To calculate a Standard or Population Standard Deviation,

Upper/ Lower Control Levels (UCL/LCL) and

Process Capability (Cpk)

Enter your Sample values below separated by commas

Use this Table to find

Upper/ Lower Control Levels (UCL/LCL) and

Process Capability (Cpk)

Standard Deviation

Population Standard Deviation

To solve the equations for S we need to find the values for:

X = Sample Value(s)

n = Number of Samples taken

n-1 = Number of Samples taken minus 1

M = Average of all Sample Values

For the just means ‘The Sum Of’, so we subtract the Mean value (M) from each reading value (X) and then multiply each result by itself. Finally add all of the totals together.

X = Sample Value(s)

n = Number of Samples taken

n-1 = Number of Samples taken minus 1

M = Average of all Sample Values

For the just means ‘The Sum Of’, so we subtract the Mean value (M) from each reading value (X) and then multiply each result by itself. Finally add all of the totals together.

Enter your Sample values below separated by commas

[n] Samples |
[n-1] Samples-1 |
[M] Average |

5 | 4 | 3 |

Readings [n] | Value [X] | Mean Avg [M] | X-M | [X-M]^2 |

1 | 1 | 3 | -2 | 4 |

2 | 2 | 3 | -1 | 1 |

3 | 3 | 3 | 0 | 0 |

4 | 4 | 3 | 1 | 1 |

5 | 5 | 3 | 2 | 4 |

10 |

Summary:

= 10

(n-1) = 4

(n) = 5

Upper Control Limit (UCL) = Average + 3 * StDev

Lower Control Limit (LCL) = Average - 3 * StDev

UCL = 7.7434

LCL = -1.7434

CpkL = Average - LCL / 3 * StDev

CpkU = 7.1109

CpkL = 3.3675

Use the lower value for Cpk Value. A Cpk of 1.33 is desired.

Cpk = 3.3675

= 10

(n-1) = 4

(n) = 5

Now find Standard Deviation using the formula S = √ / √n-1 S = √10 / √4 S = 3.1623 / 2 S = 1.5811 Standard Deviation = 1.5811 |

Now Population Standard Deviation S = √ / √n S = √10 / √5 S = 3.1623 / 2.2361 S = 1.4142 Population Standard Deviation = 1.4142 |

##### Determine Upper and Lower Control Limits UCL LCL

3 * StDev = 4.7434Upper Control Limit (UCL) = Average + 3 * StDev

Lower Control Limit (LCL) = Average - 3 * StDev

UCL = 7.7434

LCL = -1.7434

##### Determine Process Capability Cpk

CpkU = UCL - Average / 3 * StDevCpkL = Average - LCL / 3 * StDev

CpkU = 7.1109

CpkL = 3.3675

Use the lower value for Cpk Value. A Cpk of 1.33 is desired.

Cpk = 3.3675