Statistical process control examples

There are important economic consequences of a process being out of control for example, product waste and customer dissatisfaction. Hence, statistical process control does provide a way to continuously monitor process performance and improve product quahty. A typic process may go out of control due to several reasons, including... 

Detailed illustrations and examples are used throughout to develop basic statistical methodology for dealing with a broad area of applications. However, in addition to this material, there are many specialized topics as well as some very subtle areas which have not been discussed. The references should be used for more detailed information. Section 8 discusses the use of statistics in statistical process control (SPC). 

Develop a metrics system allowing for quantifiable results wherever possible for example, use statistical process control charts for manufacturing processes and correlating manufacturing deviations with consumer complaint trends. 

The identification of the fall off in plant output uses the same statistical process control methods as for product quality [D-4]. Usually, and certainly in the larger manufacturing units, these issues will be handled by the local plant support teams. However, sometimes output issues arise which are outside the more routine evolutionary techniques employed by the process control teams. A typical example is when the output from a process is constrained by a particular plant item. An improved piece of equipment needs to be identified and evaluated. The introduction of this equipment will usually necessitate process changes for maximum efficiency. This and similar packages of work are best done by an R D project team. 

The Shotscope system also maintains and displays statistical process control (SPC) data in a variety of formats, including trend charts, X-bar and R charts, histograms, and scatter diagrams. This information provides molders with the knowledge that their processes are in control, and, should they go out of control, Shotscope can alert to an out-of-control condition and divert suspect-quality parts. Furthermore, because the Shotscope system can measure and archive up to 50 process parameters (such as pressures, temperatures, times, etc.) for every shot monitored and the information archived, the processing fingerprint for any part can be stored and retrieved at any time in the future. This functionality is extremely important to any manufacturer concerned with the potential failure of a molded part in its end-use application (for example, medical devices). 

To prevent material loss due to excursions such as the previous example, robust process control systems are required throughout the supply chain from the raw materials manufacturer to the pad manufacturer and the CMP module. Invariably, incident reviews of such excursions reveal that the excursion could have been prevented or limited to only a small amount of material lost if the proper statistical process control systems had been in place. Invariably, the excursion could have been detected by careful scrutiny of an in-process parameter that was either monitored or should have been monitored by the subsupplier, pad manufacturer, and/or the CMP operation. 

Most companies keep statistical process control (SPC) charts that track the laboratory analysis of final prodncts, which are typically sampled one to three times daily. Fignre 15.34 is an example of an indnstrial SPC chart for two different controllers, for two different seven-day periods. It is easy to see which controller performed better. 

Examples of this type of data are, e.g., from the field of process modeling and multivariate statistical process control. Suppose that process measurements are taken from a chemical reactor during a certain period of time. In the same time period, process measurements are taken from the separation column following that reactor as a unit operation. The composition of the product leaving the column is also measured in the same time period and with the same measurement frequency as the process measurements. This results in three blocks of data, with one mode in common. Relationships between these blocks can be sought and, e.g., used to develop control charts [Kourti et al. 1995, MacGregor et al. 1994],... 

Three-way two-block data can be encountered, e.g., in modeling and multivariate statistical process control of batch processes. The first block contains the measured process variables at certain points in time of different batch runs. The second block might contain the quality measurements of the end products of the batches. Creating a relationship between these blocks through regression analysis or similar, can shed light on the connection of the variation in quality and the variation in process measurements. This can be used to build control charts [Boque Smilde 1999, Kourti et al. 1995], Another application is in multivariate calibration where, for example, fluorescence emission/excitation data of samples are used to predict a property of those samples [Bro 1999],... 

An example of a three-way multiblock problem was published in the area of multivariate statistical process control of batch processes [Kourti et al. 1995], Suppose, e.g., that the feed of a batch process is characterized by a composition vector of length L. If / different batch runs have been completed this results in a matrix X (I x L) of feed characteristics. The process measurements are collected in Z (I x J x K) having I batches, J variables and measured at K time points each. The M different end product quality measurements are collected in Y (/ x M). Investigating if there is a connection between X, Z and Y is a common task in process analysis. 

What we have presented here is only a small portion, and very simplified at that, of the extensive array of concepts and techniques that constitute statistical process control. It is not our aim to exhaust this subject, but only to discuss it a little as an application of the normal distribution. Deeper treatments can be found in any of many books entirely dedicated to quality or statistical process control. To learn more about these important tools you can consult, for example, Oakland and Followell (1990) or Montgomery (1997). 

In the example, a design model was first developed that indicated that optical output power is a function of laser facet power, laser placement, lens placement, and fiber alignment. To control optical output power, statistical process control must be applied to these critical process output parameters and, where apphcable, must be applied to corresponding process input parameters. 

Statistical Process Control, Fig. 1 Example of an Xbar control chart... 

These new challenges in statistical process control have motivated the laxmch of quality control-oriented topics within several international research funding programs. For example, within the European Community 7th Framework Program, the topic zero defect manufacturing has generated calls for proposals in recent years. 

SPC (Statistical Process Control) describes the method, by which the product properties to be produced are recorded by measurement. These data are then statistically evaluated and analysed by control chart, for example. Based on those results, the production process is adjusted by suitable means, preventing product characteristics deviating from the permissible tolerance. 

Statistical analysis is used to assess the consistency of a common property and to identify patterns of occurrence of characteristics. This forms the basis of the practice of statistical process control (SPG) that has become the primary method of quality control in industry and other fields of practice. In statistical process control, random samples of an output stream are selected and compared to their design standard. Variations from the desired value are determined, and the data accumulated over time are analyzed to determine patterns of variation. In an injection-molding process, for example, a variation that occurs consistently in one location of the object being molded may indicate that a modification to the overall process must be made, such as adjusting the temperature of the liquid material being injected or an alteration to the die itself to improve the plastic flow pattern. 

In the Principles of Quality course, students use advanced statistics and mathematics to work with operational data. Process technicians collect, organize, and analyze data during routine operations. The statistical approach works well with statistical process control and control charts. A variety of processes can easily be adapted to fit these quality tools. Examples of these include equipment and quality variables process variables include pressure, temperature, flow, level, and analytical parameters. 

As an example of statistical analysis of products there is statistical process control (SPC). It is an important on-line method in real time by which a production process can be monitored and control plans can be initiated to keep quality standards within acceptable limits. Statistical quality control (SQC) provides off-line analysis of the big picture such as what was the impact of previous improvements. It is important to understand how SPC operates. 

In many cases of batch and semi-batch polymerization control there are no on-line measurements of polymer quality (for example, polymer composition, molecular weight) during the batch and these measures of end-use properties are only available at the end of the batch. In this case recipe modifications from one run to the next are common. The minimal information needed to carry out this type of mn-to-run control is a static model relating the manipulated variable to the quality variables at the end of the batch. As pointed out in Ref 7, this model can be as simple as a steady-state (constant) gain relationship or a nonlinear model that includes the effects of different initial conditions and the batch time. The philosophy of statistical process control can be very useful in this case, since the polymer quality variable (for example the Mooney viscosity in elastomer manufacture) can be plotted for each successive batch on a Shewhart (%-bar) chart with the upper and lower control limits placed at three standard deviations above and below the target. 

Statistical Process Control In most cases of batch and semibatch polymerizations, the only measurements of the end-use properties are at the end of the batch. As discussed previously, these are often off-line, laboratory analyses. The same is true for the product quality variables. An example from the synthetic rubber industry is the Mooney viscosity of the rubber. Neither the Mooney viscosity (end-use property) nor its underlying product quality variables (MWD and degree of branching or cross-Unking) is measured online. In fact, in some cases, the polymer quality variables are not measured at... 

In statistical process control. Control Charts (or Quahty Control Charts) are used to determine whether the process operation is normal or abnormal. The widely used X control chart is introduced in the following example. This type of control chart is often referred to as a She-whart Chart, in honor of the pioneering statistician, Walter Shewhart, who first developed it in the 1920s. 

An instance of Process Settings comprises of aU Parameters which can be used in order to adjust the result. In the discussed example, only Process Duration was chosen. By increasing the Process Duration, the epitaxial layer thickness is getting higher, or reverse. The Process Control Settings shall be discussed in httle more depth in the sequel. In this example, the used instance of Process Control Settings is MySPCForEpiThicknessOfS pm which comprises of the information which is needed to parameterize statistical process control (SPC) in the context of gauging layer thicknesses. 

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