Presented by:

Dr. Husam Arman

Quality management: SPC II

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Histograms do not take into account changes over time.

Control charts can tell us when a process changes

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Control Chart Applications

Establish state of statistical control

Monitor a process and signal when it goes out of control

Determine process capability

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Commonly Used Control Charts

Variables data x-bar and R-charts x-bar and s-charts Charts for individuals (x-charts)

Attribute data For “defectives” (p-chart, np-chart) For “defects” (c-chart, u-chart)

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Control chart functions

Control charts are decision-making tools - they provide an economic basis for deciding whether to alter a process or leave it alone

Control charts are problem-solving tools - they provide a basis on which to formulate improvement actions

SPC exposes problems; it does not solve them!

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Control charts

Control charts are powerful aids to understanding the performance of a process over time.

PROCESS

Input Output

What’s causing variability?6

Control charts identify variation

Chance causes - “common cause” inherent to the process or random and not

controllable if only common cause present, the process is

considered stable or “in control” Assignable causes - “special cause”

variation due to outside influences if present, the process is “out of control”

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Common Causes

Special Causes

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Control charts help us learn more about processes Separate common and special causes of

variation Determine whether a process is in a state of

statistical control or out-of-control Estimate the process parameters (mean,

variation) and assess the performance of a process or its capability

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Control charts to monitor processes To monitor output, we use a control chart

we check things like the mean, range, standard deviation

To monitor a process, we typically use two control charts mean (or some other central tendency

measure) variation (typically using range or standard

deviation)

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Control chart components

Centerline shows where the process average is centered

or the central tendency of the data Upper control limit (UCL) and Lower control

limit (LCL) describes the process spread

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Control charts are practical tools to monitor the evolution of production processes.

In any production process a certain amount of natural variability will always exist (this is the cumulative effect of small and unavoidable causes)

A process that is operating in the presence of chance causes of variation only is said to be in statistical control.

Control chart

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A process that is operating in the presence of assignable causes (sources of variability that are not part of the chance causes) is said to be out of control.

Three main sources of assignable causes:

1) improperly adjusted or controlled machines (or failures);

2) operator errors;

3) defective raw materials.

Control chart

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A control chart contains A center line (CL) An upper control limit

(UCL) A lower control limit (LCL)

(LCL)

(UCL)

(CL)

Control limits are different from specification limits

Control chart

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A point that plots within the control limits indicates 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

→ Investigation and corrective action are required to find and eliminate assignable cause(s)

There is a close connection between control charts and hypothesis testing (to test if the process is in a state of statistical control: we can fail to reject or reject this hypothesis)

(LCL)

(UCL)

(CL)Basic criterion

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… in general we use L=3 → ±3·sw control limits16

Three standard deviations

99.73%

3 3

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One of the two main types of control charts is chart for VARIABLES (quality characteristics measured on a numerical scale; e.g. geometrical dimensions, weights, tensile strengths…)

- (mean) control charts

- R (range) control charts

- s2 (sample variance) control charts

- s (sample standard deviation) control charts

- xi (control charts for individual measurements)

x

Control chart

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Control chart for variables (Ch 5)

Variables are the measurable characteristics of a product or service.

Measurement data is taken and arrayed on charts.

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X-bar and R charts

The X-bar chart - used to detect changes in the mean between subgroups tests central tendency or location effects

The R chart - used to detect changes in variation within subgroups tests dispersion effects

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Step 1 Define the problem

Use other quality tools to help determine the general problem that’s occurring and the process that’s suspected of causing it. brainstorm using cause and effect diagram,

why-why, Pareto charts, etc.

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Step 2 Select a quality characteristic to be measured Identify a characteristic to study - for

example, part length or any other variable affecting performance typically choose characteristics which are

creating quality problems possible characteristics include: length, height,

viscosity, temperature, velocity, weight, volume, density, etc.

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Step 3 Choose a subgroup size to be sampled Choose homogeneous subgroups

Homogeneous subgroups are produced under the same conditions, by the same machine, the same operator, the same mold, at approximately the same time.

Try to maximize chance to detect differences between subgroups, while minimizing chance for difference with a group.

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Other guidelines

The larger the subgroup size, the more sensitive the chart becomes to small variations in the process average.

This increases data collection costs. Destructive testing may make large

subgroup sizes infeasible. Subgroup sizes smaller than 4 aren’t

representative of the distribution averages. Subgroups over 10 should use S chart.

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Step 4 Collect the data

Run the process untouched to gather initial data for control limits.

Generally, collect 20-25 subgroups (100 total samples) before calculating the control limits.

Each time a subgroup of sample size n is taken, an average is calculated for the subgroup and plotted on the control chart.

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Step 5 Determine trial centerline for the Xbar chart

The centerline should be the population mean, Since it is unknown, we use X double bar, or the

grand average of the subgroup averages.

m

m

i

i 1

XX

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1 2 3 m

1 2 3 m

x x x ... xgrand average x

mR R R ... R

mean range Rm

1) x11, x12, … , x1n R1

2) x21, x22, … , x2n R2

......

...

m) xm1, xm2, … , xmn

Rm

1x

2x

mx

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Step 6 Determine trial control limits - Xbar chart The normal curve displays the distribution of

the sample averages. A control chart is a time-dependent pictorial

representation of a normal curve. Processes that are considered under control

will have 99.73% of their graphed averages fall within six standard deviations.

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UCL & LCL calculation

deviation standard

3XLCL

3XUCL

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Determining an alternative value for the standard deviation (Xbar chart)

XCL RAXUCL 2X

RAXLCL 2X

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Step 7 Determine trial control limits - R chart The range chart shows the spread or

dispersion of the individual samples within the subgroup. If the product shows a wide spread, then the

individuals within the subgroup are not similar to each other.

Equal averages can be deceiving. Calculated similar to x-bar charts;

Use D3 & D4

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R-chart

m

m

ii

1

RR

RR 3UCLR RR 3LCLR

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Determining an alternative value for the standard deviation (R chart)

m

m

ii

1

RR

RDUCL 4R RDLCL 3R

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Example

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R-bar chart exceptions

Because range values cannot be negative, a value of 0 is given for the lower control limit of sample sizes of six or less (see D3 value in the previous table).

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Step 8 Examine the process - Interpret the charts

A process is considered to be stable and in a state of control, or under control, when the performance of the process falls within the statistically calculated control limits and exhibits only chance, or common causes.

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Consequences of misinterpreting the process Blaming people for problems that they

can’t control Spending time and money looking for

problems that do not exist Spending time and money on unnecessary

process adjustments Taking action where no action is warranted Asking for worker-related improvements

when process improvements are needed first 37

Process variation

When a system is subject to only chance causes of variation, 99.73% of the measurements will fall within 3 standard deviations If 1000 subgroups are measured, 997 will fall

within the six sigma limits.

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Chart zones

Based on our knowledge of the normal curve, a control chart exhibits a state of control when:

1. Two thirds of all points are near the center value.

2. A few of the points are on or near the center value

3. The points appear to float back and forth across the centerline.

4. The points are balanced on both sides of the centerline.

5. No points beyond the control limits.

6. No patterns or trends.39

Identifying patterns

Sudden shift in the process average Cycles Trends

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Shift in Process Average

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Identifying Potential Shifts

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Cycles

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Trend

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Step 9 Revise the charts

In certain cases, control limits are revised because: out-of-control points were included in the

calculation of the control limits. The process is in-control but the within

subgroup variation significantly improves.

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Revising the charts

Interpret the original charts Isolate the causes Take corrective action Revise the chart

Only remove points for which you can determine an assignable cause

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Step 10 Achieve the purpose

Our goal is to decrease the variation inherent in a process over time.

As we improve the process, the spread of the data will continue to decrease.

Quality improves!!

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Charts for Attributes

Fraction nonconforming (p-chart) Fixed sample size Variable sample size

np-chart for number nonconforming

Charts for defects c-chart u-chart

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Control Chart Selection

Quality Characteristic

variable attribute

n>1?

n>=10 ?

x and MRno

yes

x and s

x and Rno

yes

defective defect

constant sample size?

p-chart withvariable samplesize

no

p ornp

yes constantsampling unit?

c u

yes no

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Control Chart Design Issues

Basis for samplingSample sizeFrequency of samplingLocation of control limits

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SPC Implementation Requirements

Top management commitmentProject championInitial workable projectEmployee education and trainingAccurate measurement system

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