5a. SPC- Variables Chart.ppt

Prof G.R.C. Prof G.R.C. NairNair

Quality Control (QC)

Control – the activity of ensuring conformance to requirements and taking corrective action when necessary to correct problems

Importance– Daily management of processes– Prerequisite to longer-term improvements

Prof G.R.C. NairProf G.R.C. Nair

Inspection

Inspection should never be a means of assuring quality.

The purpose of inspection should be to gather information to understand and improve the processes that produce products and services.


4

Quality Checking Points

Receiving inspectionIn-process inspectionFinal inspection


5

Receiving Inspection

Random check procedures100 percent inspectionAcceptance sampling


6

In-Process Inspection

What to inspect?– Key quality characteristics that are related to

cost or quality (customer requirements)Where to inspect?

– Key processes, especially high-cost and value-added

How much to inspect?– All, nothing, or a sample


7

Statistical Process Control (SPC)

A methodology for monitoring a process to identify special causes of variation and signal the need to take corrective action when appropriate.

SPC relies on Shewhart’s Control Charts )


Objectives of SQC

Understand the problem of variation in all processes causing problems of quality.

Distinguish between chance or random cause and assignable cause of variation

Assess the “process capability”


Process Variation

All processes are subject to two basic types of variation:

Specific Cause (Assignable) Variation(Very few, but causes significant variations)

andChance Cause (Random) Variation

(Many insgnificant variations)


Common Cause Variation Influences all of the measurements in an

unpredictable way “Random Variation” Caused by system faults (also called chance

causes) Examples – lack of attention, poor supervision,

poor training / instructions, inappropriate work methods, fatigue

Requires a change in the system – only management can specify and implement the change


Not the operators’ fault Reducing common cause variation

improves process performance (once specific causes are eliminated )


Specific Cause Variation

Caused by local faults (also called specific causes or assignable causes)

Can be identified /corrected at the machine by the operator or supervisor by systematic study and analysis.


Examples – worn out scale, machine slippage, changes in raw material, error in program, temperature variation


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SPC Implementation Requirements

Top management commitmentProject championInitial workable projectEmployee education and trainingAccurate measurement system


• Statistical Process Control is sampling

to determine if the process is performing within acceptable limits of tolerance.


Statistical Control

Process is stable Process is predictable over time Only Random variation is present

Size

Prediction


Process not in Statistical Control

?

Size

Prediction

??

??

??

??

??

? ?

Not stableNot predictableCauses waste and inefficiency Prof G.R.C. NairProf G.R.C. Nair

Importance of Statistical Control

For a process to operate satisfactorily, it must be in a state of statistical control. S P C helps to identify specific causes for the change in quality.

Size

Prediction


Process Mean & Standard Deviation

Statistically, this means that 99.73 % of our measurements are within 3 of the process mean

-3 -2 -1 MEAN +1 2 +3

99.73%

The Process Mean is the average value of the process statistic:

Denoted by X

The standard deviation indicates the amount of spread about the process mean


Statistical Process Control (SPC)

Identifies specific causes for variation in quality and helps establish the proper corrective action

Establishes how the process should operate,when it is subject to random causes only

So it makes possible to determine when special causes are at work, based on the continual on-line monitoring of process variations


SPC Charts

SPC tool used to monitor a product’s key quality characteristics.

Control charts graphically display the history of the process average and variation, and how the operation is working now.

Compares the current performance with process history and detects special causes,if any.

It tells you whether or not your process is stable and in statistical control


Types of Process Data

Variable Data can be any value in a large range. is measured and expressed in numbers. examples: diameter (millimeters), product

weight (kgs), down loading time (seconds)


Attribute Data can only be classified into one of two classes are expressed as “yes or no,” “good or bad,” “go

or no go,” examples: color blemishes on a painted surface,

number of surface flaws on a shaft, frequent wrong number calls, over ripe fruits

Types of Process Data


SPC / SQC Charts

There are two types of charts used for controlling the quality of product/process.

They are:Charts for Variables – for controlling the

dimension / weight /any thing measurable. Charts for Attributes - for controlling the

percentages of bad / unacceptable products.


Control Charts for Variable Data X and R charts

Control Charts for Attribute Data p-charts

c-charts


What are Process Control Charts?

X-Bar Chart

Time

Upper Control Limit = UCL

Lower Control Limit = LCL

3x

2x

1x

X-bar

1x

2x

3x

Essentially, use charts with statistically determined control limits.


Setting up X and R Charts

Decide which quality characteristic(s) to monitor Decide how often you want to take samples (also

called subgroups) Determine sample size

this number is denoted ‘n’ n typically ranges from four to six n must remain constant during the period of

process observation reflected on the control chart



Collect 25 – 50 samples/subgroups. A minimum of 25 samples must be collected to initiate control charts, but 40 – 50 is recommended.

Goal is to collect data over the entire range of variation.



For each sample, calculate the sample mean, which will be denoted X. The sample mean is simply the average of the individual measurements in that particular subgroup.

For each sample, calculate the range. This range, called the sample range and denoted R, is found by subtracting the smallest observation in the sample from the largest observation. (R = Xlargest – Xsmallest).



Average of the X’s X Called X double bar

X = grand average = solid centerline on X chart

Average of R’s R

R = solid centerline on R Chart


X Chart Control Limits

On the X chart, the control limits are 3 x from the centerline. However, there are several other formulae that can be used to find the control limits. They are summarized below:

X 3x

X A2 R

X 3R/[d2 n(1/2)]

Other formula that might be helpful x = /n(1/2)

is = R/d2 Prof G.R.C. NairProf G.R.C. Nair

R Chart Control Limits

Formulae to be used to find R chart control limits(UCLR and LCLR):R 3R

Other formulae are,

UCLR = D4R

LCLR = D3R


Statistical Constants

Constants d2, d3, A2, D3, and D4

n A2 D3 D4 d2 d3

2 1.88 0 3.27 1.128 0.85253 1.02 0 2.57 1.693 0.88844 0.73 0 2.28 2.059 0.87985 0.58 0 2.11 2.326 0.8641

6 0.48 0 2.00 2.534 0.8480 7 0.42 0.08 1.92 2.704


Importance of the R Chart

The R chart is always constructed first. After constructing the R chart, the sample ranges

are plotted, and the rules are applied to test for out-of control conditions.

If the range chart is out-of-control, the X-bar chart is not valid and should not be constructed.


Bringing the R Chart into Control

Determine special cause(s)

Delete the corresponding sample(s)

Recalculate R


StepsFind X bar = ∑ X / n, (n is the sample sizeFind X bar bar = ∑ X bar / k ,(k is # of samples) Find R bar = ∑ R / kFind UCL R = D4 R bar

Find LCL R = D3 R bar

Find ULC X bar = X bar bar + A2 R bar

Find LCL X bar = X bar bar - A2 R bar

If any point falls out side the limits, rework eliminating those points


Exercise 1

The following data was obtained from a manufacturing company over a ten day period.The sample size was 5 and every day at the end of the day one sample as drawn randomly from the finished product from a machine. All the figures pertain to a single machine operated by the same operator. Prepare the X bar and R charts and commend on the process quality.


Sample No Observations

1 2 3 4 5 X R

1 10 12 13 8 9 10.4 5

2 7 10 8 11 9

3 11 12 9 12 10

4 10 9 8 13 11

5 8 11 11 7 7

6 11 8 8 11 10

7 10 12 13 13 9

8 10 12 12 10 12

9 12 13 11 12 10

10 10 13 7 9 12

R = 3.9, UCL R =D4R = 2.11*3.9 = 8.229

LCL = D3R =0*3.9 = 0

X = 10.32UCLX = X +A2R =10.32+0.58*3.9 =12.582

LCLX = X –A2R = 10.32-0.58*3.9 = 8.058


R chart

LCL=0.00

R=3.9

UCL=8.229


LCL=8.058

X=10..32

UCL=12.582

=

Comment : The above process appear to be in good control.

X Bar Chart


Exercise 2

An inspector of a company recorded the size of a part on ten days ,the sample size being 5. Plot the Control Charts and see if the process is in statistical control.


Sample No Observations

1 2 3 4 5 X R

1 25 25.01 25 25.03 25.01 25.01 0.03

2 25 25.03 25 25.04 25.03 0.04

3 25.01 25.02 25.02 25.03 25.02 25.02 0.02

4 25.01 25.02 25.02 25.01 25.04 25.02 0.03

5 25.02 25.02 25.03 25.03 25 25.02 0.03

6 25.06 25.03 25.02 25 24.99 25.02 0.07

7 24.99 24.98 25.02 25.02 24.99 25 0.04

8 25.02 25.01 25.01 24.99 25.02 25.01 0.03

9 25.03 25.01 24.97 25.01 25.03 25.01 0.06

10 25.02 24.99 24.99 24.98 24.97 24.98 0.05


R = 0.039 X = 25.01 UCLX = 25.03

LCLX = 24.99

Since the mean of the 10th sample falls out side the control limits, rework omitting that ample.

Revised X=25.014, R = 0.039 Revised UCLX = 25.04

Revised LCLX = 24.09

Revised UCLR= 0.082

Revised LCLR = 24.09. Plot the control charts.

Now the 9 samples show statistical control of the processProf G.R.C. NairProf G.R.C. Nair


5a. SPC- Variables Chart.ppt

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