1. Agenda Review homework Lecture/discussion Week 10 assignment
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. What’s causing variability?
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 measurable characteristics 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 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 D3 and 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 Two thirds of all points are near the center value.
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 Change, jump, or shift in level
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