Probabilistic Safety

Stefan Mozar

22 December 2016

2/13/20171

IEEE 2016 ISPCE-TW

Introduction

Fires & Hazardous situations occur in consumer products for various reasons

17% of household fires in Tokyo are due to consumer products (2007)

Design evaluation and safety testing is only done on a very small sample, which is not statistically representative of the population

The techniques shown in this presentation apply to high volume production items

2 2/13/2017

Literature Review

Tolerance Analysis

– Sandler: a comparative study on the differences of tolerance analysis

–Military are concerned with reliability safety, which resulted in a number of MIL standards. These set some very stringent criteria for product approval

– They are not suitable for consumer products, but show what can be done

– Tolerance engineering and Six Sigma are further developments, and Motorola developed Six Sigma

– Taguchi applied DOE to solve quality problems

– Brombacher from Philips applied these techniques to consumer products

3 2/13/2017

Design

ProcessMaterial

Problems can occur due to one of three major reasons

–Design

–Material

– Process

This study considers only the design process

Problem Illustration & Tolerance Analysis

4 2/13/2017

Small sample size

Components from similar batches introduce statistical bias

Tolerance analysis generally not done by designer or safety engineer

Protection Circuit Problem

5 2/13/2017

This illustration is about an over voltage protection circuit

Tolerance Analysis Methods

There are three well known methods for tolerance analysis:

– Root Sum Square Analysis (RSS)

– Extreme Value Analysis (EVA)

–Monte Carlo Analysis (MCA)

6 2/13/2017

Root Sum Square Analysis (RSS)

It is “commonly used” and simple form of tolerance analysis

𝐕𝐚𝐫 𝑽𝒐 = σ𝐢=𝟏𝑵 𝝏𝑽𝒐

𝛛𝒙𝒊

𝟐∙ 𝑽𝒂𝒓 𝑿𝒊

– Where:

– Vo - output voltage (but voltage can be replaced by current, power, impedance etc.)

– Xi - the dependent variable that cause the variance (e.g. resistor, capacitor etc.)

works well for DC circuits, but not for AC circuits or semiconductors due to their non-linear properties

7 2/13/2017

Extreme Value Analysis (EVA)

This method is based of on RSS, except that only the worst case tolerances are used

This results in very stringent designs, that are generally too expensive for consumer applications

The main application for this method is safety critical applications

The probability that all components would be at extreme tolerance is unlikely, thus this method is not widely used

8 2/13/2017

It is a simulation model that algebraically adds component tolerances.

The component tolerances are determined by a random number generator.

The simulation provides data that can be used to estimate design yield of a protection circuit

Monte Carlo Analysis (MCA)

9 2/13/2017

Results of over 100 simulations

Determining Sample Size for MCA

MCA provides an estimate of the expected value of a random variable, and it predicts what the error of the estimate is.

𝜀 =3𝜎

𝑁

Where,

𝜀 = error estimate

σ= standard deviation

N= number of samples

From the above we get

𝑁 =3σ

𝜀

2

10 2/13/2017

Comparison of Tolerance Analysis Methods

11 2/13/2017

Method Mean Minimum Maximum # of STDEV

ConfidenceInterval

EVA 5.013 4.423 5.604 4.414 99.999 %

RSS 5.023 4.583 5.463 3.048 99.770 %

MCA 5.032 4.416 5.648 4.265 99.998 %

Extract from Sandler’s paper

Process Capability Analysis

Process capability Analysis is a very powerful tool for engineering design.

It can use the data generated by MCA, as each simulation is equivalent to doing one set of measurement. The complete simulation corresponds to collecting the results from a batch of circuits

There are two very useful process capability parameters:

1. Process Capability

2. Process Capability Index

12 2/13/2017

Cp measures the design capability in relation to the design limits

In order to see how well the data fits within the specs Cpk is used. It shows how well the design is centered within the design specifications.

𝐶𝑃 =(𝑈𝑆𝐿−𝐿𝑆𝐿)

6𝜎

𝐶𝑃𝐾 = 𝑀𝑖𝑛

𝑈𝑆𝐿− ҧ𝑥

3𝜎

ҧ𝑥−𝐿𝑆𝐿

3𝜎

– Where

– CP – Process Capability

– CPK – Process capability Index

– USL - Upper Side Limit

– LSL – Lower Side Limit

Process Capability Index

13 2/13/2017

Normal Distribution

14 2/13/2017

Quality Levels CPK values

Super CPK > 2.0

Excellent 1.67 < CPK < 2.0

Satisfactory 1.33 < CPK < 1.67

Capable 1.00 < CPK < 1.33

Inadequate 0.67 < CPK < 1.00

Poor CPK < 0.67

CPK 0.67 1.00 1.33 1.67 2.00ppm 45500 2700 66 0.54 0.002

Interpreting Process (Design) Capability

15 2/13/2017

• The goal is to achieve Cp and Cpk of 2 or better.

• Cpk can also help make decisions about the robustness of the design.

Solving Robustness Problems

The method described here is known as Design of Experiments (DOE), or Parameter Design.

This method is used to identify parameters (components) that affect the design performance.

DOE is based on identifying the variables that affect the circuits performance, and are divided into two types.

They are design parameters and signal-to-noise ratios

Design parameters are specified by the designer and include specs such as trigger voltage level.

SNRs are either external or internal, and include items such as temperature, humidity, vibration and so on.

16 2/13/2017

The variables are put into design and noise matrices. The columns of the design matrix represent the design variables and their test results. Each row in the design matrix represents a circuit.

The columns in the noise matrix represent the noise factors, and the rows represent different levels of noise.

Solving Robustness Problems

17 2/13/2017

This is illustrated with an example of a protection circuit of a high voltage generator.

The wave forms of the trigger circuit on the left is its nominal value. That on right is the result from a MCA.

The data from the MCA was used to calculate the robustness of the circuit.

An example

18 2/13/2017

Example continued

The result obtained was :

Cpk= 0.5

This provides a yield of 96%

The trigger circuit needs to design centered

The results of a parameter design are shown in the table below

C5 is shown as the most

Significant factor. It will be used

for design centering.

19 2/13/2017

Top 5 significant parameters

1 C5 *************

2 R6 *********

3 R7 ********

4 C10 ********

5 R1 *******

The scatter diagram shows the trigger voltage vs C5. It conforms that C5 has an influence on the trigger voltage.

After modifying the circuit (increase in value of C5), the circuit was analyzed with another MCA run.

20 2/13/2017

The result were that a Cpk of 1.3 was achieved with a design yield of about 100%.

Conclusion

To prevent a hazardous situation a probabilistic evaluation of protection circuits should be done for high volume products.

The data gather from this evaluation can be used to estimate design yields.

The data can also be used for a quantitative based risk assessment of potential safety hazards

It should be understood that this method does NOT replace traditional methods of safety evaluation, but rather compliments it.

21 2/13/2017

Questions

22 2/13/2017

Thank You for Your Attention!

23 2/13/2017