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e.g., Given the control chart for the a process, and a feature to be turned on the process, determine if the tolerances specified are reasonable.

2.0046”	UCL	2.000”	+0.004”
			-0.000”
	X
2.0028”
2.0010”	LCL

			( U – L)	2.004		– 2.000		0.004		GOOD
Cp	=	UCL-----------------------------– LCL =		2.0046--------------------------------------		– 2.0010	=	0.0036--------------- = 1.11
Z1	=		2.004 – 2.0028		= 0.667			Z2 =	2.0028 – 2.000		= 1.556
			2.0046 – 2.0010						2.0046 – 2.0010
			--------------------------------------2						--------------------------------------
									2
Cpk		= min( 0.667, 1.556)			= 0.667

BAD

•If Cp or Cpk are both too large (>>2) the process may be too good, suggesting less expensive, easier processes could be considered.

•A good rule of thumb for using Cp and Cpk is that if new equipment is being purchased, try to get values above 1.5, if the equipment is already available, 1.33 is acceptable.

•Try Probs #6 pg124, #32,33 pg128

11. SIX SIGMA QUALITY

•Developed by Motorola

•A strategy to target quality problems

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• In simple terms,

Cp = 2

Cpk = 1.5

* Recall,

- if Cp = Cpk then X =µ , and the process is always centered

Cp =	U------------– L
	6σ
Cpk	= U-------------– µ	or	µ------------	– L		select the smaller of the two
	3σ			3σ
the mean typically drifts about					1.5σ , as established by historical means

and, +/-6σ quality gives 2 defaults in 1 million with no variation. with a 1.5σ variation in mean the reject rate is 3.4 in 1 million

process variance

					X variance
-3σ	-2σ	-σ	µ	σ	2σ	3σ

•This can be summarized as 6σ of variance alone ignores the drift of the process centre. Assuming the process centre varies by +/-1.5σ results in a more accurate model of production.

•The steps in implementation are,

1.Identify critical characteristics through such functions and activities as marketing, industrial design, R&D engineering, etc.

2.Identify the product elements that influence the critical characteristics defined in step 1.

3.Define the process elements that influence the critical characteristics defined in step 2.

4.Establish maximum tolerances for each product and process element defined in steps 2 and 3.

5.Determine actual capability of the elements presented in steps 2 and 3.

6.Assume Cp >= 2 and Cpk >= 1.5.