Control Chart Selection

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Types of Data

Control chart selection begins with understanding your objective and what type of data you can obtain. There are variables and attributes data and therefore there are variables and attributes control charts.

Attribute Data

Attribute data is categorical data and results from counts. The count can be number defective or number of defects.

  • Defective: an item of interest is classified as either; good/bad, pass/fail, accept/reject, right/wrong, there/not there, scratched/not scratched, etc.
  • Defect: is a subset of defective. A defective item can have one or more defects. A defective item that is scratched, chipped, has blisters, and is peeling, has a total of 4 defects.

Variables Data

Variables data is continuous data and results from measurements on a continuous scale; length, width, height, weight, time, hardness, temperature, etc.

Control Charts are usually derived from samples taken from the larger population. Sampling must be collected in such a way that it does not bias or distort the interpretation of the Control Charts.

The process must be allowed to operate normally when taking a sample. If there is any special treatment or bias given to the process over the period the data is collected, the Control Chart interpretation will be invalid.

The frequency of sampling depends on the volume of activity and the ability to detect trends and patterns in the data. At the onset, error on the side of taking extra samples, and then, if the process demonstrates its ability to stay in control reduce the sampling rate.

Control Chart Selection

Control Chart Selection for Variable/Continuous Data

Use I-MR, Xbar & R, and Xbar & S Charts

  • Sample size is 1, or you are graphing a ratio, use an I-MR chart,
  • Sample size is 2-9 use an Xbar & R chart,
  • Sample size is 10-25 use an Xbar & S chart.

Individual Values (I) and Moving Range (MR) Charts are used when each measurement represents one batch. The subgroup size is equal to one when I-MR charts are used.

An Xbar-R is used primarily to monitor and control the stability of the average value. The Xbar Chart plots the average values of each of a number of small sampled subgroups.

The averages of the process subgroups are collected in sequential, or chronological, order from the process. The Xbar Chart, together with the Rbar Chart shown, is a sensitive  method to identify assignable causes of product and process variation, and gives great insight into short-term variations.

Control Chart Selection for Attribute Data

Use NP, P, C and U Charts

Counting defective items (e.g. incorrect PO’s)

  • Use a NP chart if the sample size is constant
  • Use a P chart if the sample size varies

Counting the number of defects (e.g. number of errors in a PO)

  • Use a C chart if the sample size is constant, use a U chart if the sample size varies

The P Chart plots the proportion of nonconforming units collected from subgroups of equal or unequal size (percent defective). The proportion of defective units observed is obtained by dividing the number of defective units observed in the sample by the number of units sampled.

P Charts name comes from plotting the Proportion of defectives. When using samples of different sizes, the upper and lower control limits will not remain the same - they will look uneven. 

The U Chart plots defects per unit data collected from subgroups of equal or unequal sizes. The “U” in U Charts stands for defects per Unit. U Charts plot the proportion of defects that are occurring. 

The U Chart and the C Chart are very similar. They both are looking at defects, but the U Chart does not need a constant sample size like the sample size like the C Chart. The Control Limits on the U Chart vary with the sample size and therefore they are not uniform

Rational Subgroups

A rational subgroup, commonly called a subgroup, is simply items that are alike. They are an attempt to separate common-cause and special-cause variation.

A rational subgroup could be items:

  • Close in time,
  • Made within the same set-up,
  • Done by the same person,
  • Processed using the same method,
  • Use of the same material batch,
  • Etc.

A rational subgroup is a sample of a process characteristic in which all the items in the sample were produced under very similar conditions and in a relatively short time period.

Rational subgroups are usually small in size, typically consisting of 3 to 5 units to make up the sample. It is important that rational subgroups consist of units that were produced as closely as possible to each other, especially if you want to detect patterns, shifts and drifts.

The selection of rational subgroups enables you to accurately distinguish special cause variation from common cause variation.

In the data sheet below, 5 samples which represent one subgroup, are collected each hour.

Example of Rational Subgroups

The goal is to have a "rational" for collecting the data so that variation within each subgroup is minimized. Rational sub-grouping is a key decision in control chart selection.

By collecting data this way we force a condition where only common-cause variation is expected within each subgroup. All other variation, special-cause, will therefore lie between the subgroups.

The ultimate goal of a rational subgroup is to separate special cause variation from common cause variation.

If your process consists of multiple machines, operators or other process activities that produce streams of the same output characteristic you want to control, it is best to use separate Control Charts for each of the output streams.

Statistical Process Control Basics

Statistical Process Control

Control Charts

Control Chart Selection

Control Limits

Capability Indices - Cpk, Etc.

Process Capability Study

Statistical Process Control Control Charts

Xbar & R (Range) Chart

Xbar & s (Standard Deviation) Chart

I (Individuals) & MR (Moving Range) Chart

p Chart

np Chart

u Chart

From Control Chart Selection to Statistical Quality Control.

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