Which distribution is used to calculate the probability of producing a defect?
A probability distribution is a mathematical function that describes the likelihood of obtaining the possible values for an event. A probability distribution may be either discrete or continuous. A discrete distribution is one in which the data can only take on certain values, while a continuous distribution is one in which data can take on any value within a specified range (which may be infinite). Show
There are a variety of discrete probability distributions. The usage of discrete probability distributions depends on the properties of your data. For example, use the:
Binomial Distribution The binomial distribution is probably the most widely known of all discrete distribution. It is a type of distribution that has two possible outcomes. One typical example of using binomial distribution is flipping coins. A coin toss has only two possible outcomes: heads or tails, and each outcome has the same probability of 1/2. Let’s take a look at when the Binomial Distribution can be used! Main Characteristics of a Binomial Distribution:
ExampleQ: A warehouse ships ten printing machines, four of which are defective to a company. This company selects five of the machine at random and accepts the shipment if all five machines are non-defective. Find the probability that the company accepts the shipments when sampling with replacement. I’m going to use the formula above: Hypergeometric Distribution The hypergeometric distribution is a probability distribution that’s very similar to the binomial distribution. Both the hypergeometric distribution and the binomial distribution describe the number of times an event occurs in a fixed number of trials. The probability remains the same for every trial for the binomial distribution. In contrast, in the hypergeometric distribution, each trial changes the probability for each subsequent trial because there is no replacement. Main Characteristics of a Hypergeometric Distribution:
ExampleQ: Let’s change the previous problem a little bit. If we now sample without replacement, what’s the probability that the company accepts the shipment? We know that the total number of printing machines N is 10, and the number of machines chosen at random to be tested n is 5. Let’s define N1 as non-defective, and N2 defective, so N1 =6 and N2= 10- N1 =4. For the company to accept the shipment, we can’t have any defective machine. The number of ways to choose all non-defective machine is 6C5, and the number of ways to select 0 defective machine is 4C0. Image by AuthorPoisson Distribution Poisson distribution helps us to predict the probability of a specific event occurs within a time interval. Main Characteristics of a Poisson Distribution:
Notice that the Poisson is a limiting form of the Binomial Distribution. For large n, we have p=λ/n. ExampleQ: Suppose that the probability of suffering a side effect from a certain flu vaccine is 0.005. If 1000 persons are inoculated, find the approximate probability that at most one person suffers. Since n=1000 is a large number, we can use the Poisson approximate binomial distribution to solve the problem, where λ =pn = 0.005 * 1000 =5. P(x≤1) = P(x=0)+P(x=1) Image by AuthorQ: Phone calls are received at a certain residence as a Poisson process with parameter λ =2 per hour. If Diane takes a 10-mins shower, what’s the probability that the phone rings during that time? Given that two calls per 60 mins, we first calculate the number of calls we expect per 10 mins, λ=2 * 10 / 60 = 1/3. Now we want to calculate the probability of getting at least one call during this 10 mins, so essentially we want to compute P(X≥1), which can be written as 1 — P(X=0). Image by AuthorGeometric Distribution The geometric distribution represents the probability that a specified number of trials will take place before the first success occurs. One typical problem that follows the geometric distribution is to determine the number of times a flipped coin comes up tails before it first comes up heads. Main Characteristics of a Geometric Distribution:
ExampleQ: The probability that a machine produces a defective item is 0.01. Each item is checked as it is produced. Assume that these are independent trials, and compute the probability that at least 100 items must be checked to find one that is defective. Using the formula above, P(X≥100) → P(X>99) Image by AuthorConclusion Probability distributions are fundamental to statistics, just like data structures are to computer science. In this article, I summarized the use cases for several most common discrete probability distributions. This is just the beginning of the probability distribution journey. To learn more about different probability distributions, check out this incredibly detailed map of all univariate distributions! What type of distribution looks at the number of defects per unit?The Poisson distribution is the probability model that is used when you are counting defects.
Which probability distribution can be used in quality control statistics to count the number of defect of an atom?The Poisson distribution gives us the ability to predict the number of defects that we'll see in the next defective, and it will be a value ranging from below to above the expected value.
What are the two types of probability distribution?There are two types of probability distributions: Discrete probability distributions. Continuous probability distributions.
Which distribution is used to count the number of defective or good items in a sample in order to determine a process yield?The p chart is used when we are investigating the number of defectives in a collection of items. The binomial distribution is used as the underlying model; although either the normal or poisson approximation to the binomial is often used in the analyses associated with the p chart.
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