【算法】6西格玛

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前言

6西格玛是用来控制生产过程，保证生产良品率的一种方法。属于数据统计分析，也可以用来分析计量表之类的测量数据，查看数据的收敛性。

文章转自：http://www.npd-solutions.com/proccap.html

以防消失，拷贝如下：

PROCESS CAPABILITY

Being in control of a manufacturing process using statistical process control (SPC) is not enough. An “in-control” process can produce bad or out-of-spec product. Manufacturing processes must meet or be able to achieve product specifications. Further, product specifications must be based on customers requirements.

Process capability is the repeatability and consistency of a manufacturing process relative to the customer requirements in terms of specification limits of a product parameter. This measure is used to objectively measure the degree to which your process is or is not meeting the requirements.

Capability indices have been developed to graphically portray that measure. Capability indices let you place the distribution of your process in relation to the product specification limits. Capability indices should be used to determine whether the process, given its natural variation, is capable of meeting established specifications. It is also a measure of the manufacturability of the product with the given processes.

Capability indices can be used to compare the product/process matches and identify the poorest match (lowest capability). The poorest matches then can be targeted on a priority basis for improvement.

If we sample a group of items periodically from a production run and measure the desired specification parameter, we will get subgroup sample distributions that can be compared to that parameter’s specification limits. Two examples of this are represented below.

The diagram on the left shows a series of sample distributions that fall inside of and outside of the specification limit. This is an example of an unstable, not capable process. The right side of the diagram shows all of the distributions falling within the specification limits. This is an example of a capable process.

Process capability can be expressed with an index. Assuming that the mean of the process is centered on the target value, the process capability index Cp can be used. Cp is a simple process capability index that relates the allowable spread of the spec limits (spec range or the difference between the upper spec limit, USL, and the lower specification limit, LSL) to the measure of the actual, or natural, variation of the process, represented by 6 sigma, where sigma is the estimated process standard deviation.

If the process is in statistical control, via “normal” SPC charts, and the process mean is centered on the target, then Cp can be calculated as follows:

Cp = (USL – LSL) / 6 sigma

Cp<1 means the process variation exceeds specification, and a significant number of defects are being made.

Cp=1 means that the process is just meeting specifications. A minimum of .3% defects will be made and more if the process is not centered.

Cp>1 means that the process variation is less than the specification, however, defects might be made if the process is not centered on the target value.

While Cp relates the spread of the process relative to the specification width, it does not address how well the process average, X, is centered to the target value. Cp is often referred to as process “potential”.

Cpk measures not only the process variation with respect to allowable specifications, it also considers the location of the process average.

Cpk is taken as the smaller of either Cpl or Cpu where

Cpl = (X -LSL) / 3 sigma where X is the process mean

Cpu = (USL – X) / 3 sigma where X is the process mean

Many companies are establishing specific process capability targets. They may typically start with 1.33 for supplier qualification and have an expected goal of 2.0. If the process is near normal and in statistical control, Cpk can be used to estimate the expected percent of defective material.

Process Capability Studies are designed to see what the process is “capable” of doing under controlled conditions. The studies look at how capable the process is given ideal conditions over a short period of time (such as one hour to twenty-four hours.) The individual who is mainly responsible for a the process capability study is a Process Engineer. The Process Engineer must keep in mind the following two considerations when conducting the study.

• Eliminate or minimize special causes of variation, for example using the same operator, same batch of material, same machine and so on.
• Collect a minimum of 50 consecutive pieces in at least 10 subgroups of 5.

The benefits of conducting a Process Capability Study allows you to determine the “short” term stability and capability of a process.

Process Performance Studies are performed to identify how well a process, that is in statistical control, performs long term (for example, one week or longer). Two types of variations within the process are statistically measured: variation within subgroups and variations between subgroups. Variables should include different operators, material, tool changes, adjustments and so on. For the Process Performance Study to be successful the Process Engineer must ensure the following:

• Data is obtained over an extended period of time (a minimum of 5 days of data) under normal conditions
• A minimum of 100 pieces in 20 subgroups of 5 is gathered

The benefit of a Process Performance Study allows you to determine the “long” term stability and capability of a process.

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