Statistical Process Control Charts and Business Value Metrics
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Customer Value: (Quality, Time, Flexibility, Customer Experience, Innovation) / Price
Sustainability Paradigms: Economic (Viable, Equitable), Environment (Viable, Bearable), Social (Bearable, Equitable)
- Efficiency (Optimization), Differentiator (Innovation), Driver (Motivation) | - Audits (Assess Sustainability Performance)
Table 7.3: Factors for Calculating Three-Sigma Limits for the X (Bar) Chart and R-Chart
| Size of Sample (n) | Factor for UCL and LCL for X (Bar) Charts (A2) | Factor for LCL for R-Charts (D3) | Factor for UCL for R-Charts (D4) |
|---|---|---|---|
| 2 | 1.880 | 0 | 3.267 |
| 3 | 1.023 | 0 | 2.575 |
| 4 | 0.729 | 0 | 2.282 |
| 5 | 0.577 | 0 | 2.115 |
| 6 | 0.483 | 0 | 2.004 |
| 7 | 0.419 | 0.076 | 1.924 |
| 8 | 0.373 | 0.136 | 1.864 |
| 9 | 0.337 | 0.184 | 1.816 |
| 10 | 0.308 | 0.223 | 1.777 |
*A sample is out of control if its value falls below the LCL or above the UCL*
R = (Highest Sample - Lowest Sample) Use Size of Sample z = 3 (99.7 % CI)
R Chart: Ř (Average) X Chart: X (Bar) [Average] P Chart: P (Bar) [Average]
Center Line = Ř Center Line = X (Bar) Center Line: P (Bar)
UCL (R) = D4 * Ř UCL (X) = X (Bar) + (A2 * Ř) P (Bar) = Total Defectives / Total Number of Obser.
LCL (R) = D3 * Ř LCL (X) = X (Bar) - (A2 * Ř) Total Number of Obser. = Sample Size * Num. Of Periods
σ (P) = √(P (Bar) * (1 - P (Bar)) / n [Sample Size])
C Chart: C (Bar) UCL (P) = P (Bar) + z * σ (P)
Center Line = C (Bar) LCL (P) = P (Bar) - z * σ (P)
C (Bar) = Total Defectives / Number of Lots
UCL (C) = C (Bar) + 3√C (Bar)
UCL (C) = C (Bar) - 3√C (Bar)