Six Sigma Case Studies with Minitab®

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