Engineers must know the product reliability curve

When doing technical work in enterprises, we often encounter a phenomenon that the products have no problems in the factory, but frequently encounter failures at the user's site. Another phenomenon is that the failure rate of equipment is high when the machine is turned on and off or in applications with power grid fluctuations. As a common phenomenon, I wonder if there has been a deeper thinking about it. This involves a key concept in the methodology of technical thinking - the transition process.

Everything has two states: steady state and dynamic state. When things change from one steady state to another, it is not completed all at once, as shown in (Figure 1), but they all go through a process of change. Everyone understands this principle. It takes time for things to change in a flash. This process is called transition process. So what is the changing state of this transition process? Its process waveform is shown in (Figure 2).

Readers who have studied "Principles of Automatic Control" will find this waveform familiar. Yes, it is the step response curve of the second-order system. In this curve, the rise time tr and the overshoot δ are a pair of contradictions. The smaller tr is, the larger δ is. Conversely, the larger tr is, the smaller δ is.

For electronic products, when powered on, it is equivalent to adding a step input to the power supply end of the circuit system. In an approximate second-order system, the response curve of the step input is as shown in Figure 2. There will be a surge current and overshoot voltage in the power supply circuit. Therefore, in the selection of components and the safety design of the circuit, the device parameter indicators cannot be selected based on the indicators of steady-state parameters. For example, the withstand voltage value of the decoupling capacitor at the power input end, assuming that the power supply is 12V, the III level derating, the capacitor DC withstand voltage derating factor is 0.75, and the capacitor withstand voltage value is selected as 12/0.75=16V. This value is actually problematic because the maximum voltage point of the overshoot voltage will not be the regular 12V, but a higher voltage. How high it is depends on the damping of the circuit system. In severe cases, this overshoot voltage will even approach or even exceed 16V. At this time, the failure of the capacitor is inevitable. Even if there is no problem, this withstand voltage value is also insufficient due to the reserved margin, making it easy to be damaged when there is external interference.

This phenomenon exists in many places in the circuit system. The output waveform of the crystal oscillator, the output of the stepper motor, and the mechanical transmission pulley or gear all have the shadow of this curve. The only difference is the magnitude of tr and δ.

In addition to its role in the engineering field, this curve also plays a significant role in social life. The peak period for young engineers to leave their jobs is mostly in the 2nd to 6th year after joining the job. When they first join the job, they are still fresh and full of energy and ambition. After a few years of climax, the good impression of your leader will also have a fluctuation period similar to this curve. Personal emotions will also gradually decline due to aesthetic fatigue and lack of continuous and fresh incentives, and gradually become disappointed, tired, and dissatisfied. The final result is resignation. I named this stage "professional adolescence". Everyone will experience it, just earlier or later. Some people are slow to warm up, and the rising time of TR is very long, but δ is very small. On the contrary, they will not encounter destructive personal states. They will work steadily and make achievements relatively easier after long-term senior accumulation.

The incentive effect of salary increase on employees also conforms to the law of this curve.

The law of this curve also has the same effect on the relationship between mother-in-law and daughter-in-law and the relationship between boyfriend and girlfriend.

So what good or bad effects does this curve have on us? Does it mean that this curve, as an objective law, is an unavoidable curse? The answer is "no".

The objective laws of this curve are inevitable, but we can make good use of it through various combinations and turn disadvantages into advantages.

The breaking point of this curve is mainly the first trough. If you can't get through it, contradictions or consequences will occur. What we can do is to be aware of this rule before this stage arrives. If you can avoid it, try to avoid it. If you can't avoid it, you should stay at home and bide your time. Don't do anything radical and decisive at this time. The way to avoid it is to create a new step response curve before the trough arrives by applying external stress.

If you chase too closely, tr is too small, the overadjustment will be high, and the trough will naturally be low; if you chase too loosely, tr is too long, you will not encounter the trough problem, but the peak will never come.