How Do We Calculate Expected Defects in Quality Control Samples?

In summary, the conversation discusses the expected number of defects in a sample of 20 parts based on past data. The solution involves calculating the occurrence rate of each defect and multiplying it by the total number of parts. The final answer is 0.24, indicating that the expected number of defects in the next sample is approximately 0.24.
  • #1
Calculator14
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Homework Statement



The number of defects in a sample of 20 parts is recorded for quality control purposes; over the last year the number of defects and their occurrence rate has been : 0 defects, 82%; 1 defect, 13%; 2 defects, 4%; 3 defects, 1%. Find the expected number of defects in the next sample of 20 parts.

Homework Equations



(work shown below)

The Attempt at a Solution



1*.13+2*.04+3*.01=.24
20*.24=4.8 the expected number of defects in the next sample of 20 parts.
 
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  • #2
Hi Calculator14! :smile:
Calculator14 said:
1*.13+2*.04+3*.01=.24
20*.24=4.8 the expected number of defects in the next sample of 20 parts.

hmm … you don't know when to stop, do you? :redface:

How can the expected number be between 4 and 5 when the given probabilities only go up to 3 ??

What do you think the 0.24 is ? :wink:
 
  • #3
OHHHHHHHH! So I think I went a little too far with this, haha! My apologies tiny-tim, thank you for pointing out my mistake! I believe my answer should be .24??
 
  • #4
he he! :biggrin:

yes :smile:
 
  • #5


As a scientist, it is important to use statistics and probability to analyze and understand data. In this scenario, the number of defects in a sample of 20 parts is being observed for quality control purposes. Based on the data from the last year, we can calculate the expected number of defects in the next sample using probability.

Using the probabilities given (0 defects = 82%, 1 defect = 13%, 2 defects = 4%, and 3 defects = 1%), we can calculate the expected number of defects as follows:

Expected number of defects = (0 defects * 0.82) + (1 defect * 0.13) + (2 defects * 0.04) + (3 defects * 0.01)

= (0 * 0.82) + (1 * 0.13) + (2 * 0.04) + (3 * 0.01)

= 0 + 0.13 + 0.08 + 0.03

= 0.24

Therefore, we can expect to see an average of 0.24 defects in the next sample of 20 parts. It is important to note that this is an expected value and there is a possibility that the actual number of defects may differ from this value. However, using this calculation can help us make informed decisions and improve the quality control process.
 

Related to How Do We Calculate Expected Defects in Quality Control Samples?

1. What is the difference between statistics and probability?

Statistics is the process of collecting, organizing, analyzing, and interpreting data to make informed conclusions. Probability is the likelihood of a specific event occurring based on the available information.

2. How are statistics and probability used in research?

Statistics and probability are used in research to analyze and interpret data, make predictions, and test hypotheses. They help researchers to make informed decisions and draw accurate conclusions from their data.

3. What are the common types of probability distributions?

The common types of probability distributions include the normal distribution, binomial distribution, Poisson distribution, and exponential distribution. Each distribution has its own characteristics and is used to model different types of data.

4. How can I determine the sample size for a study?

The sample size for a study depends on factors such as the research question, desired level of confidence, and margin of error. There are various statistical formulas and online calculators that can help determine the appropriate sample size for a study.

5. Can statistics and probability be applied in everyday life?

Yes, statistics and probability can be applied in everyday life in various ways, such as making financial decisions, analyzing sports data, and understanding risk in health and safety. They help us make informed decisions based on available data and help us understand the likelihood of certain events occurring.

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