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24 PCB007 MAGAZINE I NOVEMBER 2024 Defectives are units that are considered completely unacceptable for use. Each unit is deemed defective or not—there are only two choices. In essence, a defective unit refers to the overall product. Generally, the count of defective units is assumed to follow a binomial distribution. A count of defects usually contains more information than a count of defective units. When either number can be obtained with approximately the same effort, using counts of defects rather than defective units is generally preferable. However, defect rates are rarely high enough in most production processes to create any substantive difference between counts of defects and defectives. ere are a few exceptions to this 6 . e frequency of first-time yield (FTY ) monitoring depends on your specific needs and your system's quality standards. Generally, FTY should be checked as oen as your sys- tem allows. is could be a day, week, month, or any other time frame that fits your produc- tion cycles and allocated resources and allows for meaningful analysis. Yield Statistics and Discrete Distributions Statistics is a branch of mathematics that col- lects, analyzes, interprets, and presents numer- ical data. Statistics is not merely the science of analyzing data but the art and science of collect- ing and analyzing data. Statistics are only tools to help us; they do not replace the process engi- neer's skill and intelligence. Statistics are funda- mental for process improvement activities. FTY is the percentage of units that pass through an individual process without defects. Rolled throughput yield (RTY ) estimates the probability that a unit passes through all pro- cess steps defect-free. e FTY and RTY are easy to compute, and the RTY is highly corre- lated with scrap, rework, warranty costs, and customer satisfaction. A discrete distribution is a probability distri- bution that depicts the occurrence of discrete (individually countable) outcomes, such as 1, 2, 3, yes, no, true, or false. For the most part, dis- crete distributions use up to two parameters: 1. Probability of an event, p 2. Number of trials, n A few exceptions exist to this notation, the Poisson distribution being one of them. A Poisson random variable is a discrete ran- dom variable representing the count of inde- pendent events occurring per unit of time, space, or product. Poisson random variables may represent defects per inner layer (I/L), outer layer (O/L), etc. e Poisson distribu- tion is one of the simplest distribution models, with a single parameter lambda (λ) represent- ing the mean count of events 7, 8 . A binomial random variable is a discrete ran- dom variable representing the count of defec- tive units in a sample of n independent trials when the probability of any defective unit is p. Binomial random variables may represent defective units due to shorts, opens, voids, etc. e binomial distribution is used when there are precisely two mutually exclusive trial out- comes: "pass" or "fail." e binomial distribu- tion is a simple distribution model with two " Each unit is deemed defective or not—there are only two choices. "