Julie Works At Gentry Flower Shoppe ✓ Solved

Julie Works At Gentry Flower Shoppe Which Operates At The 4 Sigma Lev

Julie works at Gentry Flower Shoppe, which operates at the 4 sigma level, with about 6,000 DPMO, which was determined recently. At that time, Gentry was found to have 1,500 total defects. They want to improve to the 5 sigma level, or about 500 DPMO. Assuming nothing else changes, what would their new total defect level have to be? Please clearly show your calculations in either MS Excel or Word file. You may also submit your handwritten paper after you scan and save it in a PDF format. No points will be given for those who do not show each step of the calculations.

Sample Paper For Above instruction

To determine the new total defect level for Gentry Flower Shoppe as it improves from a 4 sigma to a 5 sigma level, we need to understand the relationship between sigma levels and defect rates (DPMO). The process involves converting the current sigma level to DPMO, calculating the current total defects, and then determining the total defects needed at the higher sigma level, assuming the number of units processed remains constant.

Step 1: Understanding Sigma Levels and DPMO

Sigma levels are a measure of process capability, where a higher sigma level signifies fewer defects per million opportunities. Commonly, the Defects Per Million Opportunities (DPMO) is used to quantify defect rates, with the relationship between sigma level and DPMO being well-established through the Six Sigma methodology.

Step 2: Current DPMO at 4 Sigma

Gentry operates at approximately 6,000 DPMO at the 4 sigma level, with a total of 1,500 defects. To verify consistency, we connect the DPMO to total units processed. The formula linking DPMO, total defects, and total opportunities (units processed, assuming one opportunity per unit) is:

DPMO = (Number of Defects / Total Opportunities) * 1,000,000

Given that the total defects are 1,500, and DPMO is 6,000, we can find the total number of units processed:

Total Units Processed = Total Defects / (DPMO / 1,000,000) = 1,500 / (6,000 / 1,000,000) = 1,500 / 0.006 = 250,000 units

Step 3: DPMO at 5 Sigma Level

At the desired 5 sigma level, the DPMO is approximately 500. To find the maximum number of defects allowable while maintaining this defect rate, we multiply the total units processed by the new DPMO (per unit opportunity):

Maximum Defects at 5 Sigma = Total Units Processed  (DPMO / 1,000,000) = 250,000  (500 / 1,000,000) = 250,000 * 0.0005 = 125 defects

Step 4: Final Calculation

The total defect level needs to be reduced from 1,500 to approximately 125 defects to achieve a 5 sigma process level. This indicates significant process improvements are necessary, but the new total defect level must be near 125 to meet the 5 sigma defect rate guidelines.

Conclusion

Therefore, assuming the number of units processed remains constant at 250,000, the new total defect level for Gentry Flower Shoppe must be approximately 125 defects to reach the 5 sigma level, compared to the current 1,500 defects at the 4 sigma level.

References

  • Antony, J. (2002). Six Sigma in Manufacturing and Services: How to Capitalize on the Benefits of Statistical Thinking. Quality Progress, 35(6), 53–58.
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  • Pyzdek, T., & Keller, P. A. (2014). The Six Sigma Handbook: A Complete Guide for Green Belts, Black Belts, and Managers at All Levels (3rd ed.). McGraw-Hill Education.
  • Gaertner, K. (2003). Six Sigma: The Next Generation. Quality Progress, 36(5), 54–60.
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