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Chapter 18 Introduction to Quality and Statistical Process Control

Business Statistics. Chapter 18 Introduction to Quality and Statistical Process Control. Chapter Goals. After completing this chapter, you should be able to: Use the seven basic tools of quality Construct and interpret x-bar and R-charts Construct and interpret p-charts

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Chapter 18 Introduction to Quality and Statistical Process Control

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  1. Business Statistics Chapter 18Introduction to Quality and Statistical Process Control Tran Van Hoang - hoangtv@ftu.edu.vn - Business Statistics

  2. Chapter Goals After completing this chapter, you should be able to: • Use the seven basic tools of quality • Construct and interpret x-bar and R-charts • Construct and interpret p-charts • Construct and interpret c-charts Tran Van Hoang - hoangtv@ftu.edu.vn - Business Statistics

  3. Chapter Overview Quality Management and Tools for Improvement Tools for Quality Improvement Philosophy of Quality Deming’s 14 Points The Basic 7 Tools Control Charts Juran’s 10 Steps to Quality Improvement X-bar/R-charts p-charts c-charts Tran Van Hoang - hoangtv@ftu.edu.vn - Business Statistics

  4. Themes of Quality Management • Primary focus is on process improvement • Most variations in process are due to systems • Teamwork is integral to quality management • Customer satisfaction is a primary goal • Organization transformation is necessary • It is important to remove fear • Higher quality costs less Tran Van Hoang - hoangtv@ftu.edu.vn - Business Statistics

  5. Deming’s 14 Points • 1. Create a constancy of purpose toward improvement • become more competitive, stay in business, and provide jobs • 2. Adopt the new philosophy • Better to improve now than to react to problems later • 3. Stop depending on inspection to achieve quality -- build in quality from the start • Inspection to find defects at the end of production is too late • 4. Stop awarding contracts on the basis of low bids • Better to build long-run purchaser/supplier relationships Tran Van Hoang - hoangtv@ftu.edu.vn - Business Statistics

  6. Deming’s 14 Points (continued) • 5. Improve the system continuously to improve quality and thus constantly reduce costs • 6. Institute training on the job • Workers and managers must know the difference between common cause and special cause variation • 7. Institute leadership • Know the difference between leadership and supervision • 8. Drive out fear so that everyone may work effectively. • 9. Break down barriers between departments so that people can work as a team. Tran Van Hoang - hoangtv@ftu.edu.vn - Business Statistics

  7. Deming’s 14 Points (continued) • 10. Eliminate slogans and targets for the workforce • They can create adversarial relationships • 11. Eliminate quotas and management by objectives • 12. Remove barriers to pride of workmanship • 13. Institute a vigorous program of education and self-improvement • 14. Make the transformation everyone’s job Tran Van Hoang - hoangtv@ftu.edu.vn - Business Statistics

  8. Juran’s 10 Steps to Quality Improvement • 1. Build awareness of both the need for improvement and the opportunity for improvement • 2. Set goals for improvement • 3. Organize to meet the goals that have been set • 4. Provide training • 5. Implement projects aimed at solving problems Tran Van Hoang - hoangtv@ftu.edu.vn - Business Statistics

  9. Juran’s 10 Steps to Quality Improvement (continued) • 6. Report progress • 7. Give recognition • 8. Communicate the results • 9. Keep score • 10. Maintain momentum by building improvement into the company’s regular systems Tran Van Hoang - hoangtv@ftu.edu.vn - Business Statistics

  10. The Deming Cycle Plan The Deming Cycle Act Do The key is a continuous cycle of improvement Study Tran Van Hoang - hoangtv@ftu.edu.vn - Business Statistics

  11. The Basic 7 Tools • Process Flowcharts • Brainstorming • Fishbone Diagram • Histogram • Trend Charts • Scatter Plots • Statistical Process Control Charts Tran Van Hoang - hoangtv@ftu.edu.vn - Business Statistics

  12. The Basic 7 Tools (continued) • Process Flowcharts • Brainstorming • Fishbone Diagram • Histogram • Trend Charts • Scatter Plots • Statistical Process Control Charts Map out the process to better visualize and understand opportunities for improvement Tran Van Hoang - hoangtv@ftu.edu.vn - Business Statistics

  13. The Basic 7 Tools (continued) • Process Flowcharts • Brainstorming • Fishbone Diagram • Histogram • Trend Charts • Scatter Plots • Statistical Process Control Charts Fishbone (cause-and-effect) diagram: Cause 1 Cause 2 Sub-causes Problem Sub-causes Cause 4 Cause 3 Show patterns of variation Tran Van Hoang - hoangtv@ftu.edu.vn - Business Statistics

  14. The Basic 7 Tools (continued) • Process Flowcharts • Brainstorming • Fishbone Diagram • Histogram • Trend Charts • Scatter Plots • Statistical Process Control Charts Identify trend y time Examine relationships y x Tran Van Hoang - hoangtv@ftu.edu.vn - Business Statistics

  15. The Basic 7 Tools (continued) • Process Flowcharts • Brainstorming • Fishbone Diagram • Histogram • Trend Charts • Scatter Plots • Statistical Process Control Charts Examine the performance of a process over time X time Tran Van Hoang - hoangtv@ftu.edu.vn - Business Statistics

  16. Introduction to Control Charts • Control Charts are used to monitor variation in a measured value from a process • Exhibits trend • Can make correction before process is out of control • A process is a repeatable series of steps leading to a specific goal • Inherent variation refers to process variation that exists naturally. This variation can be reduced but not eliminated Tran Van Hoang - hoangtv@ftu.edu.vn - Business Statistics

  17. Process Variation Total Process Variation Common Cause Variation Special Cause Variation = + • Variation is natural; inherent in the world around us • No two products or service experiences are exactly the same • With a fine enough gauge, all things can be seen to differ Tran Van Hoang - hoangtv@ftu.edu.vn - Business Statistics

  18. Sources of Variation Total Process Variation Common Cause Variation Special Cause Variation = + Variation is often due to differences in: • People • Machines • Materials • Methods • Measurement • Environment Tran Van Hoang - hoangtv@ftu.edu.vn - Business Statistics

  19. Common Cause Variation Total Process Variation Common Cause Variation Special Cause Variation = + Common cause variation • naturally occurring and expected • the result of normal variation in materials, tools, machines, operators, and the environment Tran Van Hoang - hoangtv@ftu.edu.vn - Business Statistics

  20. Special Cause Variation Total Process Variation Common Cause Variation Special Cause Variation = + Special cause variation • abnormal or unexpected variation • has an assignable cause • variation beyond what is considered inherent to the process Tran Van Hoang - hoangtv@ftu.edu.vn - Business Statistics

  21. Statistical Process Control Charts • Show when changes in data are due to: • Special or assignable causes • Fluctuations not inherent to a process • Represents problems to be corrected • Data outside control limits or trend • Common causes or chance • Inherent random variations • Consist of numerous small causes of random variability Tran Van Hoang - hoangtv@ftu.edu.vn - Business Statistics

  22. Control Chart Basics Special Cause Variation: Range of unexpected variability UCL Common Cause Variation: range of expected variability +3σ Process Average -3σ LCL time UCL = Process Average + 3 Standard Deviations LCL = Process Average – 3 Standard Deviations Tran Van Hoang - hoangtv@ftu.edu.vn - Business Statistics

  23. Process Variability Special Cause of Variation: A measurement this far from the process average is very unlikely if only expected variation is present UCL ±3σ → 99.7% of process values should be in this range Process Average LCL time UCL = Process Average + 3 Standard Deviations LCL = Process Average – 3 Standard Deviations Tran Van Hoang - hoangtv@ftu.edu.vn - Business Statistics

  24. Statistical Process Control Charts Statistical Process Control Charts X-bar charts and R-charts p-charts c-charts Used for measured numeric data Used for proportions (attribute data) Used for number of attributes per sampling unit Tran Van Hoang - hoangtv@ftu.edu.vn - Business Statistics

  25. x-bar chart and R-chart • Used for measured numeric data from a process • Start with at least 20 subgroups of observed values • Subgroups usually contain 3 to 6 observations each Tran Van Hoang - hoangtv@ftu.edu.vn - Business Statistics

  26. Steps to create an x-chart and an R-chart • Calculate subgroup means and ranges • Compute the average of the subgroup means and the average range value • Prepare graphs of the subgroup means and ranges as a line chart Tran Van Hoang - hoangtv@ftu.edu.vn - Business Statistics

  27. Steps to create an x-chart and an R-chart (continued) • Compute the upper and lower control limits for the x-bar chart • Compute the upper and lower control limits for the R-chart • Use lines to show the control limits on the x-bar and R-charts Tran Van Hoang - hoangtv@ftu.edu.vn - Business Statistics

  28. Example: x-chart • Process measurements: Tran Van Hoang - hoangtv@ftu.edu.vn - Business Statistics

  29. Average of Subgroup Means and Ranges Average of subgroup means: Average of subgroup ranges: where: xi = ith subgroup average k = number of subgroups where: Ri = ith subgroup range k = number of subgroups Tran Van Hoang - hoangtv@ftu.edu.vn - Business Statistics

  30. Computing Control Limits • The upper and lower control limits for an x-chart are generally defined as • or UCL = Process Average + 3 Standard Deviations LCL = Process Average – 3 Standard Deviations Tran Van Hoang - hoangtv@ftu.edu.vn - Business Statistics

  31. Computing Control Limits (continued) • Since control charts were developed before it was easy to calculate σ, the interval was formed using R instead • The value A2R is used to estimate 3σ , where A2 is from Appendix Q • The upper and lower control limits are where A2 = Shewhart factor for subgroup size n from appendix Q Tran Van Hoang - hoangtv@ftu.edu.vn - Business Statistics

  32. Example: R-chart • The upper and lower control limits for an R-chart are where: D4 and D3 are taken from the Shewhart table (appendix Q) for subgroup size = n Tran Van Hoang - hoangtv@ftu.edu.vn - Business Statistics

  33. x-chart and R-chart UCL x-chart LCL time UCL R-chart LCL time Tran Van Hoang - hoangtv@ftu.edu.vn - Business Statistics

  34. Using Control Charts • Control Charts are used to check for process control H0: The process is in control i.e., variation is only due to common causes HA: The process is out of control i.e., special cause variation exists • If the process is found to be out of control, steps should be taken to find and eliminate the special causes of variation Tran Van Hoang - hoangtv@ftu.edu.vn - Business Statistics

  35. Process In Control • Process in control: points are randomly distributed around the center line and all points are within the control limits UCL LCL time Tran Van Hoang - hoangtv@ftu.edu.vn - Business Statistics

  36. Process Not in Control Out of control conditions: • One or more points outside control limits • Nine or more points in a row on one side of the center line • Six or more points movingin the same direction • 14 or more points alternating above and below the center line Tran Van Hoang - hoangtv@ftu.edu.vn - Business Statistics

  37. Process Not in Control • One or more points outside control limits • Nine or more points in a row on one side of the center line UCL UCL LCL LCL • Six or more points moving in the same direction • 14 or more points alternating above and below the center line UCL UCL LCL LCL Tran Van Hoang - hoangtv@ftu.edu.vn - Business Statistics

  38. Out-of-control Processes • When the control chart indicates an out-of-control condition (a point outside the control limits or exhibiting trend, for example) • Contains both common causes of variation and assignable causes of variation • The assignable causes of variation must be identified • If detrimental to the quality, assignable causes of variation must be removed • If increases quality, assignable causes must be incorporated into the process design Tran Van Hoang - hoangtv@ftu.edu.vn - Business Statistics

  39. p-Chart • Control chart for proportions • Is an attribute chart • Shows proportion of nonconforming items • Example -- Computer chips: Count the number of defective chips and divide by total chips inspected • Chip is either defective or not defective • Finding a defective chip can be classified a “success” Tran Van Hoang - hoangtv@ftu.edu.vn - Business Statistics

  40. p-Chart (continued) • Used with equal or unequal sample sizes (subgroups) over time • Unequal sizes should not differ by more than ±25% from average sample sizes • Easier to develop with equal sample sizes • Should have np > 5 and n(1-p) > 5 Tran Van Hoang - hoangtv@ftu.edu.vn - Business Statistics

  41. Creating a p-Chart • Calculate subgroup proportions • Compute the average of the subgroup proportions • Prepare graphs of the subgroup proportions as a line chart • Compute the upper and lower control limits • Use lines to show the control limits on the p-chart Tran Van Hoang - hoangtv@ftu.edu.vn - Business Statistics

  42. p-Chart Example Tran Van Hoang - hoangtv@ftu.edu.vn - Business Statistics

  43. Average of Subgroup Proportions The average of subgroup proportions = p If equal sample sizes: If unequal sample sizes: where: pi = sample proportion for subgroup i k = number of subgroups of size n where: ni = number of items in sample i ni = total number of items sampled in k samples Tran Van Hoang - hoangtv@ftu.edu.vn - Business Statistics

  44. Computing Control Limits • The upper and lower control limits for an p-chart are • or UCL = Average Proportion + 3 Standard Deviations LCL = Average Proportion – 3 Standard Deviations Tran Van Hoang - hoangtv@ftu.edu.vn - Business Statistics

  45. Standard Deviation of Subgroup Proportions • The estimate of the standard deviation for the subgroup proportions is If equal sample sizes: If unequal sample sizes: Generally, is computed separately for each different sample size where: = mean subgroup proportion n = common sample size Tran Van Hoang - hoangtv@ftu.edu.vn - Business Statistics

  46. Computing Control Limits (continued) • The upper and lower control limits for the p-chart are Proportions are never negative, so if the calculated lower control limit is negative, set LCL = 0 • If sample sizes are equal, this becomes Tran Van Hoang - hoangtv@ftu.edu.vn - Business Statistics

  47. p-Chart Examples • For equal sample sizes • For unequal sample sizes UCL UCL p p LCL LCL is constant since n is the same for all subgroups varies for each subgroup since ni varies Tran Van Hoang - hoangtv@ftu.edu.vn - Business Statistics

  48. c-Chart • Control chart for number of nonconformities (occurrences) per sampling unit (an area of opportunity) • Also a type of attribute chart • Shows total number of nonconforming items per unit • examples: number of flaws per pane of glass number of errors per page of code • Assume that the size of each sampling unit remains constant Tran Van Hoang - hoangtv@ftu.edu.vn - Business Statistics

  49. Mean and Standard Deviationfor a c-Chart • The mean for a c-chart is • The standard deviation for a c-chart is where: xi = number of successes per sampling unit k = number of sampling units Tran Van Hoang - hoangtv@ftu.edu.vn - Business Statistics

  50. c-Chart Control Limits The control limits for a c-chart are Tran Van Hoang - hoangtv@ftu.edu.vn - Business Statistics

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