Reliability Parametric Z-score Monitoring
HanCheng Ong
Design Reliability, Seagate Technology International, Singapore
Reliability engineering has very much been centered on looking at the
percentage of units that survives at some specified time. In fact, monitoring the
parametric performance of the product is also of great importance in areas where
failure rate is low or testing is expensive. By tracking the Reliability parametric,
we can provide feedback to the team on the areas of weaknesses so that product
improvements can be make at early design stage.
A system has been build to enable Reliability parametric data to be extracted and
stored in Oracle database. For each of the parameters that are being monitored,
its descriptive statistics can be tabulated and charted by various product
configurations. JMP scripting is used as the platform to accomplish this. The
parameters can be compared by lot configurations or performance with time.
In addition to the usual descriptive statistics such as mean and standard
deviation, Design for Six Sigma (DFSS) measure is employed. The data set for
each test configurations are distribution fitted using all available parametric
models in JMP. The best-fitted distribution is used to obtain the PPM with the
specification limits for computing the Z-score (DFSS measure of quality) for the
parameter. The Z-scores are tabulated and charted for monitoring as indicators
of quality.
Results
Random Seek Read Time Summary Table
Zscore
Mean(Rnd Seek)
Table
Std Dev(Rnd Seek)
Table
Table
Run1
Run2
Run3
Run1
Run2
Run3
Run1
Run2
Run3
25C
3.6
6.4
7.8
11.1
10.7
10.6
0.3
0.2
0.2
0C
2.8
4.9
5.8
11.6
10.9
10.8
0.2
0.2
0.2
60C
2.9
6.4
6.8
11.2
10.8
10.7
0.5
0.2
0.2
Temperature
Figure 1. Example of Parameter Trend Monitoring Table
Random Seek Read Time Zscore Chart by Run #
9.0
8.0
7.0
6.0
Zscore
Introduction
5.0
4.0
3.0
2.0
Best Fitted Parametric Model
The data set for each test configurations are distribution fitted using all
available parametric models in JMP. JMP provides a relatively large list of
common and useful distribution models (Johnson Sl, Johnson Su, Normal,
Glog, LogNormal, Exponential, Gamma, Weibull and Extreme Value). Each
distribution is tested for Goodness-of-Fit with the data set. The best fitted
distribution is used to obtain the PPM (parts per million) with capability analysis.
The specification limits are specified using the “Set Property” function in JMP.
The PPM from JMP output is then used to compute the Z-score (DFSS
measure of quality) of the parameter for each configuration of interest.
Non-Parametric Smoothing Model
In the event that none of the available distributions shows a good fit
(determined by the p-value output), the non-parametric smoothing available in
JMP will be initiated for the Z-score determination.
The Z-scores are tabulated and charted for monitoring as indicators of quality.
JMP Syntax:
Parametric Method:
Column(dt, “Parameter")<<Set Property( "Spec Limits", {LSL( lsl_para )} );
Distribution( Continuous Distribution( Column( :Parameter ), Fit Distribution( All
) ), By( :Config ));
Non-Parametric Smoothing Method:
Distribution(
Continuous Distribution( Column( :Parameter ), Fit Distribution( smooth Curve(
Spec Limits( LSL(lsl_para) )))), By( :Config ));
Figures 1 and 2 depicts the Trend table and charting of the Random Seek
Read Time parameter at various test temperature for illustration (data are
simulated).
25C
0C
Run3
Run2
Run1
Run3
Run2
Run1
Run3
Run2
0.0
Run1
Methods
1.0
60C
Figure 2. Example of Parameter Z-score Trend Monitoring Chart
Discussion
•Besides the usual statistics like mean and standard deviation, the DFSS
measure of quality, Z-score is used as the monitoring metric. Z-score takes into
account both the central tendency and dispersion.
•The parameter tables and charts are used for monitoring and feedback to the
team on the product performance. For areas where the Z-score is deemed to be
low, improvement actions will be put in place and the parameter will be remeasured after the fix is implemented.
•The Z-score is computed based on best fitted distribution and not normal
distribution which many have erroneously assumed (whether it is for convenient
sake or due to lack of knowledge).
•This method of monitoring the parameter performance using Z-score is suitable
during product design stage. When the product is stable and is in production
mode, control chart type of monitoring may be more suitable.
•Parametric Monitoring provides a good additional eye for product reliability
monitoring especially where large sample testing is not viable due to good
reliability and failures are hard to come by. It is also useful where it is expensive
to have large samples and long test duration to detect failures.
Reference
JMP User, Stats and Graph, Scripting Guides