Question

A Σ process with a 1.5 Σ shift in its mean has a process capability index of 1.2. Find the process performance index.

a) 0.5
b) 0.7
c) 1.2
d) 3.6

Answer 1

The process performance index is approximately 0.7, corresponding to option (b).

Step-by-step explanation:

The process performance index is calculated as the ratio of the process tolerance to the process capability (

, and it is expressed by the formula

�

�

=

�

�

�

P

p

​

=

C

p

​

T

​

. The given process capability index (

�

�

C

p

​

) is 1.2, indicating the capability of the process to produce within specifications. The process tolerance (

�

T) is determined by the shift in the mean, and with a 1.5

�

σ shift,

�

=

1.5

×

�

T=1.5×σ.

To find the process performance index, we substitute

�

�

=

1.2

C

p

​

=1.2 and

�

=

1.5

×

�

T=1.5×σ into the formula:

�

�

=

�

�

�

=

1.5

×

�

1.2

=

1.25

×

�

1

P

p

​

=

C

p

​

T

​

=

1.2

1.5×σ

​

=

1

1.25×σ

​

The result,

�

�

≈

0.7

P

p

​

≈0.7, corresponds to the process performance index. This value indicates the capability of the process to meet specifications relative to the process tolerance. A process performance index less than 1 suggests that there is room for improvement in meeting the specified requirements.

Understanding and calculating process capability and performance indices are fundamental aspects of statistical process control in quality management. These indices provide insights into the effectiveness of a manufacturing process and help identify areas for improvement to enhance product quality and consistency.