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?
The correct answer and explanation is :
Shifting of Mean in Six Sigma Quality Control
In Six Sigma quality control, the shifting of the mean refers to the tendency of a process to deviate from its original mean over time. Typically, a 1.5 sigma shift is considered, meaning that even if a process is initially centered within specifications, it may drift due to wear and tear, environmental factors, or variation in raw materials. To ensure a process maintains Six Sigma quality (3.4 defects per million), the process capability index (Cpk) should be at least 1.5.
Decision on Purchasing the New Machine
We need to compare the existing machine (Cpk = 1.0) with the new machine (Mean = 0.251, Std Dev = 0.005) based on process capability.
Step 1: Calculate Cpk for the New Machine
- USL (Upper Specification Limit) = 0.250 + 0.025 = 0.275
- LSL (Lower Specification Limit) = 0.250 – 0.025 = 0.225
- Process Mean (μ) = 0.251
- Standard Deviation (σ) = 0.005
Cpk is calculated as:
[
Cpk = \min \left( \frac{USL – \mu}{3\sigma}, \frac{\mu – 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
]
Step 2: Compare with the Existing Machine
- The existing machine has Cpk = 1.0, which means it operates at 3-sigma level (2700 defects per million).
- The new machine has Cpk = 1.6, which corresponds to approximately 4.8 sigma level (~32 defects per million), much closer to Six Sigma.
Final Decision
The new machine significantly improves process capability, reducing defects and bringing the process closer to Six Sigma (Cpk ≥ 1.5). The new machine should be purchased, as it aligns better with the company’s goal of reducing defects and improving quality.