Measures process capability

Bothe DR, Measuring Process Capability, Techniques and Calculations for Quality and Manufacturing Engineers, McGraw-Hill, 1997. 

Variation is an obvious measure for quality of conformance, but it must be associated with the requirements set by the specification to be of value at the design stage. Unfortunately, difficulty exists in finding the exact relationship between product tolerance and variability. Approximate relationships can be found by using process capability indices, quality metrics which are interrelated with manufacturing cost and tolerance (Lin et al., 1997). ... 

Research looking into tolerance allocation in assembly stacks is by no means new. A current theme is towards an optimization approach using complex routines and/ or cost models (Lin et al., 1997 Jeang, 1995). Advanced methods are also available, such as Monte Carlo Simulation and Method of Moment. ) (Chase and Parkinson, 1991 Wu et al., 1988). The approach presented here is based on empirical process capability measures using simple tolerance models, cost analogies and optimization... 

The measures of dimensional variability from Conformability Analysis (CA) (as described in Chapters 2 and 3), specifically the Component Manufacturing Variability Risk, q, is useful in the allocation of tolerances and subsequent analysis of their distributions in probabilistic design. The value is determined from process capability maps for the manufacturing process and knowledge of the component s material and geometry compatibility with the process. In the specific case to the th component bilateral tolerance, it was shown in Chapter 3 that the standard deviation estimates were ... 

A capability study is a statistical tool which measures the variations within a manufacturing process. Samples of the product are taken, measured and the variation is compared with a tolerance. This comparison is used to establish how capable the process is in producing the product. Process capability is attributable to a combination of the variability in all of the inputs. Machine capability is calculated when the rest of the inputs are fixed. This means that the process capability is not the same as machine capability. A capability study can be carried out on any of the inputs by fixing all the others. All processes can be described by Figure 1, where the distribution curve for a process shows the variability due to its particular elements. 

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). 

Are measures taken to maintain or exceed process capability required by the customer ... 

Process capability study report Measurement systems analysis report... 

Preliminary process capability studies are those based on measurements collected from one operating run to establish that the process is in statistical control and hence no special causes are present. Studies of unpredictable processes and the determination of associated capability indices have little value. Preliminary studies should show acceptable results for special characteristics before production approval can be given. These studies and associated indices only apply to the measurement of variables and not to attributes (see below). 

Several measures of process capability have evolved and are presented as indices Cp, Cpi, and P i. These are defined in Appendix A. 

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. 

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 ... 

Pd (15), and Au (15). Once again, STM s unique contribution in these applications arises from the small areas (ca. 2-4 A ) that are involved in the measurement process. These capabilities have enabled the mapping of the spatial distribution of electronic states. For example, cation and anion sites on GaAs surfaces have been discriminated (Stroscio, J.A. Feenstra, R.M. Newns, D.M. ... 

SixSigma [On-line], Measurement System Capability Manual, Available http //www.6sigma.us/ MeasurementsystemsMSA/measurement-systems-analysis-MSA-p.html, accessed 1 April 2009 I. Verhappen, Typical process analyzer application justification, in Analytical Instrumentation-, Practical Guides for Measurement and Control, R.E. Sherman and L. Rhodes (eds). Instrument Society of America, Research Triangle Park, 1996. 

Interference free detection limits" and "Instrument detection limits", for example, do not specify the measuremerit capabilities of a complex measurement process including sample preparation... 

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... 

Arguably, the most important aspects of quality management for PAT are the concepts of quantitative process performance characterization using process capability indices as universal descriptors, which form the basis of the measure and analyze portions of the DMAIC model. Process capability indices consider simultaneously both process variability and process specifications to determine whether... 

FIGURE 5 Relationship between sampling rate and effective resolution of process capability assessment. The curve is based on the width of the confidence intervals for estimation of mean and variance. The relationship shown does not consider the effect of reference measurement precision, which would further reduce the ability to discern changes in process capability. 

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

There is one more index that is used, the overall quality index, or the corrected process capability index, Cpk. This is the distance of the mean of the measure to the nearest tolerance limit. 

One approach that QA would use to assure itself that a given process (step) is under control is the effort associated with the concept of process capability. Ekvall and Juran [15] defined the concept as the measured inherent reproducibility of the product turned out by the process. The statistical definition of process capability is that all the measured values fall within a 6-sigma range (i.e., range of the minimum to maximum limits). The information is used to show that the process is under control over a period of time as well as determine whether there is any drifting or abnormal behavior from time to time. Process validation is a QA tool in this case because its data will be used as the origin for the data curve developed for the process capability concept. 

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