Method 1: Calculate CPK by calculating sigma
When calculating CPK, we first need to understand a key basic data, which is sigma (represented by the symbol s). This sigma is an important indicator for measuring the degree of data dispersion. In the calculation, we use the function stdevp() to obtain it. The stdevp function is a tool for calculating the population standard deviation, which can accurately reflect the dispersion of data relative to the average. After we obtain the specific value of sigma, it lays a solid foundation for the subsequent calculation of CPK.
As a key indicator for measuring process capability, CPK is determined by the smaller value between CPU and CPL, that is, CPK = min (CPU, CPL). It's like a competition where CPU and CPL are two contestants, and CPK is the winner selected from them. CPU represents the relationship between the upper specification limit (USL) and the central value (cl), and its calculation formula is CPU = (USL - cl) / 3 / sigma. It reflects the performance of process data in the direction close to the upper specification limit. For example, if we regard the process as a car driving on the road, the upper specification limit is the upper boundary of the road, and CPU is an indicator to measure how far the car is from this upper boundary and its driving ability.
On the other hand, CPL focuses on the relationship between the lower specification limit (LSL) and the central value (cl). Its calculation formula is CPL = (cl - LSL) / 3 / sigma. Also taking car driving as an example, the lower specification limit is the lower boundary of the road, and CPL measures the situation of how far the car is from this lower boundary and its driving ability. By comparing the magnitudes of CPU and CPL, we can determine the value of CPK, so as to clearly understand the actual ability of the process within the entire specification range.
Method 2: Calculate Cpks from Ca and Cp
In another calculation method, we need to calculate Ca and Cp first, and then obtain Cpks. Similarly, the calculation of sigma is also indispensable here. We still use the stdevp() function to obtain the value of sigma.
Ca, that is, process accuracy, reflects the degree of deviation between the process average and the specification center. Its calculation formula is Ca = (USL - LSL) / 6 / sigma. The specification center is the middle value of the specification range, which represents the ideal process output position. The magnitude of Ca reflects the deviation of the actual process average from this ideal position. For example, in the process of product production, if the specification range of the product has clear upper and lower limits, Ca can tell us whether the average level of the produced products deviates from this ideal center position.
Cp, namely process precision, measures the magnitude of process variation relative to the specification range. Its calculation formula is Cp = cl - specification center / ((USL - LSL) / 2). The absolute value symbol here ensures that the result is non - negative, which reflects the proportional relationship between the distance from the central value to the specification center and half of the specification range. Through the value of Cp, we can judge whether the process variation is within an acceptable range. After we calculate Ca and Cp, we can obtain the value of Cpks according to the corresponding rules, thus evaluating the process capability from another perspective.