Question

Explain the stability Analysis Rules in statistics.

Answer 1

First of all we will define some basic terms as following types:-
#Control Chart Zones(To identify the degree of variation in a given measure)

Center line: corresponds to the mean of the measure being analyzed.
Zone A: corresponds to the zone from two sigma to three sigma above/below the center line.
Zone B: corresponds to the zone from one sigma to two sigma above/below the center line.
Zone C: corresponds to the area from the center line to one sigma above/below the center line.
UCL (Upper Control Limit): corresponds to the maximum tolerance above the mean.
LCL (Lower Control Limit): corresponds to the maximum tolerance below the mean.

In order for a process to be considered under statistical control, most of its points must be near the center line, while some could be closer to the control limits — all without patterns — , but none beyond them.
#Stability analysis Rules
( to identify special causes of variation present in a given process )
Rule #1 — Beyond limits: one or more points are beyond the control limits.
Rule #2 — Zone A: 2 out of 3 consecutive points in Zone A or beyond.
Rule #3 — Zone B: 4 out of 5 consecutive points in Zone B or beyond.
Rule #4 — Zone C: 7 or more consecutive points on one side of the average (in Zone C or beyond).
Rule #5 — Trend: 7 consecutive points trending up or trending down.
Rule #6 — Mixture: 8 consecutive points with no points in Zone C.
Rule #7 — Stratification: 15 consecutive points in Zone C.
Rule #8— Over-control: 14 consecutive points alternating up and down.

#Rules Associated Patterns and Possible Causes:-

Rules #1 and #2: large shifts from the average. Possible causes: new operator performing the job; wrong setup; measurement error; process step skipped; process step not completed; power failure; equipment breakdown.
Rules#3 and #4: small shifts from the average. Possible causes: raw materials change; changes in work instructions; different measurement device/calibration; different shift; worker gained more experience for performing the job; changes in maintenance program; changes in setup procedures.
Rule #5: trends. Possible causes: tooling wear; temperature effects (e.g. cooling, heating).
Rule #6: mixtures. Possible causes: more than one process present (e.g. shifts, machines, raw material).
Rule #7: stratifications. Possible causes: more than one process present (e.g. shifts, machines, raw material).
Rule #8: over-control. Possible causes: tampering by operator; alternating raw materials

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