TECHNOLOGY OVERVIEW

Statistical Process Control Charts

The BIS.Net Team BIS.Net Team

SPC Charts were formally introduced over 100 hundred years ago by engineers and statisticians, such as Walter Shewhart, a self-taught statistician. These pioneers recognized and understood the concept of variability. When a can of beverage is produced the next can is unlikely going to be filled with the same volume as the previous can. Shewhart and others recognized that process have two components of variation. One is due to common causes and the other due to special (assignable) causes. Common cause variation is the natural variation of a process which cannot be removed, without a major change in the system. Special causes are unnatural causes the are not part of the natural variation and can in most cases be easily removed.

Variation has been labeled as Quality’s worst enemy. In manufacturing it increases the risk of producing non-conforming product. In medicine highly variable blood pressure makes it difficult to prescribe medicine.

SPC Charts were introduced to separate the signal from the noise, in other words detect assignable cause variation, with the objective of removing all unnecessary variation. Unnecessary in this case refers to variation that can be easily removed.

Concurrent with the introduction of control charts was the introduction of the philosophy of getting it right in the first place. Instead of using inspectors to remove faulty product, operators, using control charts ensured that there was no faulty product in the first place.

SPC charts, as introduced by Shewhart are no more than plotting measurements, usually averages, on a chart which has two lines drawn around a centerline. The lines are statistically determined such that any measurement falling within the two limits are natural variation which operators should not react to. Reacting to such variation only increases variation. Points falling outside control limits indicate that there is a high probability that the result was due to an assignable cause which needs to be identified and removed so that the process is purely in a state of control.

Most control charts consist of a chart to control central tendency (location) and natural variability for variables data (data that is measured on a continuous scale. Attributes charts, such as the P, NP, C, U charts are used to a lesser extent for discrete measurements such as number of defects.

Shewhart chart demonstrating the issues with spc theory Figure 1: X-Bar and Range Control Chart

Although the theory behind SPC charts makes sense, is simple to understand and hence use, and remains promoted by quality consultants, there are many caveats. The standard Shewhart Chart is insensitive to detecting changes. It can take 44 inspections before a one standard deviation change is detected. Detecting and removing changes is far more difficult then implied by the hyped promotion. Spikes can be caused for even hundreds of reasons and hence it is not a simple matter to identify causes. Because samples are taken in time, it is not possible prevent some faulty product reaching the final stages, making it controversially arguably unwise to remove all out going inspection.

Attempts have been made to increase the notoriously poor sensitivity of the Shewhart Chart through warning limits, run tests, trend tests and patter tests. These however increase false alarm rates which can cause more harm than good.

Other control charts have also been introduced to improve the sensitivity of the standard Shewhart charts. Examples include the Moving Average, Exponentially Weighted and Cusum charts. Although these do increase sensitivity (e.g. The Cusum chart takes only 9 points on average to detect a one standard deviation change) they are more complicated to understand and are not designed to detect assignable cause variation, the soul of the control chart. They are designed to detect changes in the process mean. Change Analysis in most circumstances is a better alternative.

Other variables charts have also been introduced over time, such as the Short Run SPC charts, the Modified Control Charts and Zone chart.

The most popular control chart remians arguably the Shewhart X-bar Control chart. It is allegedly robust to non-normality which is important because as Shewhart noted most data does not follow a normal distribution. Our own research and feedback does not concur with the allegations that the X-Bar chart, and others such as the moving average and Ewma, is robust to non-normality.

For example, the following control chart consists of data from an INCONTROL skewed distribution. There should only be a few false out of control points, yet there are many in both the X-Bar and Range chart. Even if the x-bar chart were robust, which it is not, other than for slightly non-normal data, the effect of non-normality on the Range chart has been overlooked.

Shewhart chart demonstrating the issues with spc theory Figure 2: Control Chart consisting of data from an in-control skewed distribution

Fortunately using machine power it non-normal xbar, Range, Sd, Moving Averages, EWMA, Cusum charts are now available in the BIS.Net SPC APP.

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