Process Capability

It is important to understand the current process capability prior to making any changes.

Early in any project (in Define for goal setting or more formally in Measure)

The simplest form of Process Capability for continuous data is known as C_p and is calculated as the ratio of the specification range divided by the process width:

where:

• s is the short-term process standarddeviation
• USL is the Upper Specification Limit
• LSL is the Lower Specification Limit

99.73% of data points lie between ±3 standard deviations in any normally distributed data.

C_p doesn't take into account the centering of the process. Figure below shows 3 graphs with same C_p but different process centering.

A second metric needs to be introduced to counter this; known as C_pk, it is defined as

C_pk represents the distance of the center of the process to the nearest specification limit in units of process width .

C_pk is positive when the mean of the process is inside the specifications; it drops to zero as the mean hits the USL or LSL.

it becomes negative as the process mean moves outside the specification range, as shown below :

Roadmap

The roadmap to calculating the Process Capability for continuous data is as follows:

Interpreting the Output

• Example output for a Process Capability Study is shown in Figure below. The key metrics to focus on are
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• Lower Specification Limit (LSL) as entered by the user.
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• Target value if entered.
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• Upper Specification Limit (USL) as entered by the user.
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• Sample Mean.
• Potential Capability C_p and C_pk as defined by the equations above .

Process Capability (expressed as C_p and C_pk) is intended to represent short-term behavior of the process. In reality processes tend to shift and drift over time; the variation stays reasonably consistent, but the mean moves to and from. Taking this into account, the longer-term variation is actually larger than short-term and so the "capability" is lower in the long term than the short. Long-term "capability" is known as Performance and the equations are identical to those for Capability (short-term), but a longer-term standard deviation (σ instead of s) is used

Empirical process studies show that most processes tend to shift and drift about 1.5 standard deviations. Lean Sigma Belts really only need to know that it happens, rather than the equations to justify why.

 

Most software packages try to emulate this short-term versus long-term standard deviation by measuring it in two different ways; for long-term the regular standard deviation of all the data is used and for short-term the value comes from an equation involving the Moving Average across the data. In Figure below , the within standard deviation represents short term and the overall standard deviation represents long term. The within value is used to calculate the C_p and C_pk, whereas the overall value is used to calculate the P_p andP_pk.

The target value for C_p in Lean Sigma is 2.0 and for P_pk it is 1.5. These are not absolute requirements in any way, but if a process exhibits Capability at this level then it can be considered to be performing very well.

At the bottom of Figure , boxes explaining likely performance of the process in terms of Parts per Million defective(PPM):

• The Observed Performance represents the PPMs of the actual data points below the LSL, above the USL, and the total of both. If no points fall outside of specification during the data collection, then the PPMs here are zero.

• The Within Performance represents the PPMs as calculated from a normal curve with the sample mean andshort-term standard deviation. The calculated curve hangs over the LSL and USL, and thus, the area under the curve outside of the specification limits gives the PPMs. These are the expected defectives on a short-term basis.

• The Overall Performance represents the PPMs as calculated from a normal curve with the sample mean andlong-term standard deviation. The calculated curve hangs over the LSL and USL, and thus, the area under the curves outside of the specification limits gives the PPMs. These are the expected defectives on a long-term basis.

 

 

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