Cp, Cpk, Pp and Ppk: Know How and When to Use Them | iSixSigma
I've often found that where JMP reports a Cpk, the PPM it predicts does . The relationship between process capability and ppm defective is. Long Term Sigma / PPM / Cpk Table. The conversion table below is similar to the one above but lets discuss the differences. It is very important to remember that. Two sided table. Cpk, Sigma level, % out of tolerance, PPM out of tolerance. , , , , , , , ,
Cp, Cpk, Cm, Cmk, control limits
Process Capability Voice of the process and Specification Expectations of the customer. Natural Variability versus Specifications for Process Capability: As seen from the earlier discussions, there are three components of process capability: Design specification or customer expectation Upper Specification Limit, Lower Specification Limit The centering of the natural process variation X-Bar Spread of the process variation s A minimum of four possible outcomes can arise when the natural process variability is compared with the design specifications or customer expectations: This process will produce conforming products as long as it remains in statistical control.
The process owner can claim that the customer should experience least difficulty and greater reliability with this product.
This should translate into higher profits. Cpk values of 1.
This means that the process is contained within four standard deviations of the process specifications. A Barely Capable Process: This process has a spread just about equal to specification width. It should be noted that if the process mean moves to the left or the right, a significant portion of product will start falling outside one of the specification limits.
This process must be closely monitored. This process is contained within three to four standard deviations of the process specifications. It is impossible for the current process to meet specifications even when it is in statistical control.Process Capability - CPK - CP - PPM - Normal Distribution - Excel Demo
For example, a billing process may generate correct or incorrect invoices. These represent categorical variables, which by definition carry an ideal USL of percent error free processing, rendering the traditional statistical measures Cp, Cpk, Pp and Ppk inapplicable to categorical variables. When working with continuous variables, the traditional statistical measures are quite useful, especially in manufacturing. The difference between capability rates Cp and Cpk and performance rates Pp and Ppk is the method of estimating the statistical population standard deviation.
The difference between the centralized rates Cp and Pp and unilateral rates Cpk and Ppk is the impact of the mean decentralization over process performance estimates.
Cp, Cpk, Pp and Ppk: Know How and When to Use Them
The following example details the impact that the different forms of calculating capability may have over the study results of a process. The first 10 parts made by a machine that manufactures the product and works during one period only were collected as samples during a period of 28 days.
Evaluation data taken from these parts was used to make a Xbar-S control chart Figure 1. Xbar-S Control Chart of Evaluation Data This chart presents only common cause variation and as such, leads to the conclusion that the process is predictable.
Calculation of process capability presents the results in Figure 2. In this case, the formula considers the quantity of variation given by standard deviation and an acceptable gap allowed by specified limits despite the mean.
Rational Subgroups A rational subgroup is a concept developed by Shewart while he was defining control graphics. It consists of a sample in which the differences in the data within a subgroup are minimized and the differences between groups are maximized.
Cp Cpk Calculator in Excel
This allows a clearer identification of how the process parameters change along a time continuum. In the example above, the process used to collect the samples allows consideration of each daily collection as a particular rational subgroup. The Cpk capability rate is calculated by the formula: It is not much use having a high Cm index if the machine setting is way off centre in relation to the middle of the tolerance range.
A high Cmk index means, then, that you have a good machine with a small spread in relation to the tolerance width, and also that it is well centred within that width.
If Cmk is equal to Cm, the machine is set to produce exactly in the middle of the tolerance range see Fig. A normal requirement is that Cmk should be at least 1. An important principle is that control limits are used along with the mean value on the control graph to control the process, unlike tolerance limits, which are used along with individual measurements to determine whether a given part meets specifications or not.
The function of control limits is to centre the process on the target value, which is usually the same as the middle of the tolerance width, and to show where the limit of a stable process lies. This means, in principle, that you have no reason to react until the control chart signals certain behaviour. A commonly used control graph is the XR graph, where the position and spread of the process are monitored with the help of sub groups and control limits.