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Virtual COMSATS Inferential Statistics Lecture-31

Virtual COMSATS Inferential Statistics Lecture-31. Ossam Chohan Assistant Professor CIIT Abbottabad. Recap of previous lecture. Sign test. Wilcoxon Rank test. Sign test for paired data. Kruskal-Wallis Test Some problems. Objective of lecture-31. Statistical Quality Control.

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Virtual COMSATS Inferential Statistics Lecture-31

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  1. Virtual COMSATSInferential StatisticsLecture-31 Ossam Chohan Assistant Professor CIIT Abbottabad

  2. Recap of previous lecture • Sign test. • Wilcoxon Rank test. • Sign test for paired data. • Kruskal-Wallis Test • Some problems. .

  3. Objective of lecture-31 • Statistical Quality Control. • Control Charts. • Six Sigma

  4. Introduction to Statistical Quality Control “An ounce of prevention is worth a pound of cure”

  5. What is Statistical Quality Control? • Statistical-What does Statistical means? • Quality-What does Quality means? • Control-What does Control means? • Statistical Quality Control – SQC??

  6. Dimensions of Quality (Products) • Performance – Will the product do the intended job? • Reliability – How often does the product fail? • Durability - How long does the product last? • Serviceability – How easy is it to repair the product? • Aesthetics – What does the product look like? • Features – What does the product do?

  7. Two Aspects of “Fitness for Use” • Quality of design: • Products are designed to be in various grades of quality. (e.g., Autos differ with respect to size, options, speed, etc.) • Service systems are designed for different grades of quality • Quality of conformance : • How well the product conforms to specifications. (e.g., If diameter of a drilled hole is within specifications then it has good quality.) • Does the service representative follow guidelines?

  8. Terminology • Quality planning • Strategic: Customers and their needs, products, measures,… • Quality assurance • Policies, procedures, work instructions, specifications, records, etc. for making sure products meet desired quality levels • Quality control and improvement • Monitoring specific results and identifying ways to eliminate causes of unsatisfactory results (reduce variability) • Suggest some techniques for SQC

  9. Control Charts The control chart is a statistical quality control tool used in the monitoring variation in the characteristics of a product or service. The control chart focuses on the time dimension and the nature of the variability in the system. The control chart may be used to study past performance and/or to evaluate present conditions.

  10. Control Charts X X X Special Cause Variation: two points outside control limit Common Cause Variation: no points outside control limit Downward Pattern: no points outside control limit; however, eight or more points in trend

  11. Control Charts • There are two types of control charts • Attribute charts like….p and c charts • Variables charts like…Mean and Range Charts

  12. Acceptance Sampling • Sample from lot to determine acceptance • More effective than 100% inspection • Reduces bad product sent to consumer • No feedback, prevention or improvement

  13. Six Sigma - Motorola • Six Sigma = 2 defects per million opportunities! • Originally production focused • identify problem; • develop measurement; • set goal; • close gap • Utilizes statistical methods • Training levels defined for personnel

  14. DMAIC – Road map • DMAIC is a structured problem-solving technique consisting of the following steps: • Define • Measure • Analyze • Improve • Control • DMAIC is usually associated with six sigma.

  15. Mean chart • Mean chart of -chart is used for controlling average quality of the product in the processes. A number of samples is drawn from the process in production at a regular interval of time and the mean computed from such samples is used as the statistic in control chart.

  16. Control limits discussion

  17. Problem-1 • A drilling machine bores holes with a mean diameter of 0.5230 cm and a standard deviation of 0.0032 cm. Calculate the 2-sigma and 3 sigma upper and lower control limits for means of samples 4, and prepare a control chart.

  18. Problem-1 Solution

  19. Problem-2 • The following data gives reading for 10 samples of size 6 each in the production of a certain component. • Draw control charts for . Can one assume that all the samples are from homogeneous lot. (Given for n=6, A2=0.483; D3=0; D4=2.004)

  20. Cont…

  21. Problem-2 Solution

  22. Cont…

  23. Cont…

  24. Range Chart (R-Chart) • R-Chart is used for controlling the quality dispersion or variability of the product in a process. A number of samples is drawn from the process in production at a regular interval of time and the range computed from such samples is used as the statistic in the control chart.

  25. Problem-3 • The following data show the values of sample mean and range (R) for 10 samples of size 6 each. Calculate the values for central line and the control limits for Mean chart and Range chart. Draw the control charts and comment on the state of control. Conversion factors for n=6 are A2=0.483, D3=0, D4=2.004

  26. Problem-3 Solution

  27. Cont…

  28. Cont…

  29. Assessment Problem-1 • Construct a control chart for mean and the range for the following data on the basis of fuses, samples of 5 being taken every hour (each set of 5 has been arranged in ascending order of magnitude). • Data is on next slide.

  30. Cont… Given for n=5, A2=0.557, D3=0, D4=2.115

  31. Assessment Problem-2 • Ten samples each of size 5 are drawn at regular intervals from a manufacturing process. The sample means and range are given on next slide. • Calculate the control limits in respect of chart and R chart. • Comment on the state of control.

  32. Six Sigma • A term δ(Greek) used in statistics to representstandard deviation from mean value, an indicator of the degree of variation in a set of a process. • Sigma measures how far a given process deviates from perfection. Higher sigma capability, better performance.

  33. A statistical concept that measures a process in terms of defects – at the six sigma level, there 3.4  defects per million opportunities. • Don’t consider it as standard rather it is quality philosophy and the way you can imporve your business processes and set the goals and have road map to reach there. • Methodology to measure and improve company’s performance, practices and systems.

  34. Different Sigma levels

  35. Six Sigma Methodology • BPMS • Business Process Management System • DMAIC • Six Sigma Improvement Methodology • DMADV • Creating new process which will perform at Six Sigma

  36. WHAT IS DMAIC?(Define, Measure, Analyse, Improve, Control) • A logical and structured approach to problem solving and process improvement. • An iterative process (continuous improvement) • A quality tool which focus on change management style.

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