Cp, Cpk, Pp and Ppk: Know How and When to U Them
The difference between Cp and Pp, as well as between Cpk and Ppk, results from the method of calculating standard deviation. Cp and Cpk consider the deviation mean within rational subgroups, while Pp and Ppk t the deviation bad on studied data.
By Daniela Marzagão
For many years industries have ud Cp, Cpk, Pp and Ppk as statistical measures of process quality capability. Some gments in manufacturing have specified minimal requirements for the parameters, even for some of their key documents, such as Advanced Product Quality Planning and ISO/TS-16949. Six Sigma, however, suggests a different evaluation of process capability by measuring against a sigma level, also known as sigma capability.
Incorporating metrics that differ from traditional ones may lead some companies to wonder about the necessity and adaptation of the metrics. It is important to emphasize that traditi
out of memoryonal capability studies as well as the u of sigma capability measures carry a similar purpo. Once the process is under statistical control and showing only normal caus, it is predictable. This is when it becomes interesting for companies to predict the current process’s probability of meeting customer specifications or requirements.
Capability Studies
powergripTraditional capability rates are calculated when a product or rvice feature is measured through a quantitative continuous variable, assuming the data follows a normal probability distribution. A normal distribution features the measurement of a mean and a standard deviation, making it possible to estimate the probability of an incident within any data t.
The most interesting values relate to the probability of data occurring outside of customer specifications. The are data appearing below the lower specification limit (LSL) or above the upper specification limit (USL). An ordinary mistake lies in using capability studies to deal with categorical data, turning the data into rates or percentiles. In such cas, determining specification limits becomes complex. For example, a billing process
may generate correct or incorrect invoices. The reprent categorical variables, which by definition carry an ideal USL of 100 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 uful, 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.
The following example details the impact that the different forms of calculating capability may have over the study results of a process. A company manufactures a product that’s acceptable dimensions, previously specified by the customer, range from 155 mm to 157 mm. The first 10 parts made by a machine that manufactures the product and works duri
ng one period only were collected as samples during a period of 28 days. Evaluation data taken from the parts was ud to make a Xbar-S control chart (Figure 1).
the greatest love of allFigure 1: Xbar-S Control Chart of Evaluation Data | |
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This chart prents only common cau variation and as such, leads to the conclusion th
at the process is predictable. Calculation of process capability prents the results in Figure 2.
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Figure 2: Process Capability of Dimension | | 千年木乃伊穿阿迪
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Calculating Cp
The Cp rate of capability is calculated from the formula:
where s reprents the standard deviation for a population taken from , with s-bar reprenting the mean of deviation for each rational subgroup and c4 reprenting a statistical coefficient of correction.
In this ca, the formula considers the quantity of variation given by standard deviation and an acceptable gap allowed by specified limits despite the mean. The results reflect the population’s standard deviation, estimated from the mean of the standard deviations within the subgroups as 0.413258, which generates a Cp of 0.81.老鼠的英文>袁腾飞mp3
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 ar
e minimized and the differences between groups are maximized. This allows a clearer identification of how the process parameters change along a time continuum. In the example above, the process ud to collect the samples allows consideration of each daily collection as a particular rational subgroup.
The Cpk capability rate is calculated by the formula:
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considering the same criteria of standard deviation.
In this ca, besides the variation in quantity, the process mean also affects the indicators. Becau the process is not perfectly centralized, the mean is clor to one of the limits and, as a conquence, prents a higher possibility of not reaching the process capability targets. In the example above, specification limits are defined as 155 mm and 157 mm. The mean (155.74) is clor to one of them than to the other, leading to a Cpk factor (0.60) that is lower than the Cp value (0.81). This implies that the LSL is mor
e difficult to achieve than the USL. Non-conformities exist at both ends of the histogram.
