Capability index

The critical characteristic on each component was analysed, calculated from the analysis and the value obtained was plotted against the process capability indices, Cpk and Cp, for the characteristic in question. See Appendix V for descriptions of the 21 components analysed, including the values of Cp and Cp from the SPC data supplied. Note that some components studied have a zero process capability index. This is a default value given if the process capability index calculated from the SPC data had a mean outside either one of the tolerance limits, which was the case for some of the components submitted. Although it is recognized that negative process capability indices are used for the aim of process improvement, they have little use in the analyses here. A correlation between positive values (or values which are at least within the tolerance limits) will yield a more deterministic relationship between design capability and estimated process capability. 

Note that the squared relationship which was initially used to model the degree of difficulty in obtaining more capable tolerances for a given manufacturing route and product design is being returned by the power law. Similarly, a relationship between the process capability index Cp and q for the components analysed is shown in... 

A standard for the minimum acceptable process capability index for any component/characteristic is normally set at = 1.33, and this standard will be used later to align costs of failure estimates. If the characteristics follow a Normal distribution, Cp = 1.33 corresponds to a fault probability of ... 

The way of measuring capability is to carry out a capability study and calculate a capability index. There are two commonly used process capability indices, Cp and Cpk. In both cases, it is assumed the data is adequately represented by the Normal distribution (see Appendix I). 

The process capability index is a means of quantifying a process to produce compo nents within the tolerances of the specification. Its formulation is shown below ... 

Where a process is producing a characteristic with a capability index greater than 2.5 it should be noted that the unnecessary precision may be expensive. Figure 2 shows process capability in terms of the tolerance on a component. The area under each distribution is equal to unity representing the total probability, hence the varying heights and widths. 

Process capability index Cp < = 1.79 Process capability index Cp = 2.1... 

Process capability index Cp, = 0 Process capability index Cp = 0... 

Following production launch, process capability and performance should be measured continually in order to demonstrate that your processes remain capable and the capability index continues to rise. Appropriate action should be taken on characteristics that are either unstable or non-capable. Action plans should be implemented to contain process output and continually improve performance. 

The capability index for a stable process defined as the quotient of tolerance width and process capability where process capability is the 6a range of a process s inherent variation. 

The capability index which accounts for process centering for a stable process using the minimum upper or lower capability index. 

Lin, H.C. and Sheen, G.J., An approximation approach for making decisions in assessing the capability index C-pk from the subsamples. Comm. Stat. Sim. Comp., 34, 191, 2005. 

Metrics for this might include number of excursions from statistical process control, but one very useful metric for controllability is process capability, or more accurately, process capability indices. Process capability compares the output of an in-control process to the specification limits by using capability indices. The comparison is made by forming the ratio of the spread between the process specifications (the specification width ) to the spread of the process values. In a six-sigma environment, this is measured by six standard deviation units for the process (the process width ). A process under control is one where almost all the measurements fall inside the specification limits. The general formula for process capability index is ... 

Process Capability Indices Process capability indices provide a quantitative measure to assess the ability of a process to produce products that meet the specifications. A commonly used process capability index, denoted as Cp, can be calculated as... 

It should be noted that the Cp value could not indicate the proper process capability if the process is not centered since Cp does not account for where the process mean is with respect to the specifications. To alleviate this issue, another process capability index, Cpk, is used ... 

The process capability index, Cpk, is related to the so-called process sigma such that a 6a process corresponds to a Cpk of exactly 2.00, or 2.0 defective parts per billion (PPB), assuming N (0, a) quality variance distribution (can alternative calculation for process sigma estimates 3.4 defective parts per million for a 6a process). Examples of the correspondence between Cpk, process sigma, and defect rate for N(0, a) distributions are shown in Figure 2. The process capability (based on observed yield) of pharmaceutical manufacturers has been cited by some benchmark studies to be roughly 0.7 (2.1a) [28]. 

A popular approach to comparing the tolerance and standard deviation of measurements is to define the process capability index, Cp or CI, as... 

Suppose over a number of results the mean error is not zero. In SPC the mean error as a percentage of the tolerance half-range (which is T when the tolerance is T) is known as the index of accuracy, or capability index for setting ... 

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