# Short training on SPC | Statistical process control |

## Training on SPC (Statistical process control)

You must have understood by reading the name of the article that I will talk about SPC today.
There is a lot of question about SPC, like: - what is it? What is its use? Why is it used?

Through this article, I will give basic information about SPC; this information will be enough for those people who are just starting in industries and for their academic knowledge.

## What is SPC?

SPC stand for Statistical process Control. It is Quality tool which is used to measure and control process variation by using statistics.
Statistics here is set of information derived from sample data.
Well SPC is Core tool of QMS, comprehensive tool published by AIAG. From interview point of view, SPC was introduced by William A shewart in 1924.

## Uses of SPC

With SPC we understand process behavior. SPC is used as a tool to develop process, identifying source of variation in process & removing them to sustain better quality. SPC can be use as problem solving tool. By SPC we try to set those manufacturing parameters which give optimum value, by which cost of manufacturing will reduce.

## SPC formulas

So SPC is use to study process behavior.  With SPC we develop our process of manufacturing, or not only develop but we strengthen our process by doing SPC. This core tool not only use in automotive sectors, but also use widely in other no automotive fields, like medical, defense.

Process behavior is understand by shape, spread &Location.
For Location we calculate mean.
For Spread we calculate Standard deviation (sigma).
For Shape we use help of Histogram.

SPC summary in short is explained in below picture:-

#### Definition of SPC words:-

Basically SPC is comprises of three words Statistical Process Control. Each word has its meaning.

Statistical: - Interpretation of Data [which we have collected] to estimate process.

Process: - Convert input into output by controlling man, machine, method & material.

Control: - Keeping process variation within spec.

Variation: - Gap/Dissimilarity between the two objects called variation. Variation can cause unwanted rejection, undesired rework, Customer dissatisfaction.

Cause of Variation:-
1.      Common cause- Which will come & cannot be control/stop.
2.      Special Cause- Which come sudden [Black Noise, Assignable cause]

Total Variability:-

Process Behavior estimation on the basis of Variation:-

Location: - MEAN [Denoted by X-bar & Âµ] arithmetical sum of all number divide by total number.

Spread: - Can be check by Range or by Standard deviation
Standard deviation (sigma) is calculated by formula.

Note:- Process variation is 6 time of standard deviation.

Shape:- Can be analysis with the help of Histogram (which will reveal amount of variation that process has in it)

Histogram is basically graphical representation of variation data. By histogram we can also see how process is spreading (we will also use standard deviation for this)

## Types of Histogram

1. Normal –Bell shape & Normal
2. Comb like
3. Positive or negative skewed
4. Precipice type
5. Plateau type
6. Bimodal
7. Isolated Peak Type
 Histogram Shapes Types

Normal distribution shape is considered OK while doing process study on the basis of process distribution,  in normal distribution process variation is within Control limit.

 Normal Distribution curve in SPC

Control Limit is used in Control Chart & Control Chart is drawn after collection of variable observation, under that chart we see how data is being distributed.

On the basis of variable data we make study to check process capability.

## Types of SPC charts

1. X-bar & R chart
2. X-bar & S chart
3. I & MR chart
4. P-chart
5. np &p chart
6. u-chart
7. c-chart & u-chart

You can understand by below picture:-

 Types of SPC Chart

### A. Variable Control Chart (X (bar) & R chart)

In variable control chart-Most commonly used chart that come in picture is X(bar) & R chart.
For X(bar) & R chart , we have to collect variable data & have to decide followings:-

1. Decide Subgroup Size
2. Decide subgroup Frequency  [Don’t confuse-It is just time interval]
3. Decide number of Sub-group

 Sub-group in variable control table

To study X(bar) & R chart, we have to some calculations:-

1. Calculate average of each subgroup. (X-bar)
2. Calculate range of each subgroup. (R=Xmax -Xmin)
3. Calculate average of average of each subgroup (X-Double bar)
4. Calculate average of Range (R-bar).
5. Calculate trial control limit for Range chart. (UCLR, LCLR)
6. Calculate control limit for Average chart. (UCLx, LCLx)

Now we have done all calculation for UCL & LCL for X̅ & R.
We decide subgroup size n=5, subgroup number 20.

 Calculation for control chart in SPC
To create X̅ Chart, we will hide all Range row, and will select X̅ data and will insert line chart.
Same procedure will be followed to create Range chart.

 Range chart in SPC
By control Chart we identify any special cause in process, see unnatural pattern in data.
Any special cause could be identify when observation cross limit lines.

## Control chart Interpretation

1. One point beyond zone A- Caused by large change in process
2. Seven point in a row on  one side of centre line-Caused by process mean shift
3. Seven point in row steadily increasing or decreasing-Caused by Mechanical wear, contamination, Chemical depletion, etc
4. Fourteen point in a row alternating up & down-Caused by over adjustment, shift to shift variation, machine to machine variation.
5. Two out of three point in row in same zone or beyond- Caused by Major special Cause variation
6. Four Out of five point in a row in same zone B and beyond.
7. Fifteen point in a row in zone C (Above or below centre line)
8. Eight point in a row on both sides of centre line with none in Zone-C

## Difference between Specification Limit and Control Limit

Specification limit are product tolerance limit, usually taken from product drawing. Example if diameter of hole in drawing is 8+1/-2 (Min- 6 mm and Max-9mm) this is product specification limit. While control limit is related to process control limit.

There is no relation between specification limit and control limit.

Control limit is based upon mean and standard deviation. Control limit will be within process width. Process width is mean+3 x standard deviation. Control limit is limit of process, beyond this the variation will come that will affect product quality somewhere.

Cp and Cpk is calculate to study the process capability and process performance.

### Cp & Pp - Process Capability & Process Performance

Process Capability (Cp & Cpk) indicates the ability of process to meet specification when process operates under common cause.
In practical situation, it is obvious to show variation due to both common and assignable cause.
So we have to analysis process behavior due to combined effect of common and assignable cause.  We indicate by Pp, Ppk.

### Process Capability: - Cp

Cp is for process capability. Which is study by process graph. Cp always show spread of curve. Process will be capable if curve is smaller to specification limit and equally distributed to both side of mean.

1. Calculate process standard deviation (Ïƒ=R̅/d2)
2. Calculate process Capability (Cp)= (USL-LSL)/6Ïƒ
Ïƒ= 0.21/2.326 ; (0.090)
Cp=(0.9-0.5)/6*0.090;
Cp=0.754

USL & LSL are maximum limit & minimum limit for spec:- 0.7±0.2
Maximum:- 0.9 & Minimum-0.5

#### Process Capability: - Cpk

Cpk is for Process performance. It show spread as well as location.

Minimum value between Cpu & CpL is consider as Cpk

Cpu=(USL-X̿)/3Ïƒ
CpL= (X̿-LSL)/3Ïƒ

Cpu= (0.9-0.718)/3*0.09 ; Cpu=0.689
CpL= (0.718-0.5)/3*0.09; Cpu=0.825

Here Cpk value will be consider 0.689 (Since is minimum)
Cp is consider only spread, not the location. While Cpk is consider both spread and location.

#### Conclusion:-

In this article i have covered only variable charts of SPC, this above explanation is sufficient to use & understand basic requirement of process. Also this information can also help those engineers who have just started career in Engineering. I will try to write on attribute control chart in SPC. It will be possible if i see support on this article.

Thank You,