6, User input, Capability Analysis Results. 8, Data source: Sheet 'CPK Data'A2:B101. 9, Calculation type: Within. 11, User Options. 12, USL = 13.0. 13, LSL = 7.5. 14, Target is not provided. 15, Subgroup size = 1. Fmodex.Dll Free Download Zip. 16, Individual plot with run length = 2. 18, Estimate StDev method.

May 2014 Your supplier has sent you the process capability charts you requested. The supplier has produced some very nice charts, obviously generated with some fancy software package – and, of course, with all those accompanying statistics. You know, things like Cpk, Ppk, sigma level, ppm out of spec and so on. Very pretty charts. Looks like your supplier is really performing for you. You note one capability chart that has a Ppk = 1.14 and a Cpk = 2.07.

Why are those different? Well, it doesn’t matter. The Cpk is above 1.33, which is what you asked the supplier for. Time to work on something else. You just missed a very important piece of information about your supplier’s performance. Know what it is?

Cpk and Ppk are two commonly used measures of process capability – how well your process is meeting your customer specifications. Software today makes it easy to plug the data in and generate the results. But, far too often, we simply take the results and move forward without thinking about what they mean. In this month’s SPC Knowledge Base publication we take an in-depth look at Cpk and Ppk.

What are they? What are they measuring? What do the values means? Which one should you rely on?

Some of the answers may well surprise you. In this publication: •. Introduction This is the third in a series of SPC Knowledge Base publications on process capability. Two months ago, we took an interactive look at process capability. We reviewed the process capability calculations, including Cp and Cpk.

You could download an Excel workbook that let you visually see how changing the average and standard deviation of your process impacts your process capability. You were able to see visually how the process shifts versus your specifications. In addition, the workbook showed how Cp, Cpk, the sigma level, and the ppm out of specification changed as the average and standard deviation changed. If you are new to process capability, please take a moment to review that. Last month’s publication was entitled “.” In that publication we took a look at the why a Cpk value by itself is not sufficient to describe the process capability.

We went through a process capability checklist designed to help you paint a true picture of your process capability – to increase the confidence you, your leadership, and your customers have in your process capability. We did not mention Ppk in either publication. Time to change that in this publication. Process Capability Review Process capability analysis answers the question of how well your process meets specifications – either those set by your customer or your internal specifications.

To calculate process capability, you need three things: •. Specification limit This is true for both Cpk and Ppk. We will assume that our data are normally distributed. Process capability indices represent a ratio of how far a specification limit is from the average to the natural variation in the process. The natural variation in the process is taken as being 3 times the process standard deviation. Figure 1 shows the general set up for determining a process capability index based on the upper specification limit (USL) with “s” being a measure of the process variation.

Figure 1: Determining a Process Capability Index The process capability index is then given by: Process capability index = (USL – Average)/(3s) To calculate process capability, you need to be able to estimate the process average and the process standard deviation. And no, it is not as easy as simply doing some calculations. Both of these statistics have to be “valid.” We explore this more detail below. Cpk and Ppk Review Both Cpk and Ppk are the minimum of two process indices. The equations for Cpk and Ppk are shown in Table 1. Table 1: Cpk and Ppk Equations The X with double bar over it is the overall average.

In the Cpk equations, σ is used to estimate the process variation. Σ is the estimated standard deviation obtained from a range control chart. In the Ppk equations, s is used to estimate the process variation.

S is the calculated standard deviation using all the data. Thus, the major difference between Cpk and Ppk is the way the process variation is estimated. So what is the difference between these two? Within Subgroup Variation vs Overall Variation The question of Cpk vs Ppk is really a question of within subgroup variation, σ, vs overall variation, s. Let’s start with s or the calculated standard deviation, which is given by the equation below. N is the total number of data points.

Look at the summation term under the square root sign. This term is squaring how far each individual data point is from the overall average, as shown in Figure 2. Figure 2: Standard Deviation (s) According to the equation, you add up the squares of those deviations, divide by the total number of points minus 1 and take the square root. You can view the calculated standard deviation as the average distance each individual data point is from the overall average.

Note that you use all the data in the calculation. This is why this standard deviation is sometimes called the overall variation. It accounts for all the variation in the data. Now we will move to s, which is usually referred to as the within subgroup variation. This estimate of the process standard deviation comes from a range control chart. For example, suppose you are using an X-R control chart with a subgroup size of five. To form a subgroup, you take 5 samples.

You calculate the average of those 5 samples. This is X and is plotted on the X chart. You also calculate the range of the subgroup values. The range, R, is the maximum value in the subgroup minus the minimum value in the subgroup.

This is shown in Figure 3. Figure 3: Within Subgroup Variation ( s) R is a measure of the variation within the subgroup.

To calculate σ, you use the following equation: R is the average range and d 2 is a control chart constant that depends on subgroup size. So, σaccounts for the variation within the subgroup. It may or may not account for all the variation as we will see below.

That Little Issue of Statistical Control! All our publications on process capability have stressed the need for the process to be in statistical control.

How often is this just ignored? Last month we gave the process capability checklist developed by Dr. Don Wheeler to paint a true picture of your process capability. That checklist had five items: •. Download El Don Marcel Mauss Pdf Free Software. If Cpk is significantly different that Ppk, the process is not in statistical control So, when you looked at the supplier chart and noticed a big difference between Cpk and Ppk, you were given a key piece of information. Your supplier’s process is not in statistical control – and you can’t be sure of what you will get in the future.

In addition, if the process is not in statistical control, Cpk and Ppk have no meaning. You cannot be sure of getting similar values in the future because of the process is not consistent and predicable. We will explore this through in the following example for two processes with the same data – just in a different order. Two Processes – Same Data, Same Ppk We will use two processes that have the same data (the data from last month’s publication). Suppose you are taking four samples per hour and forming a subgroup. You want to determine if your process is capable of meeting specifications (LSL = 65 and USL = 145).

The data for the 30 subgroups for Process 1 are shown in Table 2. Hi!!I am a regular reader of all the articles posted on your website and they are really very informative as well as useful. Thanks a lot for posting.While going through this article i feel it need corrections in two places:1. We are differentiating standard deviation between Cpk and Ppk with the help of sign s & sigma. But i have seen in formules we have used these signs but when i see the explanation then in both cases we are using 's' as symbol for standard deviation. It is creating little confusion while understading the difference.2.

You mentioned above checlist of 5 terms as adviced by Dr. In case of first point it is clearly mentioned that we need to construct the control chart to see if our data is in statistical control. Now the limits or we can say natural variation is already calculated in this first point so why are we asked to do same in point number 3 ' For a process that is in statistical control, calculate the natural variation in the process data'.Kindly clear these doubts.Thanks again for posting such a wonderful posts.RegardsAshok Pershad May 31, 2014.

Thanks for your comment. Yes, different books/articles/people handle s and sigma differently - or call them both s as you said. There is not consistency in the approach. It would be better to use the terms the 'within' and 'overall' to describe which one you are talking about. I typcially use 's' for the overall and ' s' for the within.

The natural variaiton is not the same as the control limits. THe natural variation is 6 s. The control limits are based on what you are plotting, i.e., the subgroup averages in the examples in this article. Best Regards, Bill May 31, 2014 •. When individual values are used, the moving range chart is used to estimate sigma.

The moving range chart uses the range between consecutive points. So, sigma estimated from the average moving range still looks at the variation in individual values. I don't think it makes a difference if individuals values are used or subgroups are used. I still find Cpk more valuable because it says what the proess is capable of doing in the short term.

Of course, if in control, Cpk and Ppk will be the same essentially. Mar 30, 2017 •.