Statistical process capability

Statistical Process Control (SPC) The use of statistical techniques (such as control charts) to analyze a process and take appropriate action to maintain statistical control and improve process capability. 

It is recommended at this stage of the text that the reader unfamiliar with the basic concepts of variation and process capability refer to Appendix I for an introductory treatise on statistics, and Appendix II for a discussion of process capability studies. 

In addition to understanding the statistical tolerance stack models and the FMEA process in developing a process capable solution, the designer should also address the physical assembly aspects of the tolerance stack problem. Any additional failure costs determined using CA are independent of whether the tolerances assigned to the assembly stack are capable or not. As presented in Chapter 2, the Component... 

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. 

Are mechanisms in place to identify the need for statistical techniques required for verifying the acceptability of process capability and product characteristics ... 

Process capability studies are studies conducted to obtain information about the inherent variation present in processes that are under statistical control, in order to reduce the spread of variation to less than the tolerances specified in the product specification. 

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). 

The standard does not require you to use statistical techniques but identify the need for them. Within your procedures you will therefore need a means of determining when statistical techniques will be needed to determine product characteristics and process capability. One way of doing this is to use checklists when preparing customer specifications, design specifications, and verification specifications and procedures. These checklists need to prompt the user to state whether the product characteristics or process capability will be determined using statistical techniques and if so which techniques are to be used. 

Process capability indices [49], histograms, statistical analysis of system variation, legislation [4]... 

In petrochemical and bulk commodity chemical manufacture, real-time process control has been a fact of life for many years. There is considerable understanding of processes and control of process parameters is usually maintained within tight specifications to ensure statistical process control to within six sigma, or the occurrence of one defect in a million. This has been enabled through the use of real-time analytical capability that works with programmable logic circuits to make small changes to various process inputs and physical parameters as required. 

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 ... 

The instrumental analytical techniques, developed in the last three or four decades, are almost all based on the limited signal and data processing capabilities of relatively simple analog instruments, and utilize a limited or simple theoretical basis for calculations. Apart from the rather advanced application of statistics, only a modest use of mathematical techniques in analytical chemistry has been used in these traditional analyses. 

Thanks to the outside supply of substrates, such a cell should be capable of selfmaintenance and of self-reproduction, including replication of the membrane s components. However it would not make low-molecular-weight compounds and would not have redundancies for its own defense and security - all self-repair mechanisms are missing. Also, there is the problem of leakage and lack of concentration gradients and cell division would be simply due to a physically based statistical process. 

Assessment of process capability and statistical process control brings the ability to distinguish between a stable and un-stable process and provides a means to distinguish between different causes of variability, e.g., common cause, special cause, structural (e.g., seasonal), and tampering (e.g., deliberate or unintentional). Process understanding, quality by design and capability analysis can facilitate risk-based regulatory decisions for continuous improvements ... 

One can use statistical software packages to calculate the level of control the process is under, and one may, for example, use process capability indices that compare the output of an in-control process to the specification limits. Indirect proxies for controllability metrics could also be the amount of materials and/or energy consumed per kg of product caused by excursions outside the control zone. For example, a rejected batch will become waste, and additional mass and energy will be required to replace or rework the rejected batch. 

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. 

This approach is made possible if the process (step) is demonstrated to be under a state of statistical control. A number of tests were listed by Ekvall and Juran to learn whether or not this condition exists. One approach to validating the technique involves the comparison of the process capability curve with the tolerance limits for the product. The intent of the validation is to determine whether or not the data from the process conform to the state of statistical control. It may also be used to determine whether or not quality costs can be reduced without changing the process s status. 

For another example, when the initial data indicate that a process improvement does not adversely affect the statistics associated with process capability... 

A common parameter used by quality professionals to gauge whether or not the manufacturing process and analytical methodology is within the desired state of statistical process control (SPC) is a process capability index [11], such as the Cpk value. The Cpk value is the value of the tolerance specified for the given performance characteristic divided by the actual process capability. 

The intent in this chapter is not to present in great detail the mathematics behind the statistical methods discussed. An excellent reference manual assembled by the Automotive Industry Action Group (AIAG), Fundamental Statistical Process Control, details process control systems, variation, action on special or common causes, process control and capability, process improvement, control charting, and benefits derived from using each of these tools. Reprinted with permission from the Fundamental Statistacal Process Control Reference Manual (Chrysler, Ford, General Motors Supplier uality Requirements Task Force , Measurement Systems Analysis, MSA Second Edition, 1995, ASQC Press. 

Because there are so many different ways to calculate process capability, it s common to use the wrong metric. This creates an erroneous impression of how well the process runs, and creates confusion when comparing the performance of different types of variables and processes (service, manufacturing, transactional). Therefore, this technique is best applied at first with the help of a statistical or Six Sigma expert. 

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