81
6
Process Capability Analysis at a
Manufacturing Company
This case study is about a Six Sigma project implemented by the production
manager at a manufacturing rm that produces a critical automobile part
used in cars produced by three major automobile companies. The produc-
tion manager aims to improve the capability of the manufacturing process.
Recall the following process capability ratios from Chapter 2.
=
σ
=
µ−
σ
=
−µ
σ
=
C
USL LSL
C
LSL
C
USL
CC
C
6
3
3
MIN{
,}
p
pl
pu
pk pl pu
where
USL = Upper specication limit
LSL = Lower specication limit
µ = Process mean
σ = Process standard deviation
The higher the C
p
and C
pk
values are, the better the process is.
Section 6.1 gives a brief description of the dene phase. Section 6.2 illus-
trates the measure phase with detailed instructions for using Minitab
®
. The
analyze phase is briey discussed in Section 6.3. Section 6.4 illustrates the
improve phase with detailed instructions for using Minitab
®
. Finally, the
control phase is briey discussed in Section 6.5.
82 Six Sigma Case Studies with Minitab
®
6.1 Define Phase
The production manager desires to increase the capability of the manufactur-
ing process with a USL value of 60 units and an LSL value of 50 units for the
part diameter. The problem statement is “to increase the C
p
and C
pk
values.”
6.2 Measure Phase
Twenty samples, each containing 5 parts, are collected, and their diameters
are measured. The data are shown in Table6.1.
Before C
p
and C
pk
values are calculated, it is important to check whether the
process data are normally distributed and in statistical control. The follow-
ing is the approach to do so.
Open the CHAPTER_6_1.MTW worksheet containing the data from
Table6.1 in a single column (the worksheet is available at the publisher’s web-
site; the data from the worksheet are also provided in the Appendix). Figure6.1
is a screenshot of the partial worksheet (it shows only 19 of the 100 numbers).
Figures6.2 and 6.3 illustrate how to check for normality and Figure6.4 shows
the normality test results. Because the P-value in Figure6.4 is greater than 0.05,
it is evident that the process data are normally distributed.
Figure 6.5 partially shows the data copied from Table 6.1 to the
CHAPTER_6_1.MTW worksheet. In order to check whether the data are
in statistical control, the data need to be transposed to have each sample
in a single row. Figures6.6 and 6.7 show how to transpose the data, and
Figure6.8 shows the transposed data in a new worksheet. (Do not delete the
previous worksheet because you need it for process capability analysis later.)
For clarity, the headings of the columns are revised, and the revised work-
sheet is shown in Figure6.9.
Because the data are variable data and the sample size is 5, the appropriate
control charts to construct are the
X
___
chart and R chart. Figures6.10 and 6.11
show how to construct the R chart, and Figure6.12 shows the R chart. The sam-
ple ranges are in statistical control, therefore check whether the sample means
are in statistical control. Figures6.13 and 6.14 show how to construct the
X
___
chart. It is evident from the
X
___
chart in Figure6.15 that the sample means are
also in statistical control.
Because the process data are normally distributed and are in statistical
control, we can calculate the process capability ratios now. Figures6.16 and
6.17 illustrate how to do so. Figure 6.18 shows that the USL and LSL are
entered in the respective boxes. Click on “Options” in the dialog box shown
in Figure6.18, and the dialog box shown in Figure6.19 opens. Uncheck the
Overall Analysis” box and enter the “Title” as shown in Figure6.19. Click
83Process Capability Analysis at a Manufacturing Company
TABLE6.1
Production Data before Process Improvement
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
52.9 54.3 49.3 55.9 54.5 60.7 57.7 54.6 52.7 55.7 53.8 54.4 55.8 56 54.1 57.2 54.3 52.1 55 53.6
55 55.7 53.4 51.9 58.8 53.2 52.6 56 54.5 55.9 55.7 55 54.8 53.3 53.4 55.6 54.4 53.2 54.4 55.4
55.5 55.9 52.7 56.2 54.4 56.2 54.6 53 51.3 52.9 51.7 56.2 53.2 53.8 54.4 56 54.1 52.4 54.5 56.9
54.1 58.1 51.1 55.1 56.1 54.2 55.7 56.4 55.7 53.9 52.1 54 57 56.7 53.7 52 52.6 54.4 57.1 53.1
55.9 55.1 56.5 53 57.3 54.9 54.8 51.4 52.5 59.1 56.8 53.7 56.7 55.7 57.4 57.8 51.8 52.3 52.7 53.4

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