In 2009, when I learned about the concept of WCCA (Worst-Case-Case Analysis) applied to automotive electronics reliability design from the system design specifications of vehicle manufacturers, I thought it should be considered as a fantastic tool for circuit reliability design.

So, I referred to the WCCA cases provided by the vehicle manufacturer, studied the essence of the method, carried out WCCA analysis for the power supply, switch detection, output control, CAN/LIN communication circuits commonly used in automotive electronics, and introduced the method to my colleagues.

I take the simplest NPN triode switching circuit as an example to introduce the WCCA analysis method as follows:

WCCA (worst case circuit analysis), there are usually two methods to analyze the extreme value and monte carlo simulation;
Transistor switching circuits have two states of output high and low.
WCCA analysis is performed for the output low state, and if the extreme value method is used.
Determine the target parameters
i.e. the voltage VCE between the collector C and the emitter value of the triode.
Obtained from the nature of the triode, VCE is determined by the following equation:

List the relevant parameters and their range of values, including:
Vin is the input voltage, the minimum value is 8.0V, the maximum value is 16.0V
R1 is the current limiting current, considering +/-10% deviation, with a minimum value of 4.23 kΩ and a maximum value of 5.17 kΩ.
R2 is the current limiting current, considering +/-10% deviation, with a minimum value of 1.8kΩ and a maximum value of 2.2kΩ, and
is the BE pole conduction voltage of the triode Q1, the minimum value is 0.3V, the maximum value is 1.0V; and
is the current amplification of the triode, the minimum value is 30, the maximum value is 200;
VCC is the pull-up voltage, considering +/-5% deviation, the minimum value is 4.75V, the maximum value is 5.25V.
R3 is the pull-up resistor, considering +/-10% deviation, with a minimum value of 9kΩ and a maximum value of 11kΩ;
Analyzing the monotonic relationship between the target parameters and related parameters

From the above two analytical expressions, it can be seen that the monotonicity relationship between VCE and each parameter is:
Monotonicity relationship
Calculation of extreme value,
If the calculated voltage between the CE poles is less than 0, the transistor is in saturation conduction.
That is, it is necessary to calculate the maximum value of VCE in the worst case to determine whether it is less than 0;
According to the analysis of monotonicity
VCE takes the maximum value when VCC, R1 takes the maximum value and Beta, Vin, VBE(on), R2, R3 take the minimum value;
i.e.

That is, the worst-case maximum value is less than 0, ensuring that Q1 is in saturated conduction;
If Monte Carlo (monte carlo) simulation is used, the steps are as follows:
1) Determine the target parameters
2) List the relevant parameters and their value ranges
3) Randomize the values of the input parameters according to Gaussian analysis or uniform distribution.
3) Write a numerical code to calculate the value of the target parameter from the relevant parameters according to the circuit analysis.
4) Loop for a sufficient number of times N
5) Statistically analyze the values obtained from the N simulations and calculate the mean value v and the standard deviation σ
5) The value of v-3σ is the minimum value, and the value of v+3σ is the maximum value.
6) Determine whether the maximum value meets the reliability design requirements