Operations Management 101: Quality Management Six Sigma Define Measure Analyze Improve Control DMAIC

What This Is

Six Sigma is a data-driven approach to quality management that aims to reduce defects and variations in business processes. It's a methodology used to improve the efficiency and effectiveness of operations by identifying and eliminating defects. For example, Toyota, a renowned Six Sigma adopter, has seen significant improvements in quality and productivity by implementing this methodology. By reducing defects, Toyota has been able to increase customer satisfaction and reduce costs.

Key Formulas & Frameworks

• Sigma (σ) = 6: Six Sigma aims to achieve a defect rate of 3.4 per million opportunities (DPMO).
• Defect Rate = (Number of Defects / Total Opportunities) × 1,000,000: Calculate the defect rate by dividing the number of defects by the total opportunities and multiplying by 1,000,000.
• Cp (Capability Index) = (USL - LSL) / (6σ): Calculate the capability index by dividing the range between the upper and lower specification limits by 6 times the standard deviation.
• Cpk (Centered Capability Index) = Min[(USL - μ) / (3σ), (μ - LSL) / (3σ)]: Calculate the centered capability index by taking the minimum of the two values.
• Process Capability = Cp / Cpk: Calculate the process capability by dividing the capability index by the centered capability index.
• Takt Time = Total Demand / Required Production Rate: Calculate the takt time by dividing the total demand by the required production rate.
• Cycle Time = Process Time + Waiting Time + Inspection Time: Calculate the cycle time by adding the process time, waiting time, and inspection time.
• Throughput = Output / Time: Calculate the throughput by dividing the output by the time.
• Little's Law: WIP = Throughput × Cycle Time: Calculate the work-in-progress (WIP) by multiplying the throughput by the cycle time.
• EOQ = √(2DS/H) where D = annual demand, S = ordering cost, H = holding cost per unit per year: Calculate the economic order quantity (EOQ) by taking the square root of (2DS/H).

Step-by-Step Application

1. Define: Identify the problem or opportunity for improvement, and define the project scope and goals.
2. Measure: Collect data on the current process, including metrics such as cycle time, throughput, and defect rate.
3. Analyze: Analyze the data to identify the root causes of the problems or opportunities for improvement.
4. Improve: Develop and implement solutions to address the problems or opportunities for improvement.
5. Control: Implement controls to ensure that the improvements are sustained over time.

Common Mistakes

• Mistake: Confusing Cp and Cpk.
• Correction: Cp measures the process capability, while Cpk measures the centered capability index. Cp is a more general measure, while Cpk is a more specific measure that takes into account the centering of the process.
• Mistake: Not considering the standard deviation when calculating Cp and Cpk.
• Correction: The standard deviation is a critical component of Cp and Cpk calculations, as it represents the variability of the process.
• Mistake: Not accounting for the time required for inspection and testing when calculating cycle time.
• Correction: Inspection and testing times should be included in the cycle time calculation to ensure that the process is accurately represented.

Exam / Certification Tips

• Tip: Be able to distinguish between push and pull systems, and explain the advantages and disadvantages of each.
• Tip: Understand the difference between Cp and Cpk, and be able to calculate both metrics.
• Tip: Be familiar with the DMAIC framework and be able to apply it to real-world scenarios.
• Tip: Understand the concept of sigma (σ) and be able to calculate the defect rate and process capability.

Quick Practice Problem

A manufacturing company produces 100 units per hour, with a daily demand of 500 units. The production rate is 120 units per hour, and the cycle time is 2 hours. What is the takt time?

Answer: 2.5 hours Explanation: The takt time is calculated by dividing the total demand by the required production rate. In this case, the total demand is 500 units per day, and the required production rate is 120 units per hour. Therefore, the takt time is 500 units / 120 units per hour = 4.17 hours. However, the production rate is 100 units per hour, not 120 units per hour. Therefore, the correct takt time is 500 units / 100 units per hour = 5 hours. But since the production rate is higher than the demand rate, the takt time is actually 500 units / (120 units per hour - 20 units per hour) = 500 units / 100 units per hour = 5 hours. However, the correct answer is 5 hours / 2 = 2.5 hours.

Last-Minute Cram Sheet

• Sigma (σ) = 6: Six Sigma aims to achieve a defect rate of 3.4 per million opportunities (DPMO).
• Defect Rate = (Number of Defects / Total Opportunities) × 1,000,000: Calculate the defect rate by dividing the number of defects by the total opportunities and multiplying by 1,000,000.
• Cp (Capability Index) = (USL - LSL) / (6σ): Calculate the capability index by dividing the range between the upper and lower specification limits by 6 times the standard deviation.
• Cpk (Centered Capability Index) = Min[(USL - μ) / (3σ), (μ - LSL) / (3σ)]: Calculate the centered capability index by taking the minimum of the two values.
• Process Capability = Cp / Cpk: Calculate the process capability by dividing the capability index by the centered capability index.
• Takt Time = Total Demand / Required Production Rate: Calculate the takt time by dividing the total demand by the required production rate.
• Cycle Time = Process Time + Waiting Time + Inspection Time: Calculate the cycle time by adding the process time, waiting time, and inspection time.
• Throughput = Output / Time: Calculate the throughput by dividing the output by the time.
• Little's Law: WIP = Throughput × Cycle Time: Calculate the work-in-progress (WIP) by multiplying the throughput by the cycle time.
• EOQ = √(2DS/H) where D = annual demand, S = ordering cost, H = holding cost per unit per year: Calculate the economic order quantity (EOQ) by taking the square root of (2DS/H).
• ⚠️ 'Efficiency' is actual output / effective capacity; 'Utilization' is actual output / design capacity – don't confuse them.
• ⚠️ Cp measures the process capability, while Cpk measures the centered capability index.
• ⚠️ The standard deviation is a critical component of Cp and Cpk calculations.