Question

Statistical Process Control is a critical part of tracking performance, and evaluation of process capability is an important element to track the need to closely monitor.

Using the table below and the attached X-bar, S charts, determine the process capability indices for the process (Cp, Cpk), and evaluate whether the process is capable for average surface roughness (Ra) for the inner diameter of tubing. If not, what change(s) should be made next to get Cpk ≥ 1.33? The specification requires values less than 22 microinches. Sample size (n) is 12 units. C4 = 0.9776, A3 = 0.89, B3 = 0.35, B4 = 1.65.

12	Means	Std Devs
1	8.6	1.62
2	10.0	1.18
3	10.4	2.02
4	9.5	1.56
5	8.2	1.02
6	8.8	0.82
7	8.7	2.53
8	9.3	1.51
9	10.1	2.12
10	9.4	2.02

a) Determine the control limits for the X-Bar and S Charts

b) Determine whether the process is in control (criterion: if no control limits are violated, the process is assumed to be in control)

c) Determine the process capability indices Cp and Cpk as appropriate. State if an index is not applicable.

d) Is the process capable (Cpk ≥ 1.33)?

e) What is the next step to achieve satisfactory process capability (Cpk ≥ 1.33)? State if no action is necessary.

Answer 1

a)

For monitoring mean and variance of normal distribution, the combination of and S chart is usually used.

The control limits for x bar chart type are-

• 

n statistical quality control, the and s chart is a type of control chart used to monitor variables data when samples are collected at regular intervals from a business or industrial process. This is connected traditional statistical quality control (SQC) and statistical process control (SPC). However, Woodall noted that "I believe that the use of control charts and other monitoring methods should be referred to as “statistical process monitoring,” not “statistical process control (SPC).”

A process is said to be in control or stable, if it is in statistical control. A process is in statistical control when all special causes of variation have been removed and only common cause variation remains.

Control charts are used to determine whether a process is in statistical control or not. If there are no points beyond the control limits, no trends up, down, above, or below the centerline, and no patterns, the process is said to be in statistical control.

Capability is the ability of the process to produce output that meets specifications. A process is said to be capable if nearly 100% of the output from the process is within the specifications. A process can be in control, yet fail to meet specification requirements. In this situation, you would need to take steps to improve or redesign the process.