Definition: When is a process out of control?

(p 3)

Process that is operating in the presence of assignable/systematic causes of variation => is out of control when it does not follow a random pattern

sources of variability that are not part of the chance causes

Process variability in this cases is significantly higer

Name the main sources of processes that are out of control

(p. 3)

three “Ms”: method, measurement, milieu

1) improperly adjusted or controlled machines (or failures)

2) operator errors (manpower);

3) defective raw materials.

Name the basic elements of a control chart

(p. 4, 25)

center line (CL)

upper (UCL) and lower control limit (LCL)

typically 3 sigma

upper (UWL) and lower warning limit (LWL)

tipically 2 sigma

Are control limits and specifications the same?

(p. 4, 12)

no

Control charts make it possible to identify when the process is out of control (abnormal conditions)

This does NOT mean out of specifications.

These conditions are not correlated:

A process can be out of control, but within specification limits => typically, if NT<<S.

A process can be in control, but out of specification limits => typically, when the process natural variability is too large

What are the basic criteria for evaluating a control chart

(p. 5)

A point that plots within the control limits represents a necessary (but not sufficient) condition for saying that the process is in control.

No action is necessary

A point that plots outside the control limits is evidence that the process is out of control

In the presence of random/chance causes of variation only => plotted points should exhibit a random pattern

Whats the connection between hypothesis testing and control charts

Hp0 => the process is in control state.

Possible outcomes are

(1) failing to reject Hp0

(2) rejecting Hp0

If Hp0 is rejected => investigation and corrective action are required to find and eliminate assignable cause(s)

Out of control situations trigger investigation.

Name and explain the families of control charts

(p. 8)

for variables

quality characteristics measured on a continuous numerical scale

e.g. geometrical dimensions, weights

for attributs

quality characteristics assuming only 2 states

these can be seen as binary quality characteristics

defective/non-defective

conforming/non-conforming

Name the overall conditions for a process which is out of control

(p. 13, 14)

Several criteria can be applied simultaneously to a control chart to determine whether the process is out of control.

when one (or more) point falls beyond the control limits

basic criterion

when the plotted points exhibit some nonrandom pattern (even inside the control limits).

When some consecutive points increase/decrease in magnitude => run/shift/drift

In these cases, we have a monotonic drift/shift of the process mean

Supplementary criteria are often used to increase the sensitivity of the control charts to process shifts

Name the WE-Rules (Random-Test)

(p. 15, 16, 17)

Suggestion rules for detection nonrandom patterns in control charts

One observation falls beyond the m ± 3∙s control rule

Two out of three consecutive observations fall beyond the m ± 2∙s limits warning limits

Four out of five consecutive observations fall beyond the m ± 1∙s limits

Eight observations in a row fall on one side with respect to the m value

Name the basic approaches to collect samples

(p. 21, 22)

Snapshot approach

each sample consists of units that were ideally produced at the same time (actually consecutive units of production)

This approach gives a “snapshot” of the process at each point in time where a sample is collected.

this method is used to detect (even small) changes in the process mean

Is perferred

Continous approach

each sample consists of units that are representative of all units that have been produced since the last sample (selection is distributed in the time)

If the process mean drifts between several levels (during the interval between samples) the variability within the sample can be relatively large.

this method can be used when the control chart is employed to make decisions about the acceptance of all units produced since the last sample.

According to Shewart which kind of taking sub-groups or samples is prefered?

(p. 23)

samples (or subgroups) should be selected so that if assignable causes are present:

The chance for differences between samples will be maximized,

While the chance for differences within a sample will be minimized

→ Snapshot approach is preferred

Discribe the influence of moving the control limit

(p. 24)

By moving the control limits farther from the center line, we decrease the risk of a type I error (a) => FALSE ALARMS

But widening the control limits will also increase the risk of a type II error (b) => Not detecting a defective

How can the control limits of the 𝑥 bar - R charts be calculated

(p. 36)

What is the distribution of 𝑥 bar and R

x bar chart is used for waht purpose

(p. 39)

It is used to monitor the central tendency of the process

R chart is used for waht purpose

It is used to monitor the dispersion of the process.

Name the pratical rules to detect a shift in the central bar

(p. 58)

Name the basic steps for the design of a control chart

(p. 103)

Determine the sample size (n)

Determine the frequency of sampling (or sampling period: h)

Determine the width of the control limits (LCL and UCL)

What parameter sinfluence the choice of n for designing a control chart

Statistical criteria

Economic criteria

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