/k Variation thinking 2WS02 Industrial Statistics A. Di Bucchianico

/k SPC: Philosophy Let the process do the talking: Goal: realize constant quality by controlling the process with quantitative information Constant quality means: quality with controlled and known variation around a fixed target Operator should be able to do the routine controlling

/k Variation I

/k Variation II

/k Variation III

/k Example: Dartec disqualification when outside range

/k Examples of variation patterns

/k Metric for sample variation: range easy to compute (pre-computer era!) rather accurate for sample size < 10 minimum maximum range

/k Metric for sample variation: standard deviation 2nd formula easier to compute by hand 2nd formula less rounding errors correct dimension of units n-1 to ensure that average value equals population variance (“unbiased estimator”)

/k Visualisation of sample variation Box-and Whisker plot histogram

/k all observationsfirst 60 observations

/k Variation and stability Can variation be stable? yes, if we mean that observations –follow fixed probability distribution –do not influence each other (independence) stability -> predictability How to handle a stable production process?

/k Why stable processes? behaviour is predictable processes can be left on itself: intervention may be expensive

/k Deming’s funnel experiment

/k Lessons from funnel experiment tampering a stable process may lead to increase of variation adjustments should be based on understanding of process (engineering knowledge) we need a tool to check for stability

/k Attributive versus variable two main types of measurements: –attributive (yes/no, categories) –variable (continuous data) hybrid type: –classes or bins use variable data whenever possible!

/k Statistically in control Constant mean and spread Process-inherent variation only Do not intervene Measurement Tijd X X X X X X X X X X X X X X X X X Intervene?

/k Statistically versus technically in control “Statistically in control” –stable over time /predictable “Technically in control” –within specifications

/k Statistically in control vs technically in control statistically controlled process: –inhibits only natural random fluctuations (common causes) –is stable –is predictable –may yield products out of specification technically controlled process: –presently yields products within specification –need not be stable nor predictable

/k Priorities what is preferable: –statistical control or –technically in control ?? process must first be in statistical control

/k Variation and production processes Shewhart distinguishes two forms of variation in production processes: common causes –inherent to process –cannot be removed, but are harmless special causes –external causes –must be detected and eliminated

/k Chance or noise How do we detect special causes ? use statistics to distinguish between chance and real cause

/k Shewhart control chart graphical display of product characteristic which is important for product quality Upper Control Limit Centre Line Lower Control Limit

/k Control charts

/k Why control charts? control charts are effective preventive device control charts avoid tampering of processes control charts yield diagnostic information

/k Basic principles take samples and compute statistic if statistic falls above UCL or below LCL, then out-of-control signal: e.g., how to choose control limits?

/k Normal distribution often used in SPC “justification” by Central Limit Theorem: –accumulation of many small errors

/k Meaning of control limits limits at 3 x standard deviation of plotted statistic basic example: UCL LCL

/k Example diameters of piston rings process mean: 74 mm process standard deviation: 0.01 mm measurements via repeated samples of 5 rings yields:

/k Specifications vs. natural tolerance limits never put specification limits on a control chart control chart displays inherent process variance during trial run charts (also called tolerance chart of tier chart) often yields useful graphical information