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Unformatted text preview: Section 6.4 – 6.6 Process Capability Analysis When a process is under control, it is predictable and μ and σ are reasonably stable over – time. Then it becomes necessary to check if the process meets the specifications or requirements. Process capability analysis (PCA) is evaluated with process performance with process requirements. The sample results used to construct the control charts can also be used to estimate process parameters μ and σ . That is, for example . c s σ or d R σ ; x μ 4 2 ˆ ˆ ˆ = = = Also, using the normality assumption on the quality characteristic s X i ' , we can obtain proportion of units out side the specification limit. Note here that s and , R x repectively denote the mean of sample means, sample ranges and sample standard deviations. Also, ) ( and ) ( 4 4 2 2 n c c n d d = = depend on the sample size n (see Table XI on Page 580 of your text). An estimate of the process spread is σ ˆ 6 , since for normal distribution 99.73% of the process observation lie ]. ˆ 3 ˆ , ˆ 3 ˆ [ σ μ σ μ + 1 Let USL and LSL denote the upper specification and lower specification limits. Assume the ). , ( N ~ X σ μ qc Then the proportion ( or the probability) of X’s above the USL is . ˆ ˆ USL P USL) X ( P = = σ μ Z Similarly, the proportion (or the probability) of X’s below LSL is . ˆ ˆ LSL P LSL) X ( P < = < = σ μ Z Nonconformance rates are expressed in terms of percentages or in parts per million (ppm). Definition. One nonconforming (or defective) unit out of million items is called 1 ppm. See the Table Below: Percentage % ppm 10.0 5 1 0.1 .01 100,000 50,000 10,000 1000 100 .001 .0001 10 1 Process Capability Indices 2 When the process is under control, the process spread ] ˆ 3 ˆ , ˆ 3 ˆ [ σ μ σ μ + = I = Actual spread … (1) The width of the above interval = 6 σ ˆ . This shows how the process is performing....
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This note was uploaded on 07/25/2008 for the course STT 351 taught by Professor Palaniappan during the Summer '08 term at Michigan State University.
 Summer '08
 Palaniappan

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