# How to Calculate Z Score Values

D

#### dbulak

Forgot how to calculate.

I am looking at some information that was given to me.

Exact thickness 125.00
usl+2.00
lsl -2.00

mean 124.99
cpk 1.883
sigma .352

Zusl: 5.721
Zlsl: -5.648
Zmin: 5.648

I haven't been able to come up with where they got th Z vaues from.

I haven't done these calculations for a long time. Can anyone help.

#### Atul Khandekar

##### Quite Involved in Discussions
Z-score tells how many 'sigmas' away a certain value is from the mean in a normal distribution.

For a given value x, zX= (x - Mean)/sigma

zUSL = no of sigmas the USL is away from the mean
= (USL - XBAR) / sigma
= ( 127 - 124.99) / 0.352
= 5.7102

zLSL = no of sigmas the LSL is away from the mean
= (LSL - XBAR) / sigma
= ( 123 - 124.99) / 0.352
= -5.6534
These values are slightly different from the ones you have given. May be bit of rounding-off.

From the Z-table you can calculate the area under the curve and then the Estimated Out-of-spec.

- Atul

#### Marc

##### Hunkered Down for the Duration
Staff member
Thanks, Atul!

S Supplier Disruption Score and how to calculate it Quality Tools, Improvement and Analysis 4
U Calculate Z-Score for Non-Normal Data - I have two set of data Statistical Analysis Tools, Techniques and SPC 9
R Sampling Plans - ISO 2859-1: 1999 - How to calculate the switching score? Inspection, Prints (Drawings), Testing, Sampling and Related Topics 3
A How to calculate weights for customer satisfaction score? Misc. Quality Assurance and Business Systems Related Topics 4
Commercial excel templates that calculate overhead, hourly rates, fee proposal Excel .xls Spreadsheet Templates and Tools 0
How to calculate benefits? Moving some developed non controlled software/automation systems Service Industry Specific Topics 2
Calculate number of people in processes, considering cycle time/takt time = quantity of people Lean in Manufacturing and Service Industries 9
How to calculate the maximum allowable hysteresis of a pressure gauge General Measurement Device and Calibration Topics 1
How to Calculate the producer Risk AQL - Acceptable Quality Level 25
Methods to Calculate Available Production Rate ISO 9000, ISO 9001, and ISO 9004 Quality Management Systems Standards 0
Why calculate LCL in P-chart? Statistical Analysis Tools, Techniques and SPC 4
How to calculate CPK with n = 1 Manufacturing and Related Processes 2
Add-On software for VMC to calculate setting time, Idle Time, OEE etc.. Manufacturing and Related Processes 2
L How to calculate the Probability of Deficiency of the AQL of an Inspection AQL - Acceptable Quality Level 16
V How to Calculate Unbiasing Constant C4 Statistical Analysis Tools, Techniques and SPC 1
J How to Calculate OEE Indicator for a Workshop (15 Machines) Lean in Manufacturing and Service Industries 6
R How to calculate UCL (Upper COntrol Limit) and LCL (Lower Control Limit) Statistical Analysis Tools, Techniques and SPC 5
I want to calculate reliability at 750 hours Reliability Analysis - Predictions, Testing and Standards 8
R How To Calculate & Print CDF and Lower Bound CDF value for some t(time) with Minitab? Using Minitab Software 1
How to calculate the Premium Freight charges Service Industry Specific Topics 4
A How to calculate Mean and standard deviation without sample size in Minitab Using Minitab Software 5
When do I need to calculate Process OEE? Manufacturing and Related Processes 12
How to calculate Thread Pitch Diameter for non standard TPI like 5/8" 17.75 NF3 Manufacturing and Related Processes 3
C Definition and Way to Calculate some Metrics Lean in Manufacturing and Service Industries 6
M How calculate P value for Linearity and Bias using Excel Gage R&R (GR&R) and MSA (Measurement Systems Analysis) 8
Formula that will calculate the NoGo Major Diameter of an M20 x 1.5 6H Thread gage Inspection, Prints (Drawings), Testing, Sampling and Related Topics 3
M How to calculate Cg and Cgk for a 2-Dimensional Area Gage R&R (GR&R) and MSA (Measurement Systems Analysis) 4
T Calculation Question - Calculate the runner weight for a part Manufacturing and Related Processes 2
M Spreadsheet on How to Calculate SMT Capacity wanted Manufacturing and Related Processes 2
F How to Calculate the unbiased Standard Deviation in Excel using Minitab Formula Capability, Accuracy and Stability - Processes, Machines, etc. 6
Spreadsheet that will Calculate Audit Duration times based on IAF MD5 and MD11 Excel .xls Spreadsheet Templates and Tools 6
Calculate PPMs by going back to Date of Production or Date Noticed Quality Tools, Improvement and Analysis 7
M How to calculate MTTF (Mean Time to Failure) Reliability Analysis - Predictions, Testing and Standards 1
H How to calculate the Lot Reject Rate Inspection, Prints (Drawings), Testing, Sampling and Related Topics 4
L How calculate the number of samples Statistical Analysis Tools, Techniques and SPC 2
A Simple 125 piece part Capabilty Excel .xls sheet to calculate Cpk Capability, Accuracy and Stability - Processes, Machines, etc. 3
R How to calculate MMC when is placed after datum Inspection, Prints (Drawings), Testing, Sampling and Related Topics 4
S Which one is better to calculate, Cpk or Ppk? Statistical Analysis Tools, Techniques and SPC 11
C How to calculate P value on Probability Plot Statistical Analysis Tools, Techniques and SPC 1
IAQG OASIS - New tool to calculate Audit Time AS9100, IAQG, NADCAP and Aerospace related Standards and Requirements 1
M How to calculate dimensions of trapezoid ? Quality Tools, Improvement and Analysis 3
How to calculate Surveillance Audit Days in Corporate Audit Scheme IATF 16949 - Automotive Quality Systems Standard 4
S How to calculate Supplier PPM at Receiving Inspection Document Control Systems, Procedures, Forms and Templates 2
How to Calculate Sample Size at 95% Confidence Interval on Surface Roughness Inspection, Prints (Drawings), Testing, Sampling and Related Topics 1
R How to calculate the value add time? Lean in Manufacturing and Service Industries 2
Should I calculate both Cp and Cpk for a Unilateral Tolerance? Statistical Analysis Tools, Techniques and SPC 8
H Continuous Monitoring Instrument Data Validation and how to calculate Outliers Quality Tools, Improvement and Analysis 1
How to calculate the Air Flow Rate in clause 201.12.4.4.105 of IEC 60601-2-16:2012 IEC 60601 - Medical Electrical Equipment Safety Standards Series 1
A How to calculate Cpk & Ppk if the tolerance changes during the period? Capability, Accuracy and Stability - Processes, Machines, etc. 5
S PPAP - How to calculate tolerance on basic dimension APQP and PPAP 5