# Demonstration Reliability Test Formula with allowance for 'x' Failures

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#### Disenchanted9000

Hi all,

I am in search of a formula that will provide the number of test units required to demonstrate a reliability figure with allowance for 'x' failures.

I know of this formula which allows for zero failures:

N=(ln(1-confidence)/ln(R)), where N is the number of units (round up this answer), R is the reliability from 0-1. Confidence level is also 0-1. Straight forward.

Then, I found this formula which is confusing and also solves for confidence.

______________f_____n!
(1-confidence)= Σ ----------- x (1-R)^i x R^(n-i)
_____________i=0_ i! x (n-i)!

Yikes! Brain hurting....

Need a similar formula to solve for number of units.

Thanks. Robert

#### Miner

##### Forum Moderator
Look starting at page 167 (p. 175 of the pdf file) of Sample Size Calculations Practical Methods for Engineers and Scientists.

The text shows a worked out problem then follows up by demonstrating how to obtain the same solution in Minitab.

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#### Disenchanted9000

Thanks v9991. I think the link to "src.alionscience.com/toolbox/oneshotcalc" is what I was looking for. Will try in Excel.

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#### Disenchanted9000

Thanks Miner. I have a read. Lots of examples to work through.

A Accelerated Reliability Demonstration Test Reliability Analysis - Predictions, Testing and Standards 4
Demonstration Test Plan for Reliability of Big Equipment Reliability Analysis - Predictions, Testing and Standards 5
"Time of Demonstration" requirement for Reliability Test Reliability Analysis - Predictions, Testing and Standards 1
Reliability Lifetime Requirement Demonstration Test Reliability Analysis - Predictions, Testing and Standards 3
Demonstration of equivalence EU Medical Device Regulations 3
Demonstration of Equivalence - Need for comparing biological characteristics for an SamD EU Medical Device Regulations 1
Exemption Clauses for Research, Demonstration, etc. Other Medical Device Regulations World-Wide 2
Clinical Evaluation MEDDEV 2.7.1 Rev 4 demonstration of equivalence EU Medical Device Regulations 6
Israel Demonstration Medical Device Requirements Other Medical Device Regulations World-Wide 5
R Exporting to Korea a demonstration only medical device Other Medical Device Regulations World-Wide 2
Medical Device Manufacturer Demonstration Equipment Other US Medical Device Regulations 6
D CE Marking for Demonstration / Evaluation Boards CE Marking (Conformité Européene) / CB Scheme 2
A Sale of Demonstration Units - How should we document it from GMP standpoint? 21 CFR Part 820 - US FDA Quality System Regulations (QSR) 3
H Electronic Approval Demonstration - Use of the voting option in Outlook Document Control Systems, Procedures, Forms and Templates 17
G Production rate demonstration? APQP Manual 4.1 ? Significant Production Run APQP and PPAP 7
Best/Worst Production Demonstration Runs (PDR) - Share yours Manufacturing and Related Processes 3
B Demonstration of auditor competence. General Auditing Discussions 10
Par.5.6.1 Demonstration of suitability, adequacy and effectiveness of QMS ISO 9000, ISO 9001, and ISO 9004 Quality Management Systems Standards 4
Demonstration Of Pavlov's Theory of Bureaucracy Philosophy, Gurus, Innovation and Evolution 1
Reliability issue - Frequent component failure of the product Reliability Analysis - Predictions, Testing and Standards 0
Forklift Reliability Analysis Manufacturing and Related Processes 6
Reliability Testing - Weibull Analysis Help Reliability Analysis - Predictions, Testing and Standards 4
ISO 2859-2 LQL sampling plan linked to %confidence/%reliability Inspection, Prints (Drawings), Testing, Sampling and Related Topics 2
95% reliability for calibration frequency Calibration Frequency (Interval) 7
How to Plan and Test the Reliability of Medical Devices Reliability Analysis - Predictions, Testing and Standards 1
Reliability Block Diagrams (RBDs) helper for review. Reliability Analysis - Predictions, Testing and Standards 1
Sample Size Calculation (Confidence Interval and Reliability) - Medical Devices Reliability Analysis - Predictions, Testing and Standards 9
K Taguchi Experiments for Factorial Design Analysis - Reliability of Minitab Results Using Minitab Software 1
Calculating Reliability for Subsystems in Series Reliability Analysis - Predictions, Testing and Standards 15
N Reliability Testing of a Single-Use (Disposable) Medical Device Reliability Analysis - Predictions, Testing and Standards 4
Regression for MTBF (Medical Device: Repairs vs Install Base) with Reliability Data Reliability Analysis - Predictions, Testing and Standards 16
Reliability calculation for repairable system Reliability Analysis - Predictions, Testing and Standards 14
I want to calculate reliability at 750 hours Reliability Analysis - Predictions, Testing and Standards 8
Metrology Laser Reliability General Measurement Device and Calibration Topics 2
S Reliability Software Recommendations Reliability Analysis - Predictions, Testing and Standards 4
D Cpk relation to Reliability Capability, Accuracy and Stability - Processes, Machines, etc. 4
Formula to tie together - Confidence/Reliability Level AQL? LTPD? Reliability Analysis - Predictions, Testing and Standards 3
M Defining Reliability and Confidence Levels Reliability Analysis - Predictions, Testing and Standards 8
R Standard for Reliability/Performance Test on a Electro Mechanical Device IEC 60601 - Medical Electrical Equipment Safety Standards Series 1
C Reliability Testing Protocol on a new Peristaltic Pump Reliability Analysis - Predictions, Testing and Standards 14
A Assessing a Preventive Maintenance Strategy - Reliability or Maintenance Statistics Reliability Analysis - Predictions, Testing and Standards 2
A Repairable System Reliability Analysis: Uptime/Downtime Hours, Failure Modes Data Reliability Analysis - Predictions, Testing and Standards 2
D Reliability of an Attribute Inspection based on Historical Data Capability, Accuracy and Stability - Processes, Machines, etc. 8
S Reliability Calculation - MTBF/MTTF for Static Mounts of Rail Industry Reliability Analysis - Predictions, Testing and Standards 2
R Minitab - Reliability / Survival Distribution Analysis Using Minitab Software 1
C CRE (Certified Reliability Engineer) Exam 03/02/2013 Professional Certifications and Degrees 11
R Military Land Vehicle Reliability with Only 1 vehicle & Only 1 Endurance Test Reliability Analysis - Predictions, Testing and Standards 5
J Reliability Prove-out, Pass-Fail Testing Reliability Analysis - Predictions, Testing and Standards 2
J Relationship between Quality, Reliability, Price and Delivery Misc. Quality Assurance and Business Systems Related Topics 7
L Determining Cpk based on a given Sample Size, Confidence Level, & Reliability Inspection, Prints (Drawings), Testing, Sampling and Related Topics 2