Page 155 - Six Sigma Advanced Tools for Black Belts and Master Black Belts

Char Count= 0
August 31, 2006
2:57
JWBK119-10
140 Process Capability Analysis for Non-Normal Data with MINITAB
Histogram of Data
3-Parameter Loglogistic
14 Loc 0.8271
Scale 0.2900
12 Thresh 10.01
N 30
10
Frequency 8 6

4
2

0
10 12 14 16 18
Data
Figure 10.6 Histogram and three-parameter loglogistic fit for case study data.

It is generally good practice to plot the distribution over the histogram make sure
the fit is good enough. The graph in Figure 10.6 provides convincing evidence that
the three-parameter loglogistic distribution provides an excellent fit for the data.
After the best-fit distribution has been identified, the process capability can be
estimated easily by computer. Figure 10.7 shows that the estimated C pk is 5.94, which
is close to what we expected. (Note that instead of C pk , P pk is given in the graph. In Six
Sigma, P pk is the long-term capability while C pk is the short-term process capability.
MINITAB assumes that the data is long term for non-normal data. In this chapter, we
will skip the discussion on whether the data is long term or short term, and treat all
estimated capability the C pk .)

Process Capability of Data
Calculations Based on Loglogistic Distribution Model
USL
Process Data Overall Capability
LSL Pp
Target PPL
USL 91.00000 PPU 5.94
Sample Mean 12.61467 Ppk 5.94
Sample N 30
Location 0.82715 Exp. Overall Performance
Scale 0.29003 PPM < LSL
Threshold 10.01439 PPM > USL 4.55621
PPM Total 4.55621
Observed Performance
PPM < LSL
PPM > USL 0
PPM Total 0

11 22 33 44 55 66 77 88

Figure 10.7 Process capability analysis using three-parameter loglogistic fit.