Statistical Process Control (SPC)

SPC Rules

1.     Minimum number of samples

2.     Process in control

3.     Normality tests

4.     Max number of missing values in subgroup

5.     Certain stats in range

6.     User/Auto determination of method of standard deviation

SPC Reference Table

Statistic

Symbol(s)

Description

Equation/Formula

CM4D Variable(s)

Actual

 

The value measured for a characteristic in a particular sample is called an “actual” value.

Actuals are not calculated by CM4D. They are inputs based on the inspection of an actual physical part.

~act,char~

Alarm Value Comparison

 

Can compare values to one or two other values.

 

 

Assignable Causes

 

Can assign a cause for bad data. Causes are stored in the database, follow the data, and can be displayed in charts. Data can be masked from use in statistics, or hidden in database. See the topic Assign Causes for more information.

 

 

Bilateral Spec Limits

USL

LSL

Upper and lower spec limits

Spec Limits are inputs based on the design specifications

~USL~

~LSL~

Box Hi

Hibox

Value of member of DataSet that has the largest value that is less than or equal to UIF

 

~boxhi~

Box Lo

Lobox

Value of member of DataSet that has the smallest value that is more than or equal to LIF

 

~boxlo~

Correlation Coefficient

 

Linear Correlation Coefficient measures the strength and the direction of a linear relationship between two variables.

  • Also sometimes referred to as the Pearson product moment correlation coefficient in honor of its developer, Karl Pearson.

where n is the number of pairs of data.

~cc~

~rp~

Cp

Cp

Capability index (potential capability)

~cp~

Cpk

Cpk

Capability index (potential capability corrected for centering)

For bilateral tolerancing Cpk = the lower of CPU and CPL

For unilateral tolerancing Cpk = validof CPU and CPL

~cpk~

CpM

CpM

Capability of process index influenced by the difference between the sample mean and the nominal target value.

~cpm~

CR

CR

Capability Ratio

~cr~

Deviation

 

The term Deviation refers to the difference between a true measurement (or actual) for a given sample and the design (or nominal) value for a characteristic. Deviations have both magnitude and direction.

Deviation = (actual - nominal)

~dev,char~

Extreme Outliers

 

A value that lies above the UOF or below the LOF.

 

 

Fixed Subgroup Size

 

Size of each subgroup within a DataSet, from 2 to 25

This is a value that is manually set in CM4D within the Query Properties dialog.

 

Group Estimated Standard Deviation

Alternate calculation for Standard Deviation under certain conditions. If subgroup size is invalid, or if the process is not in control, then the value is calculated as S.

or

 

Group Standard Deviation

S

Measure of variation among a sample of data

~stddev~

Group Target Standard Deviation

Standard deviation using a target (nominal) value in place of Mean. Used to calculate Cpm.

 

Hi

The highest value in the specified DataSet row.

 

~hi~

Inter Quartile Range

IQR

The difference between Upper Quartile and Lower Quartile.

Q3 - Q1

~iqr~

Invalid Count

 

Count of invalid data, or number of cells that do not contain valid data, or do not contain any data.

~invalidcount~

Kurtosis

 

Measure of flatness of a distribution

 

~kurtosis~

Lo

The lowest value in the specified DataSet row.

 

~lo~

Lower Control Limit for MA

LCLMA

Control limit for a particular characteristic for a particular use.

~lclma~

Lower Control Limit for MR

LCLMR

Control limit for a particular characteristic for a particular use.

~lclmr~

Lower Control Limit for R

LCLR

Control limit for a particular characteristic for a particular use.

~lclr~

Lower Control Limit for S

LCLS

Control limit for a particular characteristic for a particular use.

~lcls~

Lower Control Limit for X with MR

LCLXMR

Control limit for a particular characteristic for a particular use

~lclxmr~

Lower Control Limit for XBar with R

Control limit for a particular characteristic for a particular use

~lclxbs~

Lower Control Limit for XBar with S

Control limit for a particular characteristic for a particular use

~uclxbs~

Lower Inner Fence

LIF

 

Q1-1.5(IQR)

~lif~

Lower Outer Fence

LOF

 

Q1-3.0(IQR)

~lof~

Lower Quartile

Q1

Value of the data member where 75% of the data members are larger, and 25% are smaller

Data is sorted ascending

If N is odd, Q1 is the k value

If N is even, Q1 is the average of the k1 and k2 values

~q1~

Mean

The mean value of the valid data within a DataSet. The mean is the sum of values divided by the number (sample size) of values (a.k.a. the average value of a set of numbers).

~mean~

Mean Average

The mean (average) value of the mean values of valid subgroups within a DataSet.

~mean,ga~

Mean Moving Average

 

The mean (average) value of the moving average values of valid subgroups within a DataSet.

 

~mean,ma~

Mean Moving Range

 

The mean (average) value of the moving range values of valid subgroups within a DataSet.

 

~mean,mr~

Mean Range

The mean (average) value of the range of values of valid subgroups within a DataSet.

~mean,r~

Mean Standard Deviation

The mean (average) value of the standard deviation values of valid subgroups within a DataSet.

~mean,s~

Median

Q2

Value of the data member where 50% of the data members are larger, and 50% are smaller.

Data is sorted ascending

If N is odd, Q2 is the k2 value

If N is even, Q2 is the average of the k1 and k2 values

k1 = N/2

k2= (N + 1)/2

k3 = (N + 2)/2

~q2~

Missing Data in a Subgroup

 

If data is missing within a subgroup, it will be replaced with the mean of the other values within the subgroup.

 

 

No Spec Count

 

Count of cells in DataSet that do not have spec limits or tolerances.

 

~nospeccount~

Nominal

 

The value assigned to a given characteristic by design is called the nominal. It represents the target for the given value.

Nominals are not calculated by CM4D. They are inputs based on the design.

~nom,char~

Out of Spec Count

 

Count of cells in a DataSet that are out of spec or tolerance

 

~outofspeccount~

Outliers

 

A value that lies above the BoxHi or below the BoxLo.

 

 

Percent Invalid

 

Percentage of cells in a DataSet that contain invalid data, or no data.

~percentinvalid~

Percent Valid

 

Percentage of cells in a DataSet that contain valid data.

~percentvalid~

Population Standard Deviation

A.k.a. sigma, standard deviation of an entire population of data.

 

Pp

Pp

Performance index.

~pp~

Ppk

Ppk

Performance index.

For bilateral tolerancing Ppk = the lower of PPU and PPL

For unilateral tolerancing Ppk = validof PPU and PPL

~ppk~

PR

PR

Performance ratio.

~pr~

Range

R

The range of data of the DataSet row.

~range~

Skewness

 

Measure of symmetry of distribution

 

 

~skewness~

Subgroup Standard Deviation

Standard deviation of a subgroup within a sample of data. Used to calculate Sbar.

n=subgroup size

 

Sum

 

The sum of all valid data within a DataSet row.

~sum~

Total Count

Count of expected data, or the number of cells in a DataSet.

(Number of Columns) * (Number of Rows)

~totalcount~

Upper Control Limit for MA

UCLMA

Control limit for a particular characteristic for a particular use.

~uclma~

Upper Control Limit for MR

UCLMR

Control limit for a particular characteristic for a particular use.

~uclmr~

Upper Control Limit for R

UCLR

Control limit for a particular characteristic for a particular use.

~uclr~

Upper Control Limit for S

UCLS

Control limit for a particular characteristic for a particular use.

~ucls~

Upper Control Limit for X with MR

UCLXMR

Control limit for a particular characteristic for a particular use.

~uclxmr~

Upper Control Limit for XBar with R

Control limit for a particular characteristic for a particular use.

~uclxbr~

Upper Control Limit for XBar with S

Control limit for a particular characteristic for a particular use.

~uclxbs~

Upper Inner Fence

UIF

 

Q3+1.5(IQR)

~uif~

Upper Outer Fence

UOF

 

Q3+3.0(IQR)

~uof~

Upper Quartile

Q3

Value of the data member where 25% of the data members are larger, and 75% are smaller.

Data is sorted descending

If N is odd, Q3 is the k value

If N is even, Q3 is the average of the k1 and k2 values

~q3~

Valid Count

N

Count of valid data, or the number of DataSet cells that contain valid data. Not all cells in a DataSet have valid values. Data may be missing or masked via an assignable cause.

 

~validcount~

Variance

 

Returns the Variance value of a DataSet row. In a population of samples, the Variance value is the mean of the squares of the difference between the respective samples and their mean. Basically, it is the measure of the spread of data, or the standard deviation, squared.

~variance~

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