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# Statistical Process Control

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The presentation is about basic statistical techniques and how statistics can be used effectively in the quality control and process control. It also presents statistical package Minitab version 16 and some of its applications in the field of statistical process control.

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### Statistical Process Control

1. 1. Statistical Process Control Relating Applied Statistics to Quality Control
2. 2. Contents  Introduction to Statistics    Descriptive Analysis Inferential Analysis Statistical Quality Control  Descriptive Statistics  Statistical Process Control (SPC)   SPC: 7 Basic Quality Tools Acceptance Sampling
3. 3. Introduction to Statistics The Nature of Statistics and the Collection of Data
4. 4. What is Statistics? A branch of mathematics used to summarize, analyze, and interpret a group of numbers or observations
5. 5. Descriptive Statistics Procedures used to summarize, organize, and make sense of a set of scores or observations Typically presented graphically, in tabular form (in tables), or as summary statistics (single values)
6. 6. Inferential Statistics Procedures used that allow researchers to infer or generalize observations made with samples to the larger population from which they were selected
7. 7. Before we go… Which type of tables, graphs, and summary measures to use with our data? Data Measurements or observations that are typically numeric Datum = raw score (a single measurement or observation)
8. 8. Data Concepts Sources of Data Internal vs. External Data Elementary Units & Variables Population vs. Sample Qualitative vs. Quantitative Variables Observational Study (Survey) Experiment Census Sample Survey
9. 9. Why Sampling? Reducing cost of collecting and processing data Sampling can provide more accurate data than a census Census is physically impossible Sampling can provide more detailed information than a census Census is senseless whenever the acquisition of the desired information destroys the elementary units of interest Census is senseless whenever it produces information that comes too late
10. 10. Samples Types & Errors Sampling Techniques Probability Simple Random Systematic Stratified Non-Probability Cluster Convenience Judgmental Quota
11. 11. Probability Sampling Simple Random Sample Systematic Sampling Stratified Sampling Cluster Sampling
12. 12. Non-Probability Sampling Convenience Most convenient based on researcher judgment Most Easy Most Dangerous Judgmental Quota Researcher selects people according to some fixed quota
13. 13. Sampling Error  Random Error: arise from random fluctuations in the measurements  Systematic Error (Bias): consistent and repeatable (constant offset)
14. 14. Variable Data Types Qualitative = Quality (Categorical Variables) Quantitative = Quantity (Numeric Variables)
15. 15. Levels of Measurement Variable Data Qualitative (Categorical) Nominal (no natural order between the categories) Quantitative Ordinal (ordering) Discrete (variable takes on a limited number of outcomes) Ratio (there is a true zero) continuous data where the differences (intervals) between the numbers are comparable Interval (no true zero) Continuous (variables can take on tiniest fractional values) Type Measurement Level
16. 16. Minitab 16 Software A statistical software used to analyze data o Calculating basic statistics o Graphing data o Running hypothesis tests
17. 17. Starting Minitab 16
18. 18. Minitab Interface
19. 19. Opening a Worksheet
20. 20. Descriptive Statistics The Effective Presentation of Data
21. 21. The Presentation of Data Tables & Graphs Tables Absolute Frequency Distribution Graphs Frequency Histograms Relative Frequency Distribution Bar & Column Charts Cumulative Frequency Distribution Line Graphs Pie Charts Stem-&-Leaf Diagrams Box-&-Whisker Diagrams
22. 22. Absolute Frequency Distribution Absolute Class Frequency (number of companies in class) Class (size of profit in million of dollars) Tally Count -1,500 to under 0 || | 0 to under 500 || |||| |||| |||| ||| |||| |||| |||| |||| 41 500 to under 1,000 || |||| |||| ||| |||| |||| |||| | 32 1,000 to under 1,500 || || |||| 9 1,500 to under 2,000 || ||| 6 2,000 to under 2,500 || ||| 6 2,500 to under 5,500 || | 3 Total 3 100
23. 23. Relative Frequency Distribution Absolute Class Frequency (number of companies in class) Class (size of profit in million of dollars) -1,500 to under 0 Relative Class Frequency (proportion of all companies in class) 3 .03 0 to under 500 41 .41 500 to under 1,000 32 .32 1,000 to under 1,500 9 .09 1,500 to under 2,000 6 .06 2,000 to under 2,500 6 .06 2,500 to under 5,500 3 .03 100 1.00 Total
24. 24. Cumulative Frequency Distribution Class (size of profit in million of dollars) -1,500 to under 0 Cumulative Absolute Class Frequency (number of companies in class or lower ones) Absolute Class Frequency (number of companies in class) Relative Class Frequency (proportion of all companies in class) Cumulative Relative Class Frequency (proportion of all companies in class or lower ones) 3 3 .03 .03 0 to under 500 41 3 + 41 = 44 .41 .03 + .41 = .44 500 to under 1,000 32 44 + 32 = 76 .32 .44 + .32 = .76 1,000 to under 1,500 9 76 + 9 = 85 .09 .76 + .09 = .85 1,500 to under 2,000 6 85 + 6 = 91 .06 .85 + .06 = .91 2,000 to under 2,500 6 91 + 6 = 97 .06 .91 + .06 = .97 2,500 to under 5,500 3 97 + 3 = 100 .03 .97 + .03 = 1.00
25. 25. Producing Frequency Table
26. 26. The Frequency Histogram Absolute or relative class frequencies are represented by bars (vertical rectangular areas)
27. 27. The Frequency Polygon A graphical device for understanding the shapes of distributions - A good choice for displaying cumulative frequency distributions
28. 28. Bar & Column Charts A chart with rectangular bars with lengths proportional to the values that they represent. The bars can be plotted vertically or horizontally.
29. 29. Histograms vs. Bar Graphs
30. 30. Line Graph A graph that shows information that is connected in some way (such as change over time)
31. 31. Pie Chart A special chart that uses "pie slices" to show relative sizes of data
32. 32. Stem-&-Leaf Diagram A special table where each data value is split into a "leaf" (usually the last digit) and a "stem" (the other digits)
33. 33. Box-&-Whisker Diagram (Boxplot) A way of summarizing a set of data measured on an interval scale - used to show the shape of the distribution, its central value, and variability
34. 34. The Presentation of Data Summary Measures Continuous Measures of Central Tendency (Location) Mean µ Median M Mode Mo Quartiles (Percentiles) Ordinal Nominal Continuous Ordinal Continuous Range Variance σ2 Standard Deviation σ Measures of Dispersion (Variability) Measures of Shape Proportion π Skewness Sk Kurtosis K Continuous
35. 35. Standard Normal Distribution
36. 36. Statistics Formulas Descriptive Statistics Statistic Formula Mean Median (50% Quartile) Mode Most frequent value Range Maximum - Minimum Variance Standard Deviation Skewness Kurtosis Quartiles Cut into 4 equal parts Order Data Cuts = Quartiles
37. 37. Skewness
38. 38. Kurtosis
39. 39. Minitab Application
40. 40. Inferential Statistics
41. 41. Inferential Analysis Hypothesis Testing Relationship among Variables
42. 42. Hypothesis Testing (Significance Testing) A systematic approach to assessing tentative beliefs about reality. It involves confronting those beliefs with evidence and deciding, in light of this evidence, whether the beliefs can be maintained as reasonable or must be discarded as untenable.
43. 43. Hypothesis Testing Steps State the Hypothesis H0 vs. Ha Select a test statistic z or t Derive a decision rule Level of Significance α Take a sample, compute the test statistic, & confront it with the decision rule Significance Value (p-value)
44. 44. Making a Decision Types of Error
45. 45. Test of Normality
46. 46. Relationship among Variables Relationship between two variables can be checked by drawing scatterplots or running statistical tests.
47. 47. Scatterplots
48. 48. Minitab Application
49. 49. Correlation Perfect Weak
50. 50. Minitab Application
51. 51. Testing Relationship among Variables Variables Test Both Variables are Nominal Chi-square Independent Variable is Nominal & T-Test (Independent Variable has only two Dependent Variable is Interval or Ratio categories) ANOVA (Independent Variable has more than two categories) Both Variables are Interval or Ratio Correlation or Regression
52. 52. Chi-Square X2 Test Testing the Alleged Independence of two Qualitative Variables Contingency Table A table that classifies data according to two or more categories, associated with each of two qualitative variables that may or may not be statistically independent It shows all possible combinations of categories, or contingencies, which counts for its name.
53. 53. T-Test How to test for differences between means from two separate groups of subjects.
54. 54. ANOVA Analysis of Variance Used to determine whether there are any significant differences between the means of three or more independent (unrelated) groups
55. 55. Regression Simple Regression Analysis A statistical technique that establishes an equation that allows the unknown value of one variable to be estimated from the known value of one other variable
56. 56. Statistical Quality Control The general category of statistical tools used to evaluate organizational quality
57. 57. Statistical Quality Control (SQC) Descriptive Statistics Statistical Process Control (SPC) Acceptance Sampling
58. 58. Descriptive Statistics Statistics used to describe quality characteristics and relationships Acceptance Sampling Statistical Process Control (SPC) A statistical tool that involves inspecting a random sample of the The process of randomly inspecting a sample of goods and deciding whether to accept the entire lot based on the results output from a process and deciding whether the process is Process Capability producing products with The ability of a production process to characteristics that fall within a meet or exceed preset speciﬁcations predetermined range All three of these statistical quality control categories are helpful in measuring and evaluating the quality of products or services. However, statistical process control (SPC) tools are used most frequently because they identify quality problems during the production process.
59. 59. Why SPC is the Most Important Tool of the SQC?  Measure the value of a quality characteristic  Help to identify a change or variation in some quality characteristic of the product or process
60. 60. Some Information about SPC  SPC can be applied to any process.  There is inherent variation in any process which can be measured and “controlled”.  SPC doesn’t eliminate variation, but it does allow the user to track special cause variation.  “SPC is a statistical method of separating variation resulting from special causes from natural variation and to establish and maintain consistency in the process, enabling process improvement.” (Goetsch & Davis, 2003. p. 631)
61. 61. Sources of Variation Common Causes of Variation Based on random causes that cannot be identified, unavoidable & due to slight differences in processing Assignable Causes of Variation can be precisely identiﬁed & eliminated
62. 62. Descriptive Statistics  Describing certain characteristics of a product & a process  Measures of Central Tendency (mean)  Measures of Variability (standard deviation & range)  Measures of the Distribution of Data
63. 63. Statistical Process Control Methods – 7 Basic Quality Tools Control Chart Check Sheet Pareto Chart Flow Chart Cause-&-Effect Diagram Histogram Scatter Diagram
64. 64. 1. Control Chart  A graph that shows whether a sample of data falls within the common or normal range of variation  A control chart has upper and lower control limits that separate common from assignable causes of variation.  A process is out of control when a plot of data reveals that one or more samples fall outside the control limits.
65. 65. Types of Control Chart Characteristics measured by Control Chart Variables Attributes A product characteristic that can be measured and has a continuum of values (e.g.,height, weight, or volume). A product characteristic that has a discrete value and can be counted P & C Charts
66. 66. Control Charts for Variables Range (R) Charts  
67. 67. Minitab Application
68. 68. Control Charts for Attributes P-Charts C-Charts  
69. 69. Minitab Application
70. 70. Process Capability  The ability of the process to produce within a specification  Cp compares the natural variation of the process to the specification width  Cpk compares the natural variation of the process to the specification width and target
71. 71. Process Capability Process Capability is the range in which all output can be produced – the inherent capability of the process Cpk Values
72. 72. Minitab Application
73. 73. Acceptance Sampling An inspection procedure used to determine whether to accept or reject a specific quantity of materials Acceptance Sampling Sampling Plans Producer’s Risk & Consumer’s Risk Managing Levels of Risk
74. 74. Sampling Plan  A plan for acceptance sampling that precisely speciﬁes the parameters of the sampling process and the acceptance/rejection criteria  No 100% Inspection  The most widely used sampling plans are given by Military Standard (MIL-STD-105E)  Determines the quality level of an incoming shipment or at the end of production  Judges whether quality level is within the level that has been predetermined
75. 75. Types of Sampling Plans Single-Sampling Plan Sequential-Sampling Plan A decision to accept or reject a lot based on the results of one random sample from the lot. A plan in which the consumer randomly selects items from the lot and inspects them one by one. Double-Sampling Plan A plan in which management specifies two sample sizes and two acceptance numbers; if the quality of the lot is very good or very bad, the consumer can make a decision to accept or reject the lot on the basis of the first sample, which is smaller than in the single-sampling plan. Sampling by Attribute Sampling by Variable
76. 76. The Single Sampling Procedure Take a Random Sample of size n from the Lot of size N Inspect all items in the Sample Defectives found = d Yes d≤c? Accept Lot No Reject Lot Do 100% Inspection Return Lot
77. 77. Acceptance Sampling Risks The Lot is actually Good The Lot is actually Bad The Lot is Accepted Correct Decision Confidence = 1 – α Incorrect Decision β Risk (Consumer’s Risk) The Lot is Rejected Incorrect Decision α Risk (Producer’s Risk) Correct Decision Power = 1 - β
78. 78. OC Curve The Operating Characteristics Curve A graph that describes how well a sampling plan discriminates between good and bad lots
79. 79. Quality & Risk Decisions  Acceptable Quality Level (AQL): The small percentage of defects that consumers are willing to accept.  Producer’s Risk (α): The chance that a lot containing an acceptable quality level will be rejected.  Lot Tolerance Proportion Defective (LTPD): The upper limit of the percentage of defective items consumers are willing to tolerate.  Consumer’s Risk (β): The chance of accepting a lot that contains a greater number of defects than the LTPD limit.
80. 80. Average Outgoing Quality (AOQ) 
81. 81. Create a Sampling Plan
82. 82. Compare a Sampling Plan
83. 83. 2. Check Sheet A simple document that is used for collecting data in realtime and at the location where the data is generated.
84. 84. 3. Pareto Chart A bar chart that is used to analyze the frequency of problems or causes in a process
85. 85. 4. Flow Chart  Used for analyzing a sequence of events in a process  Can be used to understand a complex process in order to find the relationships and dependencies between events  MS Visio Software
86. 86. 5. Cause-&-Effect Diagram Fishbone Diagram: help organize ideas & identify relationships, encourages brainstorming for ideas
87. 87. 6. Histogram A graphical representation of the distribution of data
88. 88. 7. Scatterplot A graph of plotted points that show the relationship between two sets of data
89. 89. “ Thank You! Presenter: Marwa Abo Amra statistician.marwa@gmail.com ”
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