THE CONCEPT OF PROCESS CAPABILITY

After special causes have been identified and eliminated, a process is said to be in state of statistical control. One of the products of attaining statistical control is that a process then become predictable, and it makes sense to evaluate its ability to satisfy requirements that are placed on it. If statistical control is not achieved, then the process average and standard deviation are unstable and, correspondingly, calculation based on data from such a process are unreliable.

According to Nicholas R. Farnum (1994), process capability is judged by comparing process performance with process requirement. Since meeting specification limits is one of the most basic requirements, capability analyses usually involve the specification limits somewhere in their calculations. If the process limits both fall within specification limits that mean when the process is ‘in control’, then the process is said to be capable, otherwise it is not capable. Thus, before one proceeds with a capability study, it is important to verify that the specification limits have been accurately determined.

This definition of process capability is rough one. For instance, it implies that a process would be considered capable if its process limits just coincided with the specification limits. From the normal tables, this would mean that about 0.27% of the output would be outside of the specifications. Given the current emphasis on achieving nonconforming rates only a few part per million, a process whose non-conformance rate is 0.27% would be unacceptable for modern quality improvement programs.

Besides that, according to Pyzdek (1985). The processes of capability analysis have two different stages that involve:-

1. Carrying the process into a state of statistical control for a reasonable period of time.2. Comparing the long-term process performance to management or engineering

requirements.

The process of the analysis is to figure out two different results with either attribute data or continuous data, but the whole of process must be in the form of statistical control pattern, and has been for a reasonable period of time. Under statistical analysis of process capability data, there have several methods to analysing for example; using control chart whether is attributes data or variables data, and process capability indexes.

Natural Variability versus Specifications for Process Capability:

As seen from the earlier discussions, there are three components of process capability:1. Design specification or customer expectation ( Upper Specification Limit, Lower

Specification Limit )2. The centering of the natural process variation ( X-Bar )3. Spread of the process variation ( s )

There are four possible outcomes can arise when the natural process variability is compared with the design specifications or customer expectations:

1. This process will produce conforming products as long as it remains in statistical control. The process owner can claim that the customer should experience least difficulty and greater reliability with this product. This should translate into higher profits and the Cp > 1.33 (A Highly Capable Process).

A Highly Capable Process: Voice of the Process < Specification (or Customer Expectations)

2. This process has a spread just about equal to specification width. It should be noted that if the process mean moves to the left or the right, a significant portion of product will start falling outside one of the specification limits. This process must be closely monitored. The Cp for this process is Cp = 1 to 1.33 (A Barely Capable Process).

A Barely Capable Process: Voice of the Process = Customer Expectations.

3. It is impossible for the current process to meet specifications even when it is in statistical control. If the specifications are realistic, an effort must be immediately made to improve the process (i.e. reduce variation) to the point where it is capable of producing consistently within specifications. The only way to improve product quality is to change the process, the material, equipment, or work methods, in order to reduce the variation. The Cp for this process Cp = Cp < 1 (The Process is not Capable).

A Non-Capable Process: Voice of the Process > Customer Expectations

4. Last but not lease this example show a situation that the variability (σ) and specification width is assumed to be the same as in case 2, but the process average is off-center. In such cases, adjustment is required to move the process mean back to target. If no action is taken, a substantial portion of the output will fall outside the specification limit even though the process might be in statistical control. The Cp for this process Cp = Cp < 1 ( The Process is not Capable )

An adjustment in the centring of the process will result in nearly all output meeting specification, notice that the process is capable of meeting specification but cannot because centring problems.

These example show us why it is important and to understand the variation in the process output. If we can determine what the true state of quality is and how well a process can meet the design specification then we can take action to improve the process and the quality of our product. This is the purpose of having process capability analysis.

PROCESS CAPABILITY INDEX

According to James R. Evans (1991), the relationship between the natural variation of

a process and the design specifications is often qualified by a measure called the process

capability index, Cp. Many manufacturers use Cp to monitor the quality of their suppliers,

and it is even used in purchasing contracts.

Process capability index (cpk) is the measure of process capability. It shows how

closely a process is able to produce the output to its overall specifications. According to

Johannes Ledolter & Claude W. Burrill (1999), a common used measure of capability is the

Cp capability index. It is given by

Formula:

Cp = USL – LSL = allowable spread

6σ actual spread

LSL and USL are the lowel and upper specification limits, and σ is the process standard

deviation. Note that for the time being we assume that the process characteristics are known.

LSL is the allowable process spread, and the Cp relates the allowable spread to the actual

process spread. For capable processes we expect that the actual process spread is smaller than

the allowable spread, and the Cp is the larger one. A large value of Cp indicates that the

process variability is small when compared to the width of specification interval. The larger

this index, the better.

From our data, (data is taken from the Table 1 page 55), we can calculate the Cp,

USL = 375, LCL = 270

Standard deviation (σ): sd =√∑ f x2−n x2

n−1

= √ 15369707.5−150 (319.34 )2

150−1

= √ 15369707.5−150(101978.03)149

= √489.95

= 22.13

Cp = USL – LSL

6s

= 375 – 270

6(22.13)

= 105

132.78

Cp = 0.790

The Cp index is interpreted as follows. Based on Nicholas R. Farnum (1994), if Cp =

1.0, the process is said to be ‘marginally capable’ of meeting its specification limits. Thus, it

is desirable that value of Cp exceed 1.0, since then the likelihood is higher that the

measurements will be able to stay within the specification limits. A Cp that exceed 1.33 is

usually considered very good and is commonly used as a goal by many companies. On the

other hand, Cp’s less 1.0 imply that a process is not capable of meeting its specifications. So,

based on Cp’s result that we get, our process is not capable. This is because our natural

variation is larger than the tolerance spread, and make Cp will be less than 1.0. If the natural

variation is smaller than the tolerance spread, we would expect very good quality in this

situation, which means the value of Cp is greater than 1.0. So, the action that we can take to

solve this problem is improve by reducing common causes of variation in process variables.