Six Sigma vs. Three Sigma: Understanding Quality Costs

Posted on Jan 26, 2025 in Business Administration and Innovation Management

Six Sigma vs. Three Sigma: Understanding the Difference

The difference between three sigma and six sigma lies in the percentage of observations that fall within specification limits [LSL, USL].

  • Three Sigma Process: Approximately 99.73% of products fall within specifications if the process is centered at the target (LSL+USL)/2. This is because about 99.73% of a normal population falls within three standard deviations from its mean. A three sigma process centered at the target has 2700 ppm (parts per million) defective products.
  • Six Sigma Process: 99.99966% of products fall within specifications when centered at the target. This translates to 0.002 ppm defective products. If a 1.5 standard deviation shift in the mean is allowed, a six sigma process has 3.4 ppm defective products.

Cost of Quality (COQ) vs. Cost of Poor Quality (COPQ)

  • COQ (Cost of Quality): Includes the cost of prevention, which encompasses the cost to implement fixes that should have been in place initially. It represents the total cost associated with achieving both good and poor quality.
  • COPQ (Cost of Poor Quality): Excludes the cost of achieving good quality. It only includes costs incurred due to bad quality, such as inspections to detect existing defects. Mistake-proofing, self-inspection, and SPC monitors are not included in COPQ.

Direct Cost of Poor Quality

Direct COPQ includes any cost directly resulting from poor quality. This encompasses:

  • Costs associated with finding and fixing defects.
  • Costs of lawsuits, customer complaints, and product recalls due to poor quality.

It does not include the cost of lost sales or damaged reputation. Direct COPQ can be directly derived from entries in the company ledger.

We can further categorize Direct COPQ into:

  • Poor Quality Control Cost: Appraisal costs incurred to ensure only acceptable products and services reach the customer.
  • Resultant Poor Quality Cost: Costs incurred because unacceptable products and services were delivered to internal or external customers. This arises because things were not done right the first time.
    • Internal Error Cost: Costs incurred to repair poor quality before the product reaches the customer.
    • External Error Cost: Costs incurred when the product has already reached the customer.

Hidden Cost of Poor Quality

Hidden COPQ includes:

  • Failing to meet customer expectations.
  • Opportunity for increased efficiency.
  • Potential for higher profits.
  • Loss in market share.
  • Loss of production due to increased production cycle time.
  • Labor costs associated with ordering replacement materials.

Example: Calculating Class Limits and Frequency

Given:

  • MaxX = 8.5 mm
  • MinX = 7.8 mm
  • Number of classes (k) = √20 ≈ 4.47, rounded down to 4

Calculate the class width (H):

H = ((8.5 + 0.05) – (7.8 – 0.05)) / 4 = 0.20

Class Limits:

  • 7.75 mm
  • 7.95 mm
  • 8.15 mm
  • 8.35 mm
  • 8.55 mm

Determine the frequency of each bin based on your data.

Latest Start Time Calculation

Latest Start Time = Latest Completion Time – Task Time