SPC (Statistical Process Control)

This is the First Number the Original Manufacturer Asks

When a new part number is awarded to a supplier in the Busan-Gyeongnam automotive parts industry, the PPAP documents must be submitted, and the process capability index must be included in them. During mass production, the original manufacturer also asks during regular audits, "What is the Cpk for this characteristic?" If you cannot answer or explain the basis for the number, it becomes a point of criticism on the spot.

The process capability index can be summarized in one sentence like this: How small is our process variation compared to the tolerance range allowed by the specification.

Cp Considers Only the Width, Cpk Considers Both Width and Position

Cp  = (USL - LSL) / (6σ)          ← Specification width ÷ process width. Position is not considered
Cpu = (USL - Mean) / (3σ)         ← Upper margin
Cpl = (Mean - LSL) / (3σ)         ← Lower margin
Cpk = min(Cpu, Cpl)               ← The narrower side reflects the process capability

Let's calculate with actual numbers. (This is different data from the previous section. The mean is shifted upwards.)

Item: Shaft OD        Specification φ20 ± 0.03   (LSL 19.970 / USL 20.030)
Process mean = 20.012 mm
Within subgroup standard deviation σ = Rbar / d2 = 0.006 mm

  Cp  = (20.030 - 19.970) / (6 × 0.006) = 0.060 / 0.036 = 1.67
  Cpu = (20.030 - 20.012) / (3 × 0.006) = 0.018 / 0.018 = 1.00
  Cpl = (20.012 - 19.970) / (3 × 0.006) = 0.042 / 0.018 = 2.33

  Cpk = min(1.00, 2.33) = 1.00

Cp is 1.67, which is excellent, but Cpk is 1.00. This is because the variation is sufficiently small, but the mean is shifted upwards.

High Cp, Low Cpk = Skew

The degree of skew is quantified by the K value.

Specification center M = (20.030 + 19.970) / 2 = 20.000
Specification width T = 0.060

  K = |M - Mean| / (T / 2)
    = |20.000 - 20.012| / 0.030
    = 0.012 / 0.030
    = 0.4

Verification: Cpk = Cp × (1 - K) = 1.67 × (1 - 0.4) = 1.67 × 0.6 = 1.00  (Consistent)

Here, the course of action becomes clearly divided.

> You must look at both Cp and Cpk to know what needs to be fixed. > - High Cp, low Cpk → Skew problem. Just move the mean. Tool offset correction, setup standard value change — can be done in half a day with little cost > - Both Cp and Cpk are low → Variation problem. Must improve equipment precision, process, and material deviation — takes several months and investment > - Cp = Cpk → The mean is exactly at the specification center

In the above example, if the mean is lowered by only 0.012 mm, Cpk increases to 1.67. Before writing a report suggesting equipment replacement, check Cp first.

Cp/Cpk vs Pp/Ppk — Difference in σ

The formulas are the same. Only the way to calculate σ differs.

Let's calculate using the same process.

Same item, same specification, mean 20.012

  Within subgroup σ (Rbar / d2)   = 0.006
  Overall s (all data)           = 0.009      ← Includes variation between subgroups, so it's larger

  Cp  = 0.060 / (6 × 0.006) = 1.67
  Cpk = (20.030 - 20.012) / (3 × 0.006) = 0.018 / 0.018 = 1.00

  Pp  = 0.060 / (6 × 0.009) = 1.11
  Ppk = (20.030 - 20.012) / (3 × 0.009) = 0.018 / 0.027 = 0.67

Cpk is 1.00, but Ppk is 0.67. This difference indicates that the process is stable within subgroups, but there is variation between subgroups. The causes are usually known.

• Shifts in setup standards between shifts
• Mean shifts when material lots change
• Temperature differences between morning and afternoon
• Differences between immediately after tool change and tool wear

Looking back at the control chart, signals from Rule 2 (consecutive on one side) or Rule 3 (trend) would already have been detected.

> If you only look at Cpk and exclude Ppk, it contradicts the actual quality the customer receives. Customers don't know our subgroup structure and experience the overall variation. If the two values are similar, it's stable; if they differ significantly, it's a signal of subgroup variation.

Why Cpk ≥ 1.33 is the Standard

Cpk 1.00 means the end of the 3σ range is exactly at the specification line. If the mean shifts slightly, defects immediately occur. At 1.33, there is a 4σ margin to the specification line, so even if the mean shifts by 1σ, 3σ remains. This number ensures a control margin.

The standard practice in the automotive parts industry is as follows.

> These values are general practices of the AIAG/IATF family. The final standard is the customer's special requirements (CSR) and the values specified in the management plan. They vary by original manufacturer and by characteristic, so check the documents and use them accordingly. In supplier practice, it's common to resubmit because "we thought 1.33 was enough, but that part number required 1.67."

Check Before Calculating

1. Confirm the Measurement System First (MSA)

If the measurement variation is large, it can be mistaken for process variation. Even if the process is fine, Cpk may be low, and unnecessary equipment improvements may be made.

2. Confirm the Process is in Control Next

Cpk from a process with abnormal signals on the control chart is just a number game. Follow the order: stabilize → then evaluate capability. Changing the order can result in a completely different Cpk next month.

3. Data Quantity and Normality

• 25 subgroups or more (n=5 means 125 data points) is the usual standard. A Cpk calculated from 30 data points cannot be used as a basis
• Confirm the distribution with a histogram or normality test
• Do not delete outliers without explanation. If deleted, record the cause and action

For One-Sided Specifications

Characteristics with only an upper limit, such as flatness, wobble, and gloss, cannot calculate Cp. Since there's no lower limit, the specification width is undefined. Only Cpu is calculated and used as Cpk.

Flatness specification: 0.020 or less  (Only USL exists)
Mean 0.008, σ 0.003

  Cpu = (0.020 - 0.008) / (3 × 0.003) = 0.012 / 0.009 = 1.33
  Cpk = 1.33          (Cp is undefined)

Such characteristics often have asymmetric distributions cut off at zero, so the ppm calculated under the normality assumption may differ from the actual. Check the distribution shape together.

Practical Checklist

• Confirm whether the characteristic is a special characteristic (CC/SC) in the management plan
• Confirm that the measurement equipment's Gage R&R %GRR is 30% or less
• Ensure data from at least 25 subgroups
• Confirm stability first using the control chart (complete investigation of abnormal points)
• Confirm histogram and normality
• Calculate both Cp and Cpk — distinguish between skew and variation
• Calculate both Cpk and Ppk — check for subgroup variation
• Confirm the target value in the customer's requirements (CSR/management plan)
• Establish block (100% inspection) and permanent measures if the standard is not met