Question

a.) if a manifactoring company has a DPMO of 250, what is its quality sigma rating? what is it Cp?

b.) z(LTL) = -2.8 and z(UTL)= 3.1. what is the process quality sigma rating? what is the process Cp and its current Cpk?

Answer 1

Defects per Million Opportunities, or DPMO, is a metric that indicates the number of defects in a process per one million opportunities.

DPMO is calculated by the number of defects divided by (the number of units times the number of opportunities), multiplied by one million.

Sigma Performance Levels – One to Six Sigma
Sigma Level	Defects (or Errors) Per Million Opportunities (DPMO)	Yield (or Produced or Delivered) Correctly (%)
1	691,462	30.85
2	308,538	69.146
3	66,807	93.319
4	6,210	99.379
5	233	99.9767
6	3.4	99.9997

250 DPMO is clearly in more than 233 hence level 4 Sigma level.

Index	Description
	Estimates what the process is capable of producing if the process mean were to be centered between the specification limits. Assumes process output is approximately normally distributed.

For sigma level 4

Cpk	Sigma level (σ)	Area under the probability density function {\displaystyle \Phi (\sigma )}	Process yield	Process fallout (in terms of DPMO/PPM)
0.33	1	0.6826894921	68.27%	317311
0.67	2	0.9544997361	95.45%	45500
1.00	3	0.9973002039	99.73%	2700
1.33	4	0.9999366575	99.99%	63
1.67	5	0.9999994267	99.9999%	1
2.00	6	0.9999999980	99.9999998%	0.002

Cp= 4

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