1 / 73

Operations Management

Operations Management. Supplement 6 – Statistical Process Control. Operations Management, 9e . Outline. Quality and Strategy Defining Quality Different Views / Implications / Baldridge / Cost of Quality (COQ) Ethics and Quality Management

lala
Download Presentation

Operations Management

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Operations Management Supplement 6 – Statistical Process Control Operations Management, 9e

  2. Outline • Quality and Strategy • Defining Quality • Different Views / Implications / Baldridge / Cost of Quality (COQ) • Ethics and Quality Management • International Quality Standards (ISO 9000 and 14000) • Total Quality Management (TQM) • W. Edwards Deming • Seven Concepts of TQM • The Role of Inspection Continuous improvement Six Sigma Employee empowerment Benchmarking Just-in-time (JIT) Taguchi concepts Knowledge of 7 TQM tools • Check sheeets • Scatter Diagrams • Cause-and-Effect Diagrams • Pareto Charts • Flowcharts • Histograms • SPC (Supplement 6) Will not cover or test Taguchi concepts (Quality Loss Function) on pg 202

  3. Control Charts Constructed from historical data, the purpose of control charts is to help distinguish between natural variations and variations due to assignable causes Walter Shewart of Bell Laboratories made the distinction between the common and special causes of variation . . . He developed a simple but powerful tool to separate the two – the control chart. - page 222

  4. Statistical Process Control (SPC) A process used to monitor standards by taking measurements and corrective action as a product or service is being produced. (Pg. 222) The application of statistical techniques to the control of processes. The application of statistical techniques to monitor and adjust an operation. (APICS)

  5. Statistical Process Control (SPC)Outline 1) Variation – Natural and Assignable 2) Control Charts for VARIABLES (eg, size and weight) • Using x-Charts (Mean Charts) • Using R-Charts (Range Charts) 3) Control Charts for ATTRIBUTES (eg, good/bad, pass/fail) • Using p-Charts • Using c-Charts

  6. We Will Not Cover • Acceptance Sampling (pg ) • OC Curves • Producer’s Risk / Consumer’s Risk • AQL • LTPD • Average Outgoing Quality (pg ) • Cp and Cpk

  7. Statistical Process Control (SPC) • Variability is inherent in every process • Natural or common causes • Special or assignable causes • SPC provides a statistical signal when assignable causes are present • The goal is to detect and eliminate assignable causes of variation

  8. When buying jeans- Do you know your size? Variation and Process Control Then WHY do you try them on?

  9. What is Variation? Nothing Ever Happens Exactly The Same Way Twice Variation is the Cause of This Phenomenon Understanding Variation Is Critical To Effective Management And Significant Business Results

  10. Common Cause Variationor Natural Variations(or Routine Variation) • Affect virtually all production processes. • Natural Variations are expected, and occur within processes that are in statistical control. • As a group, natural variations form a probability distribution. • For any distribution there is a measure of central tendency (mean or the average value) and dispersion (standard deviation, s) • If the distribution falls within acceptable limits, the process is said to be “in control” and natural variations are tolerated.

  11. Special Cause Variationor Assignable Variations(or Exceptional Variation) • Generally, special cause variations are due to a change in the process. • Variations that can be traced to a specific reason. • Machine wear • Misadjusted equipment • Training • Bad materials Identify and eliminate assignable variation.

  12. Types of Variation Special Cause:something different happening at a certaintime or place • Common Cause: always present to some degree in the process It is critical to be able to distinguish between them.

  13. Why Does It Matter? Because we want to avoid: • Missing signals- Not taking action when action is appropriate • Misreading noise to be a signal of a change • Wasting time by taking action when none is appropriate • TAMPERING!!

  14. What happened? I’ll go find out. What’s going on? I’m looking! I’m looking! I’m looking Tampering Drives the Search for Answers… But there aren’t any!! The Big Gear Turns The Big Gear Turns A Notch And The Little Gears Whirl In A Frenzy Trying To Keep Up

  15. Each of these represents one sample of five boxes of cereal # # # # # Frequency # # # # # # # # # # # # # # # # # # # # # Weight SPC Uses Samples To measure the process, we take samples and analyze the sample statistics following these steps (a) Samples of the product, say five boxes of cereal taken off the filling machine line, vary from each other in weight or length, etc - continuous Figure S6.1

  16. The solid line represents the distribution Frequency Weight (b) After enough samples are taken from a stable process, they form a pattern called a distribution

  17. Central tendency Variation Shape Frequency Weight Weight Weight (c) There are many types of distributions, including the normal (bell-shaped) distribution, but distributions do differ in terms of central tendency (mean), standard deviation or variance, and shape

  18. Prediction Frequency Time Weight (d) If only natural causes of variation are present, the output of a process forms a distribution that is stable over time and is predictable

  19. ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? Prediction Frequency Time Weight (e) If assignable causes are present, the process output is not stable over time and is not predictable The manager’s first objective is to ensure that the process is capable of operating under control, with only natural variation. The second objective is to identify and eliminate assignable variations so that the process will remain under control, and be predictable. “Since prediction is the essence of management, the ability to know what to expect when a process is behaving predictably is invaluable.”

  20. Control Charts Constructed from historical data, the purpose of control charts is to help distinguish between natural variations and variations due to assignable causes

  21. (a) In statistical control and capable of producing within control limits Frequency Upper control limit Lower control limit (b) In statistical control but not capable of producing within control limits (c) Out of control Size (weight, length, speed, etc.) Process Control Figure S6.2

  22. Types of Data Variables Attributes • Characteristics that can take any real value • May be in whole or in fractional numbers • Continuous random variables • Defect-related characteristics • Classify products as either good or bad or count defects • Categorical or discrete random variables Matters in terms of which Control Chart to use.

  23. Attribute Data vs. Continuous Data Let's say you are measuring the size of a marble. To be within specification, the marble must be at least 25mm but no bigger than 27mm. If you measure and simply count the number of marbles that are out of spec (good vs bad) you are collecting attribute data. However, if you are actually measuring each marble and recording the size (i.e 25.2mm, 26.1mm, 27.5mm, etc) that's continuous data, and you actually get more information about what you're measuring from continuous data than from attribute data.

  24. CONTROL CHARTS FOR VARIABLES (Continuous Data) • X-bar chart (x): tells us whether changes have occurred in the mean or in the central tendency of a process. • R chart: indicates whether or not a gain or loss in dispersion has occurred. R charts track the range within a sample.

  25. The mean of the sampling distribution (x) will be the same as the population mean m x = m s n The standard deviation of the sampling distribution (sx) will equal the population standard deviation (s) divided by the square root of the sample size, n sx = Central Limit Theorem Regardless of the distribution of the population, the distribution of sample means drawn from the population will tend to follow a normal curve

  26. Three population distributions Mean of sample means = x Beta Standard deviation of the sample means Normal = sx = Uniform s n | | | | | | | -3sx -2sx -1sx x +1sx +2sx +3sx 95.45% fall within ± 2sx 99.73% of all x fall within ± 3sx Population and Sampling Distributions Distribution of sample means Figure S6.3

  27. For variables that have continuous dimensions • Weight, speed, length, strength, etc. • x-charts are to control the central tendency of the process • R-charts are to control the dispersion of the process • These two charts must be used together Control Charts for Variables

  28. Setting Control Chart Limits – Continuous (Variables) Data To calculate UCL and LCL for x-Charts when we know s POM: Module = Quality Control File-New-x bar charts Select mean, standard deviation (since that’s what we know) Enter the # of sigma depending on what we want the Control Limits to include (for example, 3s = 99.73%) Enter sample size, mean and standard deviation Solve, and POM will return the UCL and LCL.

  29. Hour 1 Sample Weight of Number Oat Flakes 1 17 2 13 3 16 4 18 5 17 6 16 7 15 8 17 9 16 Mean 16.1 s = 1 Hour Mean Hour Mean 1 16.1 7 15.2 2 16.8 8 16.4 3 15.5 9 16.3 4 16.5 10 14.8 5 16.5 11 14.2 6 16.4 12 17.3 n = 9 Example S1 Pg. 226-227 Control limits to include 99.73% Avg Mean of the 12 samples = 16 Std Dev = 1 Sample Size = 9 LCL = 15 oz UCL = 17 oz

  30. Example S1 Pg. 226-227Calculating Control Limits in POM

  31. Variation due to assignable causes Out of control 17 = UCL Variation due to natural causes 16 = Mean 15 = LCL Variation due to assignable causes | | | | | | | | | | | | 1 2 3 4 5 6 7 8 9 10 11 12 Out of control Sample number Setting Control Chart Limits Control Chart for sample of 9 boxes

  32. Setting Control Chart Limits – Continuous (Variables) Data To calculate UCL and LCL for x-Charts when we DO NOT know s POM: Module = Quality Control File-New-x bar charts Select mean, range Enter the # of sigma depending on what we want the Control Limits to include (for example, 3s = 99.73%) Enter sample size, mean and range Solve, and POM will return the UCL and LCL.

  33. Process average x = 16.01 ounces Average range R = .25 Sample size n = 5 Example S2 Pg. 228 In POM, File New, X-Bar, Data Form: Mean, Range UCL = 16.154 LCL = 15.866

  34. So that is how we calculate UCL and LCL for X-bar charts, (when we know std dev. and when we do not know it) which is appropriate for continuous data. X-bar charts are for the process AVERAGE.

  35. R – Chart • Type of variables control chart • Shows sample ranges over time • Difference between smallest and largest values in sample • Monitors process variability • Independent from process mean We need R-Charts because in addition to being interested in the process average, we need to know the process dispersion or Range.

  36. Setting Control Chart Limits – Continuous (Variables) Data To calculate UCL and LCL for Range Charts POM: Module = Quality Control File-New-x bar charts Select mean, range Enter the # of sigma depending on what we want the Control Limits to include (for example, 3s = 99.73%) Enter sample size and range (leave the mean blank) Solve, and POM will return the UCL and LCL.

  37. Average range R = 5.3 pounds Sample size n = 5 Setting Control Limits For R-ChartExample S3 Pg. 228 POM: x-bar, data form = mean,range SS = 5, Avg Range = 5.3 3 sigma UCL = 11.2 pounds LCL = 0 pounds

  38. So now we know how to calculate UCL and LCL for both the process average and the process range or dispersion. So far we are only talking about control charts for VARIABLES (continuous dimensions).

  39. (a) These sampling distributions result in the charts below (Sampling mean is shifting upward but range is consistent) UCL (x-chart detects shift in central tendency) x-chart LCL UCL (R-chart does not detect change in mean) R-chart LCL Mean and Range Charts Figure S6.5

  40. (b) These sampling distributions result in the charts below (Sampling mean is constant but dispersion is increasing) UCL (x-chart does not detect the increase in dispersion) x-chart LCL UCL (R-chart detects increase in dispersion) R-chart LCL Mean and Range Charts Figure S6.5

  41. Key point: both x-bar and R charts are required to accurately track a process.

  42. Limitations of Mean-Based Metrics • Any comparisons are LIMITED • Can’t identify patterns or trends • Actions based on averaged data may be FLAWED • Single points give no indications of the SHAPE, CENTER or SPREAD • Our customers feel and rememberVARIATION, not AVERAGES On AVERAGE He’s Comfortable!!

  43. Control Charts for Attributes(Rather than Continuous) • For variables that are categorical • Good/bad, yes/no, acceptable/unacceptable • Measurement is typically counting defectives • Two types of attribute control charts: • Percent defective (p-chart) • Number of defects (c-chart)

  44. Sample Number Fraction Sample Number Fraction Number of Errors Defective Number of Errors Defective 1 6 .06 11 6 .06 2 5 .05 12 1 .01 3 0 .00 13 8 .08 4 1 .01 14 7 .07 5 4 .04 15 5 .05 6 2 .02 16 4 .04 7 5 .05 17 11 .11 8 3 .03 18 3 .03 9 3 .03 19 0 .00 10 2 .02 20 4 .04 Total = 80 Example S4 (Pg 231)p-Chart for Data Entry In POM, File-New, P Charts, # of Samples = 20 Enter sample size = 100 and the defects for each.

  45. S4 P-chart POM Example One data entry clerk is out of control.

  46. UCLp= 0.10 .11 – .10 – .09 – .08 – .07 – .06 – .05 – .04 – .03 – .02 – .01 – .00 – LCLp= 0.00 UCLp = p + zsp= .04 + 3(.02) = .10 ^ Fraction defective p = 0.04 LCLp = p - zsp = .04 - 3(.02) = 0 ^ | | | | | | | | | | 2 4 6 8 10 12 14 16 18 20 Sample number p-Chart for Data Entry

  47. UCLp= 0.10 .11 – .10 – .09 – .08 – .07 – .06 – .05 – .04 – .03 – .02 – .01 – .00 – LCLp= 0.00 UCLp = p + zsp= .04 + 3(.02) = .10 ^ Fraction defective p = 0.04 LCLp = p - zsp = .04 - 3(.02) = 0 ^ | | | | | | | | | | 2 4 6 8 10 12 14 16 18 20 Sample number p-Chart for Data Entry Possible assignable causes present

  48. Example S5 (Pg. 233) c-Chart for Cab Company Over a 9-day period, received the following number of from irate passengers: 3, 0, 8, 9, 6, 7, 4, 9, 8 total = 54. File-New, c-Chart, enter # of samples = 9

  49. Upper control limit Target Lower control limit Patterns in Control Charts Normal behavior. Process is “in control.” Figure S6.7

  50. Upper control limit Target Lower control limit Patterns in Control Charts One plot out above (or below). Investigate for cause. Process is “out of control.” Figure S6.7

More Related