Review homework Ch 4 – 8, 10, 24, 26, 36, 44, 49 Lecture/discussion Variable control charts

1. Agenda Week 9 • Review homework • Ch 4 – 8, 10, 24, 26, 36, 44, 49 • Lecture/discussion • Variable control charts • SPC at Maine Medical • Week 10 assignment • Homework • Ch 5 – 2, 8, 18, and control chart handout • Read Chapters 6 and 7 • Process Capability • Other Variable Control Charts Control Charts

2. Control Charts Chapter Five Control Charts

3. Control chart functions • Control charts are decision-making tools - they provide an economic basis for deciding whether to alter a process or leave it alone • Control charts are problem-solving tools - they provide a basis on which to formulate improvement actions • SPC exposes problems; it does not solve them! Control Charts

4. Control charts • Control charts are powerful aids to understanding the performance of a process over time. Output Input PROCESS What’s causing variability? Control Charts

5. Control charts identify variation • Chance causes - “common cause” • inherent to the process or random and not controllable • if only common cause present, the process is considered stable or “in control” • Assignable causes - “special cause” • variation due to outside influences • if present, the process is “out of control” Control Charts

6. Control charts help us learn more about processes • Separate common and special causes of variation • Determine whether a process is in a state of statistical control or out-of-control • Estimate the process parameters (mean, variation) and assess the performance of a process or its capability Control Charts

7. Control charts to monitor processes • To monitor output, we use a control chart • we check things like the mean, range, standard deviation • To monitor a process, we typically use two control charts • mean (or some other central tendency measure) • variation (typically using range or standard deviation) Control Charts

8. Control chart components • Centerline • shows where the process average is centered or the central tendency of the data • Upper control limit (UCL) and Lower control limit (LCL) • describes the process spread Control Charts

9. Control chart for variables (Ch 5) • Variables are the measurablecharacteristics of a product or service. • Measurement data is taken and arrayed on charts. Control Charts

10. X-bar and R charts • The X-bar chart - used to detect changes in the mean between subgroups • tests central tendency or location effects • The R chart - used to detect changes in variation within subgroups • tests dispersion effects Control Charts

11. Step 1 Define the problem • Use other quality tools to help determine the general problem that’s occurring and the process that’s suspected of causing it. • brainstorm using cause and effect diagram, why-why, Pareto charts, etc. Control Charts

12. Step 2 Select a quality characteristic to be measured • Identify a characteristic to study - for example, part length or any other variable affecting performance • typically choose characteristics which are creating quality problems • possible characteristics include: length, height, viscosity, color, temperature, velocity, weight, volume, density, etc. Control Charts

13. Step 3 Choose a subgroup size to be sampled • Choose homogeneous subgroups • Homogeneous subgroups are produced under the same conditions, by the same machine, the same operator, the same mold, at approximately the same time. • Try to maximize chance to detect differences between subgroups, while minimizing chance for difference with a group. Control Charts

14. Other guidelines • The larger the subgroup size, the more sensitive the chart becomes to small variations. • This increases data collection costs. • Destructive testing may make large subgroup sizes infeasible. • Subgroup sizes smaller than 4 aren’t representative of the distribution averages. • Subgroups over 10 should use S chart. Control Charts

15. Step 4 Collect the data • Run the process untouched to gather initial data for control limits. • Generally, collect 20-25 subgroups (100 total samples) before calculating the control limits. • Each time a subgroup of sample size n is taken, an average is calculated for the subgroup and plotted on the control chart. Control Charts

16. Step 5 Determine trial centerline • The centerline should be the population mean,  • Since it is unknown, we use X double bar, or the grand average of the subgroup averages. Control Charts

17. Step 6 Determine trial control limits - Xbar chart • The normal curve displays the distribution of the sample averages. • A control chart is a time-dependent pictorial representation of a normal curve. • Processes that are considered under control will have 99.73% of their graphed averages fall within six standard deviations. Control Charts

18. UCL LCL calculation Control Charts

19. Determining an alternative value for the standard deviation Control Charts

20. Step 7 Determine trial control limits - R chart • The range chart shows the spread or dispersion of the individual samples within the subgroup. • If the product shows a wide spread, then the individuals within the subgroup are not similar to each other. • Equal averages can be deceiving. • Calculated similar to x-bar charts; • Use D3and D4 (appendix 2) Control Charts

21. R-bar chart exceptions • Because range values cannot be negative, a value of 0 is given for the lower control limit of sample sizes of six or less. Control Charts

22. Step 8 Examine the process - Interpret the charts • A process is considered to be stable and in a state of control, or under control, when the performance of the process falls within the statistically calculated control limits and exhibits only chance, or common causes. Control Charts

23. Consequences of misinterpreting the process • Blaming people for problems that they cannot control • Spending time and money looking for problems that do not exist • Spending time and money on unnecessary process adjustments • Taking action where no action is warranted • Asking for worker-related improvements when process improvements are needed first Control Charts

24. Process variation • When a system is subject to only chance causes of variation, 99.73% of the measurements will fall within 3 standard deviations • If 1000 subgroups are measured, 997 will fall within the six sigma limits. Control Charts

25. Chart zones • Based on our knowledge of the normal curve, a control chart exhibits a state of control when: • Two thirds of all points are near the center value. • The points appear to float back and forth across the centerline. • The points are balanced on both sides of the centerline. • No points beyond the control limits. • No patterns or trends. Control Charts

26. Identifying patterns • Trends • steady, progressive changes in level • Change, jump, or shift in level • Runs - 7 points above or below; six increasing or decreasing, clusters • Recurring cycles • Two populations • Mistakes Control Charts

27. Step 9 Revise the charts • In certain cases, control limits are revised because: • out-of-control points were included in the calculation of the control limits. • The process is in-control but the within subgroup variation significantly improves. Control Charts

28. Revising the charts • Interpret the original charts • Isolate the causes • Take corrective action • Revise the chart • Only remove points for which you can determine an assignable cause Control Charts

29. Step 10 Achieve the purpose • Our goal is to decrease the variation inherent in a process over time. • As we improve the process, the spread of the data will continue to decrease. • Quality improves!! Control Charts