Introduction to Engineering: Control Charts

Presenter: Prof. Eric A. Suess, Department of Statistics, CSU Hayward

email: esuess@csuhayward.edu

As part of your Engineering degree you will take many Statistics courses that will introduce you to many important statistical ideas that are commonly used by engineers.  These topics include

• probability methods and models: Binomial distribution, Normal distribution, Central Limit Theorem, Stochastic Models
• statistical inference procedures: descriptive methods, experimental design, confidence interval and hypothesis tests

There are many other topics of importance that are used which are taught in Stat 3601, 3602, 3603.

Today we will discuss a topic from 3601, Process Control charts.  Ref. Shaffer and McClave, Probability and Statistics for Engineers, 1995, pp330-347.

Process Control is a very important part of manufacturing.  There are two ways people monitor manufacturing processes: (1) by inspecting and rejecting the defective parts and (2) maintaining a continuous monitoring of a process to check for special causes of variation that are beyond the common causes of variation.

In all production processes there is some variation.  In processing bags of chips the weight of the contents deposited into the bags may not always be the same, but should be within an acceptable range.  The common causes variation are assumed to follow a Normal Distribution with mean µ and standard deviation s .  The special causes variation are assumed to change the mean or variation of the Normal Distribution from which the samples are taken.  It is the special causes variation that put a process out-of-control and the common causes variation is considered to be a natural part of the production process when it is in-control.

X-bar and R charts:  In SPSS and Minitab X-Bar and R charts are produced by the subgroups over time.

Example: A control chart is to be started fir a new machine that fills boxes of cereal by weight.  Five observations on amount if fill are taken every hour until 20 such samples are obtained.  The data are given in the SPSS file cereal.sav and in the Minitab file cereal.mtw.  Construct a control chart for means and another for variation, based on these data.  Interpret the results.

In SPSS click on Graphs > Control..., select X-Bar, R, s and then click Define.  For the Process Management select amount and for the Subgroup Defined by: select sample.  Make sure the default Charts are selected, X-Bar and range.  Finally, click on OK.

In MINITAB click on Stat > Control Charts > XBar-R...  For the Single Column select amount and for the Subgroup Size select sample.  Finally, click on OK.

What do you see in your control charts?  Is the process in-control or out-of-control?

P-charts: SPSS and MINITAB can create process control charts summarizing the proportion or number of nonconforming units within subgroups over time.

Example:  A process that produces transistors is sampled every 4 hours.  At each time point, 50 transistors are randomly sampled, and the number of defectives x is observed.  The data for 24 samples are given in the SPSS file trans.sav and in the MINITAB file trans.mtw.  Construct a control chart based on these samples.

In SPSS click on Graphs > Control..., at the bottom select Cases are subgoups and select p, np and finally click Define.  For the Number Nonconforming: select x and for the Subgoups Labeled by: select sample.  For the Sample Size select constant and enter 50.  Finally, click on OK.

In MINITAB click on Stat > Control Charts > P...  For the Variable select x and for the Subgroup Size enter 50.  Finally, click on OK.

What do you see in your control chart? Is the process in-control or out-of-control?