1. Basic concepts

 

vDevelopment history:

 

       Reliability engineering has experienced the initial stage in the 1950s, the comprehensive development stage in the 1960s, the mature stage in the 1970s, the deeper and broader development stage in the 1980s, and the transition to integration, automation, intelligence and practicality since the 1990s. The development stage has made reliability engineering an important engineering technology discipline to improve product quality. Reliability engineering has developed from the reliability of electronic products to the reliability of mechanical and non-electronic products; from the reliability of hardware to the reliability of software; from focusing on reliability statistical tests to emphasizing reliability engineering tests, through environmental stress screening and reliability enhancement tests to expose product faults, thereby improving product reliability; developing from reliability engineering to credibility engineering including maintenance engineering, testing engineering, and support engineering; developing from the reliability of military equipment to Reliability of civilian products.

 

vDependability is a collective term. It is used to express availability and its influencing factors: reliability, maintainability, and supportability. It is only used for general descriptions in non-quantitative terms. When quantitative description is required, it must be discussed separately. v Product reliability (reliability) is abbreviated as R, which is "the ability of a product to complete specified functions under specified conditions and within a specified time."

 

          ⑴ Specified conditions: including environmental conditions and working conditions during use.

 

          ⑵ Specified time: refers to the specified working hours. Because the longer the working time, the lower the reliability level.

 

         ⑶ Specified functions: refers to the normal working indicators given in the product specifications. Failure to complete the specified function is called a failure.

 

vInherent reliability: It is an inherent characteristic of the product that is given during design and manufacturing, and can be controlled during product development.

 

vReliability in use: It is a characteristic of a product's ability to maintain performance during actual use. In addition to being related to inherent reliability, it is also affected by factors such as the installation, operation and maintenance of the product.

 

vBasic reliability: It is the duration or probability that a product will be fault-free under specified conditions. It reflects the product’s requirements for maintenance manpower. Therefore, when assessing the basic reliability of a product, all life units and all failures of the product should be counted, not limited to failures that occur during the mission, nor are they limited to failures that endanger the success of the mission.

 

vTask reliability: It is the ability of the product to complete the specified functions within the specified task profile. When evaluating product mission reliability, only faults that occur during the mission and affect the completion of the mission will be considered. Therefore, it is necessary to clarify the criteria for task failure.

 

vThe biggest difference between reliability and performance is: performance is a deterministic concept, while product reliability is an uncertain concept. Whether a product fails or not is accidental or random. Before failure occurs, for a given product, It is impossible to know exactly when the failure will occur. Product reliability is the ability of a product to maintain its performance over time; to maintain performance for a long time is to not break down, or to be able to repair it quickly if it breaks down is a very important quality characteristic of a product. To make products highly reliable and easy to maintain, reliability and maintainability design, testing and management must be carried out during product development. This is also an important reason why quality professionals must be familiar with the basics of reliability.

 

2. Faults and their classification

 

(1) According to fault patterns

 

vAccidental failure: It is a failure caused by accidental factors and can only be predicted through probability statistics.

 

v Wear failure: It is a failure that can be predicted through prior detection or monitoring. It is caused by the gradual decline of product performance over time. Wear and tear failures can be prevented through preventive maintenance and extend the service life of the product.

 

(2) According to the consequences caused by the failure

 

vFatal failure: The product cannot complete the specified task or may cause heavy losses to people or things, and ultimately cause the task to fail.

 

vNon-fatal failure: does not affect the completion of the task, but will lead to unplanned maintenance

 

(3) According to the statistical characteristics of faults

 

vIndependent fault: refers to not caused by another fault

 

vSlave fault: caused by another fault

 

3. Maintainability concept:

 

v. When a product is repaired according to prescribed procedures and methods under specified conditions and within a specified period of time, the ability to maintain or restore to a specified state is called "maintainability", abbreviated as M.

 

v Under specified conditions, the ratio of the total repair time MT within the specified period to the total number of failures of the products to be repaired n is called the "mean time to repair" (mean time to repair), abbreviated as MTTR=MT/n. This is a basic parameter for product maintainability.

 

For example, when 100 products have been working for one million hours, a total of 50 failures occurred, and the total maintenance time was 50 hours, then the MTTR of the product = 50hr/50 times = 1hr/time.

 

4. Usability concept:

 

vAvailability is the ability of a product to be in a state where it can perform specified functions under specified conditions and within a specified moment or time interval, provided that the required external resources are guaranteed. In layman's terms, it means "use it when you need it."

 

The time when the product can work is recorded as UP (uptime), and the time when the product cannot work is recorded as NT (down time). The total time TT=UT+NT, where NT=MT+DT, then TT=UT+MT+DT

 

  A0=UT/TT=UT/(UT+NT)=UT/(UT+MT+DT)

 

     Divide the numerator and denominator by the number of repairs n due to failures during this period, then since MTBF=UT/n, MTTR=MT/n, MDT=DT/n, we get:

 

     A0=MTBF/(MTBF+MTTR+MDT)

 

5. The relationship between reliability and product quality:

 

   vProduct quality is the ability of a set of inherent characteristics of a product to meet customer and other related requirements. Customers have many requirements for the inherent characteristics of products, including performance characteristics, special characteristics, timeliness, adaptability, etc.

 

vPerformance characteristics: performance indicators of the product’s normal operation.

 

vTimeliness: the delivery date of the product.

 

vAdaptability: the ability to meet people’s usage requirements.

 

vSpecial features: reliability, maintainability, and supportability.

 

v Product reliability is the ability of the product to maintain its performance over time. The performance must be maintained for a long time without failure, and failure must be repaired quickly.

 

Section 2: Common parameters of reliability and maintainability and bathtub curve

 

  1. Commonly used measurement parameters for reliability and maintainability:

 

vReliability and reliability function

 

       The probability that a product completes the specified function under specified conditions and within the specified time is called reliability, represented by R(t):

 

    T——working time before product failure;

 

    t - specified time.

 

   Generally, the following formula can be used to calculate:

 

   R(t)=(N0-r(t))/N0

 

        N0——When t=0, the number of products working under specified conditions;

 

       r(t)——The number of products that failed during the working time from 0 to time t.

 

2. Cumulative fault distribution function:

 

vThe probability that a product loses its specified functions under specified conditions and within a specified period of time is the cumulative failure probability (also known as unreliability).

 

      The cumulative failure probability of a product is a function of time, generally expressed by F(t): F(t)=P(T≤t)

 

      Since product failure and non-failure are two opposite events, it is obvious that

 

        R(t)+F(t)=1

 

         F(t)=1-R(t)

 

3. Fault density function:

 

vFault density function f(t) is the derivative of the cumulative fault distribution function.

 

     f(t)=d F(t)/dt

 

Its physical meaning is the probability of failure occurring per unit time within the time interval (t, t+dt). It is equal to the ratio of the number of product failures to the total number of products in one unit time after time t.

 

[Note] For the user, the total number is generally unknown, so the use value of f(t) is not great for the user.

 

4. Failure rate function:

 

For products that v has worked to a certain time t and has not yet failed (the number is NR (t)), the probability of failure per unit time within the time interval (t, t + dt) is called the failure rate of the product at time t .

 

The failure rate is generally expressed by λ(t). Right now:

 

λ(t)=f(t)/R(t)

 

In general, λ(t) can be calculated using the following formula:

 

     λ(t)=Δr(t)/Ns(t)Δt

 

In the formula, Δr(t)—the number of product failures within Δt time after time t;

 

    Δt——the time interval taken;

 

    Ns(t)——The number of products without failure at time t.