Statistical process control Shewhart Chart

Many of the quality improvement goals for implementation of PAT in the pharmaceutical industry have been achieved by companies in other industries, such as automobile production and consumer electronics, as a direct result of adopting principles of quality management. The lineage of modern quality management can be traced to the work of Walter Shewhart, a statistician for Bell Laboratories in the mid-1920s [17]. His observation that statistical analysis of the dimensions of industrial products over time could be used to control the quality of production laid the foundation for modern control charts. Shewhart is considered to be the father of statistical process control (SPC) his work provides the first evidence of the transition from product quality (by inspection) to the concept of quality processes [18,19]. 

Figure 5.19 Shewhart chart for statistical process control.

The effects of environment are treated using factor analysis and damage is detected using statistical process control with the multivariate Shewhart-T control charts. 

However, risk in the process world has an even more fundamental role that is far more just to fulfill the Agency s expectation about process understanding and product safety it is the basis and rational for MSPC. In fact, it is what the original intent of Walter Andrew Shewhart (1891-1967) had in mind when he invented the notion of statistical process control (SPC) and the control Shewhart chart. Although not couched in precisely the language of risk, it was at the heart of what he was trying to do at Bell labs at the time [11]. 

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. 

The terms statistical process control SPC) and statistical quality control (SQC) refer to a collection of statistically-based techniques that rely on quality control charts to monitor product quality. These terms tend to be used on an interchangeable basis. However, the term SPC is sometimes used to refer to a broader set of statistical techniques that are employed to improve process performance as well as product quality (MacGregor, 1988). In this chapter, we emphasize the classical SPC techniques that are based on quality control charts (also called control charts). The simplest control chart, a Shewhart chart, merely consists of measurements plotted vs. sample number, and control limits that indicate the upper and lower limits for normal process operation. 

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. 

A form of this approach has long been followed by RT Corporation in the USA. In their certification of soils, sediments and waste materials they give a certified value, a normal confidence interval and a prediction interval . A rigorous statistical process is employed, based on that first described by Kadafar (1982,), to produce the two intervals the prediction interval (PI) and the confidence interval (Cl). The prediction interval is a wider range than the confidence interval. The analyst should expect results to fall 19 times out of 20 into the prediction interval. In real-world QC procedures, the PI value is of value where Shewhart (1931) charts are used and batch, daily, or weekly QC values are recorded see Section 4.1. Provided the recorded value falls inside the PI 95 % of the time, the method can be considered to be in control. So occasional abnormal results, where the accumulated uncertainty of the analytical procedure cause an outher value, need no longer cause concern. 

An example of a Shewhart Chart is shown below for a hypothetical powder fill process. Five vials of product were sampled every hour and the net content of each vial was determined. The Shewhart Chart is shown in Fig. 1. The Average Chart indicates lack of statistical control at subgroups 3, 4, 9, 14, and 17. Further study of the Average Chart indicates a possible shift in the process mean at subgroup 12, and the Range Chart shows an increase at subgroup 6. Subsequent special cause investigation determined that the shift in process... 

Shewhart control charts enable average process performance to be monitored, as reflected by the sample mean. It is also advantageous to monitor process variability. Process variability within a sample of k measurements can be characterized by its range, standard deviation, or sample variance. Consequently, control charts are often used for one of these three statistics. 

This is the most common variable control chart. The principles that were developed by Shewhart are applied to the data and the statistical calculations for mean and control limits are completed. To be in statistical control a process must fall within three standard deviations from the mean of the data. At least 25 data points are necessary to calculate the control limits for a process. Once the control limits have been calculated, they stay the same unless a change has been made to the process. If a data point falls outside the calculated control limits a special cause is sought out for the variation. This control chart uses the constants that were developed by Shewhart to estimate the standard deviation of the data. The formulas that are used and the development of a control chart can be found in any good SPC textbook, therefore I will not be covering that material here. 

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