Explain the concept of shifting of mean of a process in case of Six Sigma quality control? As a manager, you have an option to buy a new machine that can produce your product with mean of 0.251 and standard deviation of 0.005. You are excited because the company’s long-term goal is no more than 3.4 defects per million for this product, and this machine may be the innovation you need. The design specifications for the product are in the range of .250-0.025, .250+.025. There is also an existing machine, which has a Cpk of 1.0 and manufactures the same product. Now, you must decide whether you should buy the new machine or continue with the existing machine. What will be your decision and Why?(12 Marks)
The correct answer and explanation is :
Shifting of Mean in Six Sigma Quality Control
In Six Sigma quality control, the process mean shift refers to the deviation of the process mean from the target value over time. In real-world production, a shift of ±1.5σ (1.5 standard deviations) is considered when assessing process capability. This accounts for variations that naturally occur due to equipment wear, environmental conditions, and other factors. Therefore, while a Six Sigma process is typically expected to produce only 0.002 defects per million (DPM) under ideal conditions, with a 1.5σ shift, the defect rate increases to 3.4 DPM.
Evaluating the Machines
We compare the new and existing machines using Cpk (Process Capability Index) and check if they meet the Six Sigma quality goal.
Step 1: Calculate Cpk for New Machine
- Given:
- Mean (μ) = 0.251
- Standard deviation (σ) = 0.005
- Specification limits = [0.225, 0.275]
Cpk is calculated as:
[
Cpk = \min\left(\frac{\text{USL} – \mu}{3\sigma}, \frac{\mu – \text{LSL}}{3\sigma}\right)
]
[
Cpk = \min\left(\frac{0.275 – 0.251}{3(0.005)}, \frac{0.251 – 0.225}{3(0.005)}\right)
]
[
Cpk = \min\left(\frac{0.024}{0.015}, \frac{0.026}{0.015}\right) = \min(1.6, 1.73) = 1.6
]
Since Cpk > 1.5, the new machine meets Six Sigma standards.
Step 2: Compare with Existing Machine
- The existing machine has Cpk = 1.0, which means it only achieves 3-sigma quality, leading to 2700 defects per million (DPM)—far from the Six Sigma goal.
Decision & Justification
Since the new machine has Cpk = 1.6, which is significantly better than the existing machine’s Cpk of 1.0, it produces fewer defects and aligns better with the company’s goal of 3.4 DPM. Thus, purchasing the new machine is the best decision as it enhances quality, reduces waste, and ensures long-term cost savings.