Process Capability Overview
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Once a process is in statistical control, that is producing consistently, you probably then want to determine if it is capable, that is meeting specification limits and producing "good" parts. You determine capability by comparing the width of the process variation with the width of the specification limits. The process needs to be in control before you assess its capability; if it is not, then you will get incorrect estimates of process capability.

You can assess process capability graphically by drawing capability histograms and capability plots. These graphics help you assess the distribution of your data and verify that the process is in control. You can also calculate capability indices, which are ratios of the specification tolerance to the natural process variation. Capability indices, or statistics, are a simple way of assessing process capability. Because the process information is reduced to a single number, you can use capability statistics to compare the capability of one process to another.

Choosing a capability command

Minitab provides you with the options of identifying the distribution that fits your data or to transform your data to follow normal distribution, prior to using capability analysis. Depending on the nature of data and its distribution, you can perform capability analyses for:

·    normal or nonnormal probability models (for measurement data)

·    normal data that might have a strong source of between-subgroup variation

·    binomial or Poisson probability models (for attributes or count data)

It is essential to choose the correct distribution when conducting a capability analysis. You can use individual distribution identification to select the distribution that best fits your data prior to conducting a capability analysis. For example, Minitab provides capability analyses based on both normal and nonnormal probability models. The commands that use a normal probability model provide a more complete set of statistics, but your data must approximate the normal distribution for the statistics to be appropriate for the data. For example, Capability Analysis (Normal) estimates expected parts per million out-of-spec using the normal probability model. Interpretation of these statistics rests on two assumptions: that the data are from a stable process, and that they follow an approximately normal distribution. Similarly, Capability Analysis (Nonnormal) calculates parts per million out-of-spec using a nonnormal distribution that best fits your data. In both cases, the validity of the statistics depends on the validity of the assumed distribution.

If the data are badly skewed, the estimated proportion of defective items may be extremely over or under estimated. In that case, it is better to either transform the data to make the normal distribution a more appropriate model, or choose a nonnormal probability model for the data. With Minitab, you can transform the data using Johnson distribution system or Box-Cox power transformation or use nonnormal probability model. Nonnormal data compares these two methods.

If you suspect that there may be a strong between-subgroup source of variation in your process, use Capability Analysis (Between/Within) or Capability Sixpack (Between/Within). Subgroup data may have, in addition to random error within subgroups, random variation between subgroups. Understanding both sources of subgroup variation may provide you with a more realistic estimate of the potential capability of a process. Capability Analysis (Between/Within) and Capability Sixpack (Between/Within) computes both within and between standard deviations and then pools them to calculate the total standard deviation.

Minitab also provides capability analyses for attributes (count) data, based on the binomial and Poisson probability models. For example, products may be compared against a standard and classified as defective or not (use Capability Analysis (Binomial)). You can also classify products based on the number of defects (use Capability Analysis (Poisson)).

Here is a summary of Minitab's capability commands:

·    Individual Distribution Identification allows you to fit data with 15 parametertric distribution families. Based on probability plots and goodness-of-fit tests, you can choose a distribution that best fits your data prior to conducting a capability analysis. The report also includes probability plot to assess whether a distribution fits your data well.

·    Johnson Transformation transforms your data to follow normal distribution using Johnson distribution system. The report includes probability plot and Anderson-Darling statistics for original and transformed data for comparison. Minitab also allows you to store the transformed data for future analysis.

·    Capability Analysis (Normal) produces a process capability report when your data follow a normal distribution. The report includes a capability histogram overlaid with a distribution curve based on the distribution parameters to assess whether your data follows the selected distribution. The report also includes a table of process capability statistics, including both within and overall statistics.

·    Capability Analysis (Between/Within) draws a capability histogram of the individual measurements overlaid with normal curves, which helps you make a visual assessment of the assumption of normality. Use this analysis for subgroup data in which there is a strong between-subgroup source of variation, in addition to the within-subgroup variation. The report also includes a table of between/within and overall process capability statistics.

·    Capability Analysis (Nonnormal) draws a capability histogram of the individual measurements overlaid with a distribution curve based on the process parameters. This helps you make a visual assessment of the assumption that your data follow a specified distribution. The report also includes a table of overall process capability statistics.

·    Capability Analysis Multiple Variables (Normal) allows you to compare process capability for multiple variables following or transformed to follow a normal distribution. You can also use this feature to perform capability analysis for a process with one output but having a grouping variable associated with it. For example, you want to compare the width of the parts from the same process before and after a process improvement. The report includes histogram with overlaid normal curve and capability statistics for each variable or group.

·    Capability Analysis Multiple Variables (Nonnormal) allows you to compare process capability for multiple variables that do not follow or transformed to follow normal distribution. You can also use this feature when a grouping variable is associated with a continuous variable. For example, you want to compare the width of parts from the same process before and after a process improvement. The report includes histogram with overlaid distribution cure based on process parameters and capability statistics for each variable or group.

·    Capability Analysis (Binomial) is appropriate when your data consists of the number of defectives out of the total number of parts sampled. The report draws a P chart, which helps you verify that the process is in a state of control. The report also includes a chart of cumulative %defectives, histogram of %defectives, and defective rate plot.

·    Capability Analysis (Poisson) is appropriate when your data take the form of the number of defects per item. The report draws a U chart, which helps you to verify that the process is in a state of control. The report also includes a chart of the cumulative mean DPU (defects per unit), histogram of DPU, and a defect rate plot.

·    Capability Sixpack (Normal) combines the following charts into a single display, along with a subset of the capability statistics:

-    an Xbar (or Individuals), R or S (or Moving Range), and run chart, which can be used to verify that the process is in a state of control

-    a capability histogram and normal probability plot, which can be used to verify that the data are normally distributed

-    a capability plot, which displays the process variability compared to the specifications

·    Capability Sixpack (Between/Within) is appropriate for subgroup data in which there is a strong between-subgroup source of variation. Capability Sixpack (Between/Within) combines the following charts into a single display, along with a subset of the capability statistics:

-    an Individuals, Moving Range, and R or S Chart, which can be used to verify that the process is in a state of control

-    a capability histogram and normal probability plot, which can be used to verify that the data are normally distributed

-    a capability plot, which displays the process variability compared to specifications

·    Capability Sixpack (Nonnormal) combines the following charts into a single display, along with a subset of the capability statistics:

-    an Xbar (or Individuals), R (or Moving Range), and run chart, which can be used to verify that the process is in a state of control

-    a capability histogram and probability plot, which can be used to verify that the data come from a specified distribution

-    a capability plot, which displays the process variability compared to the specifications