STATISTICAL PROCESS CONTROL

Statistical Process Control

Statistical Process Control

Q1: Explain the differences between Xbar / R charts and the CUSUM chart indicating the relative advantages and disadvantages of both types of SPC chart, indicating where these two forms of SPC charts would be best applied in an industrial context.

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.).

R chart.

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

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 (see example below), 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).

Cumulative Sum charts

Cumulative Sum charts, or Cusum charts, are an alternative to Shewhart control charts. While Shewhart control charts are widely used and the control violations well documented, there may be conditions to which ...