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 specication limit

LSL = Lower specication 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 dene phase. Section 6.2 illus-

trates the measure phase with detailed instructions for using Minitab

®

. The

analyze phase is briey discussed in Section 6.3. Section 6.4 illustrates the

improve phase with detailed instructions for using Minitab

®

. Finally, the

control phase is briey 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 Table6.1.

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

Table6.1 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). Figure6.1

is a screenshot of the partial worksheet (it shows only 19 of the 100 numbers).

Figures6.2 and 6.3 illustrate how to check for normality and Figure6.4 shows

the normality test results. Because the P-value in Figure6.4 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. Figures6.6 and 6.7 show how to transpose the data, and

Figure6.8 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 Figure6.9.

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. Figures6.10 and 6.11

show how to construct the R chart, and Figure6.12 shows the R chart. The sam-

ple ranges are in statistical control, therefore check whether the sample means

are in statistical control. Figures6.13 and 6.14 show how to construct the

X

___

chart. It is evident from the

X

___

chart in Figure6.15 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. Figures6.16 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 Figure6.18, and the dialog box shown in Figure6.19 opens. Uncheck the

“Overall Analysis” box and enter the “Title” as shown in Figure6.19. Click

83Process Capability Analysis at a Manufacturing Company

TABLE6.1

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

Get *Six Sigma Case Studies with Minitab®* now with O’Reilly online learning.

O’Reilly members experience live online training, plus books, videos, and digital content from 200+ publishers.