 -1 +2 +3 +4 +5 The Empirical Rule • 68.27 % of the data will fall within +/- 1 standard deviation • 95.45 % of the data will fall within +/- 2 standard deviations • 99.73 % of the data will fall within +/- 3 standard deviations • 99.9937 % of the data will fall within +/- 4 standard deviations • 99.999943 % of the data will fall within +/- 5 standard deviations • 99.9999998 % of the data will fall within +/- 6 standard deviations

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