Quality Control Introductory Overview - Common Types of Charts

The types of charts are often classified according to the type of quality characteristic that they are supposed to monitor: there are quality control charts for variables and control charts for attributes.

Specifically, the following charts are commonly constructed for controlling variables:

X-bar chart. In this chart the sample means are plotted in order to control the mean value of a variable (e.g., size of piston rings, strength of materials, etc.).

X chart, individual observations chart. In this chart, individual observations or measurements are plotted in order to control the mean value of a variable; these types of charts are similar to X-bar charts, if you think of the values for the individual observations as means for samples of size 1. X charts for individual observations are often constructed in situations when the production process naturally produces a relatively small number of individual items. Note that, in STATISTICA Quality Control, moving average (MA) and exponentially weighted moving average (EWMA) charts can also be constructed for individual observations (for N of 1).

Moving average (MA) chart, Exponentially weighted moving average (EWMA) chart. In these types of charts, instead of means or individual observations, a moving average smoother is applied to make any trends or drift (of the means away from the center line) more apparent (by smoothing out the "noise). Note that these charts can also be constructed for individual observations (i.e., for N=1).

Cumulative sum (CuSum) chart. In this chart, instead of plotting individual observations, a running sum of the deviations of the individual measurements from the center line or specification is drawn. This chart is particularly powerful in detecting small drift: While in a standard X chart such drift may not generate an out-of-control condition over a large number of samples, the CuSum chart is very sensitive in this respect and will quickly detect such small changes. Note that STATISTICA computes the recommended tabular or algorithmic CuSum chart, and not the "old-style" V-mask control limits which were commonly in use when these charts were (literally) made by hand. See Montgomery (1996, Chapter 7) for details and recommendations.

R chart. In this chart, the sample ranges are plotted in order to control the variability of a variable.

MR chart. This chart is customarily used in conjunction with charts for individual observations (X, CuSum), in order to control the variability of a variable. Instead of sample ranges, the (moving) ranges of adjacent data points (individual observations) are plotted.

S chart. In this chart, the sample standard deviations are plotted in order to control the variability of a variable.

S2 chart. In this chart, the sample variances are plotted in order to control the variability of a variable.

For controlling quality characteristics that represent attributes of the product, the following charts are commonly constructed:

C chart. In this chart, we plot the number of defectives (per batch, per day, per machine, per 100 feet of pipe, etc.). This chart assumes that defects of the quality attribute are rare, and the control limits in this chart are computed based on the Poisson distribution (distribution of rare events).

U chart. In this chart we plot the rate of defectives, that is, the number of defectives divided by the number of units inspected (the n; e.g., feet of pipe, number of batches). Unlike the C chart, this chart does not require a constant number of units, and it can be used, for example, when the batches (samples) are of different sizes.

Np chart. In this chart, we plot the number of defectives (per batch, per day, per machine) as in the C chart. However, the control limits in this chart are not based on the distribution of rare events, but rather on the binomial distribution. Therefore, this chart should be used if the occurrence of defectives is not rare (e.g., they occur in more than 5% of the units inspected). For example, we may use this chart to control the number of units produced with minor flaws.

P chart. In this chart, we plot the percent of defectives (per batch, per day, per machine, etc.) as in the U chart. However, the control limits in this chart are not based on the distribution of rare events but rather on the binomial distribution (of proportions). Therefore, this chart is most applicable to situations where the occurrence of defectives is not rare (e.g., we expect the percent of defectives to be more than 5% of the total number of units produced).

All of these charts can be adapted for short production runs (short run charts).