Statistics 简明教程
Statistics - Process Capability (Cp) & Process Performance (Pp)
Process Capability
过程能力可以定义为过程相对于其规格的可测量属性。它以过程能力指数 ${C_p}$ 表示。过程能力指数用于检查过程产生的输出的变异性，并将变异性与产品公差进行比较。 ${C_p}$ 由以下公式控制：
Process capability can be defined as a measurable property of a process relative to its specification. It is expressed as a process capability index ${C_p}$. The process capability index is used to check the variability of the output generated by the process and to compare the variablity with the product tolerance. ${C_p}$ is governed by following formula:
Formula
其中——
Where −
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${USL}$ = Upper Specification Limit.
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${LSL}$ = Lower Specification Limit.
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${\mu}$ = estimated mean of the process.
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${\sigma}$ = estimated variability of the process, standard deviation.
过程能力指数 ${C_p}$ 的值越高，过程越好。
Higher the value of process capability index ${C_p}$, better is the process.
Example
考虑一辆汽车及其停车位的案例。车库尺寸表示规格限，而汽车定义为过程输出。此处，过程能力将说明汽车尺寸、车库尺寸以及汽车停放在车库中间有多远之间的关系。如果汽车尺寸比车库尺寸小很多，则可以轻松将汽车停入其中。如果汽车尺寸与车库尺寸相比非常小，则可以从中心任意距离停入。就过程控制而言，这种变化较小的过程允许轻松地将汽车停放在车库中，并满足客户的要求。让我们根据过程能力指数 ${C_p}$ 来考虑上述示例。
Consider the case of a car and its parking garage. garage size states the specification limits and car defines the process output. Here process capability will tell the relatonship between car size, garage size and how far from middle of the garage you can parked the car. If car size is litter smaller than garage size then you can easily fit your car into it. If car size is very small compared to garage size then it can fit from any distance from center. In term of process of control, such process with little variation, allows to park car easily in garage and meets the customer’s requirement. Let’s see the above stated example in terms of process capability index ${C_p}$.
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${C_p = \frac{1}{2}}$ - garage size is smaller than car and can not accomodate your car.
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${C_p = 1}$ - garage size is just sufficient for car and can accomodate your car only.
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${C_p = 2}$ - garage size is two times than your car and can accomodate two cars at a time.
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${C_p = 3}$ - garage size is three times than your car and can accomodate three cars at a time.
Process Performance
过程性能用于检查使用该过程生成的样本的符合性。它表示为过程性能指标 ${P_p}$。它检查是否满足客户要求。它与过程能力的不同之处在于过程性能适用于特定批次材料。为了支持批次中的差异，抽样方法可能需要相当大。过程性能仅在无法评估过程控制时使用。${P_p}$ 受以下公式支配：
Process performance works to check the conformance of the sample generated using the process. It is expressed as a process performance index ${P_p}$. It checks whether it is meeting customer requirement or not. It varies from Process Capability in the fact that Process Performance is applicable to a particular batch of material. Sampling method may need to be quite substancial to support of the variation in the batch. Process Performance is only to be used when a process control cannot be evaluated. ${P_p}$ is governed by following formula: