๐Ÿ“Š SPC Control Charts Practice Lab

Chapter 13 โ€” Think like a quality analyst. Answer like a pro.

Question 1 of 8 Score: 0 / 0
Question 1 of 6 Score: 0 / 0
Question 1 of 8 Score: 0 / 0
Question 1 of 8 Score: 0 / 0

p-Chart โ€” Proportion Defective

Attribute data ยท Binary (pass/fail) ยท Tracks % defective units

pฬ„ = total defectives / (n ร— k) UCL = pฬ„ + 3โˆš[ pฬ„(1โˆ’pฬ„) / n ] LCL = pฬ„ โˆ’ 3โˆš[ pฬ„(1โˆ’pฬ„) / n ] (โ‰ฅ 0)

Ex: % wrong orders per day, % defective chips per batch

c-Chart โ€” Count of Defects

Attribute data ยท Count ยท Tracks # defects per unit/time

cฬ„ = total defects / k UCL = cฬ„ + 3โˆš(cฬ„) LCL = cฬ„ โˆ’ 3โˆš(cฬ„) (โ‰ฅ 0)

Ex: scratches per windshield, broken chips per bag, errors per report

Xฬ„ & R Charts โ€” Variable Data

Variable (continuous) data ยท Subgroups of n โ‰ˆ 2โ€“10

Xฬ„ Chart: UCL = Xฬฟ + Aโ‚‚Rฬ„ LCL = Xฬฟ โˆ’ Aโ‚‚Rฬ„ R Chart: UCL = Dโ‚„Rฬ„ LCL = Dโ‚ƒRฬ„ Exhibit 13.7 (n=5): Aโ‚‚=0.58, Dโ‚ƒ=0, Dโ‚„=2.11 (n=4): Aโ‚‚=0.73, Dโ‚ƒ=0, Dโ‚„=2.28

Ex: bag weight (g), fill volume (ml), bolt length (mm)

Process Capability โ€” Cpk

Measures if process fits within spec limits ยท Must be in control first!

Cpk = min[ (Xฬฟ โˆ’ LSL) / 3ฯƒ , (USL โˆ’ Xฬฟ) / 3ฯƒ ] Cpk โ‰ฅ 1.0 โ†’ process is capable Cpk โ‰ฅ 1.33 โ†’ good standard Cpk < 1.0 โ†’ process NOT capable

Key: process must be in statistical control BEFORE assessing Cpk

Out-of-Control Signals (Exhibit 13.5)

โ‘  Point beyond UCL or LCL
โ‘ก Two points near a control limit (same side)
โ‘ข Run of 5+ points on one side of center line
โ‘ฃ Trend โ€” 5+ points continuously increasing or decreasing
โ‘ค Erratic behavior โ€” wide swings
โ‘ฅ Sudden shift in level

Exhibit 13.7 โ€” Factors for Xฬ„ & R Charts

n Aโ‚‚ Dโ‚ƒ Dโ‚„