QALT test planning

[JON_BK]

I am having difficulties to understand how to conclude information of following test planning results,
- http://www.weibull.com/AccelTestWeb/chapter13__231.gif
- confidence level
- bounds ratio

My test planning is relating to case where two temperature stress levels are used and unfortunately I have only 12 samples available for test. Some engineering jugdement was utilized to estimate Weibull parameters and based on the test plan results I am worried about quite big variance at B10 to be demonstrated. However confidence level seems to be resonable 73% when bounds ratio is 3. Should I worry about potentially too small sample size or just push Go button?

[Pantelis]

If your CB's are reasonable as you say I would push GO...

[JON_BK]

Thank you for support. However I am still challenged by the design team having a lot of Six Sigma knowlegde to explain and justify test starting as test time and costs are big compared to project resources.
Luckily some usage rate acceleration can be applied and there is also potential to apply degradation analysis to make testing faster. These are the actual results of test plan, time scale is in days. All support how to explain in plain English this to design team (why we should not worry about Standard Deviation of Tp 951 days before and during testing) highly appriaciated.

2 Level Statistically Optimum Plan

Use Level Unreliability Criterion0,1 (B10)

Distribution Weibull Beta 4

Stress Count 1

Test Duration 1095

Allocated Units 12

Stress 1

Stress Relation Arrhenius

Use Stress 345
Highest Stress 365

Probabilities of Failure
P(Test Duration, Use Stress) 0,011
P(Test Duration, Highest Stress) 0,9

Results
Stress Level Portion Units Units on Test Probability of Failure
Low Stress Level 355 0,775 9 0,1667
High Stress Level 365 0,225 3 0,9

Tp (Time at Unreliability) 1924
Standard Deviation of Tp 951

[Harry]

The ALT Test plan tool in ALTA 7 provides the analytical solutions. Maybe it is not easy to imagine and explain the effect of the “Bound Ratio”, for example, how wide the confidence bound is when Bound Ratio = 3. In ALTA 7, there is another tool “SimMuatic” can be used to visually display the bounds. SimuMatic provides simulation results which should be very close to the analytical solution. For detail, please see:

http://reliability-discussion.com/showthread.php?t=2519 (http://reliability-discussion.com/showthread.php?t=2519)
http://www.reliasoft.com/newsletter/v8i1/plans.htm (http://www.reliasoft.com/newsletter/v8i1/plans.htm)

By playing with SimuMatic, you can show the 6-sigma guys that the relation between Confidence Level and Bound Ratio. In the examples shipped with ALTA 7, there is an example (Test Plan Using Simulation (SimuMatic).ralp) shows how to use SimuMatic to design a test plan. You can plot the one-sided confidence bounds in SimuMatic.

The expected variance of the Tp (BX life) is dramatically affected by the assumed beta value. If you increase beta, it will decrease. 6-sigma theory is based on the normal distribution assumption. This is not the case in life data analysis. One common practice in life data analysis is to use the logarithm transform of the life and assume the transformed value is normally distributed. In fact, this theory is used in the test plan to calculate the bound and bound ratio. For your case:

Tp = 1924; Std (Tp) = 951; Var(Tp) = 951^2 = 904401;
ln(Tp) = 7.56; Var(ln(Tp)) is calcualted by: Var(ln(Tp)) = 1/(Tp^2)*Var(Tp) = 0.244; Std(ln(Tp)) = 0.49.

So at the logarithm scale, the standard deviation is not too bad. The two-sided bounds at 73% confidence level is calculated:
Upper: ln(Tp)+1.103*std(ln(Tp)) = 7.56 + 1.103*0.49 = 8.10047;
Lower: ln(Tp)-1.103*std(ln(Tp)) = 7.56 – 1.103*0.49 = 7.0195;
1.103 is the (1-(1-0.73)/2) normal percentile.

Transform them back to the linear scale, the upper bound is exp(8.10047) = 3296 and the lower bound is 1118. The bound ratio is 3296/1118 = 2.95. The little difference between this result and the result in the software is caused by the precision.