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Reliability Physics and Engineering
Before purchasing a large number of devices, a customer will likely ask the supplier about the defect level for the product being offered. The customer’s reliability inquiry is often expressed as: what is the defect level for the population of such devices in terms of number of defective devices per hundred, number of defective devices per thousand, number of defective devices per million (dpm), etc.? To determine the fraction defective, a sample of the devices is randomly selected from the population and this sample is tested/stressed to determine the fraction defective. After the fraction defective is determined for the sample, then it is only natural to ask: based on the sample size used, what is the confidence interval for the population fraction defective? To answer this critically important question, we must understand the basics of sampling theory.
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1.
To find the fraction of defective medical devices, from a large population of such devices, a sample size of 100 devices was randomly selected from the population and tested. One defective device was found. Using the Chi square distribution, what is the 90 % confidence interval for the fraction defective of the population of such devices?
2.
To find the fraction defective of a large population of stainless steel pipes, a sample size of 50 pipes was randomly selected from the population of such pipes and the sample was pressurized to 1,000 psi. Zero defects were found. Using the Chi square distribution, what is the 90 % confidence interval for the fraction defective of the population of such pipes?
3.
An electronics store is worried about the defect level for a large population of TVs being sold. Using the Chi square distribution, what sample size should be randomly selected from the population, turned on and tested, to ensure (at 90 % confidence level) that the fraction defective is ≤ 0.5 %? Assume that we accept only on finding zero defects in the sample.
4.
Valves, going into the cooling system of a nuclear reactor, must have a very low level fraction defective ≤ 0.1 %. Using the Chi square distribution, at the 90 % confidence level, what sample size should be randomly drawn from a large population of such valves and then tested/stressed with accepting only on zero defective valves being found in the sample?
5.
Balloons are being tested for defectivity. Using the Chi square distribution, at the 90 % confidence level, how many balloons should be randomly drawn from a large population of such balloons and pressurized/tested to claim that the fraction of defective balloons in the population is ≤1 %?
(a)
Assume that you accept only when finding zero defects in the sample of size SS.
(b)
Assume that you accept only when finding one or fewer defects in the sample of size SS.
(c)
Assume that you accept only when finding two or fewer defects in the sample of size SS.
(a)
Assume that you accept only when finding zero defects in the sample of size SS.
(b)
Assume that you accept only when finding one or fewer defects in the sample of size SS.
(c)
Assume that you accept only when finding two or fewer defects in the sample of size SS.
6.
A sample size of 25 Orings was randomly selected from a large population of such Orings and the results for the sample followed closely a normal distribution with a mean/median value of (
x
_{50})
_{s} = 181.6 mm and with a standard deviation of
σ
_{s} = 3.2 mm. What are the 90 % confidence intervals for the population
x
_{50} and the population
σ?
7.
In an electromigration test, 30 metal conductors were randomly selected from a large population of such conductors and stressed at a constant current density until the timetofailure for each conductor was recorded. The timetofailure data for the sample was described well by a lognormal distribution with a median timetofailure of (
t
_{50})
_{s} = 412 h and with a logarithmic standard deviation of
σ
_{s} = 0.52. What are the 90 % confidence intervals for the population
t
_{50} and
σ?
8.
In a corrosion test, 26 devices were randomly selected from a large population of such devices and stressed at a constant humidity and temperature until the time tofailure for each device was recorded. The timetofailure data for the sample was described well by a lognormal distribution with a median timetofailure of (
t
_{50})
_{s} = 212 h and with a logarithmic standard deviation of
σ
_{s} = 0.42. What are the 90 % confidence intervals for the population
t
_{50} and
σ?
9.
In a thermal cycling fatigue test, a sample of 29 devices was randomly selected from a large population of such devices and the sample was cycled from 65 to +150 °C until failure occurred. The cyclestofailure data for the sample was described well by a lognormal distribution with a median cycle tofailure of (CTF
_{50})
_{s} = 812 cycles and a logarithmic standard deviation of
σ
_{s} = 0.64. What are the 90 % confidence intervals for the population CTF
_{50} and
σ?
10.
In a timedependent dielectric breakdown (TDDB) test, a sample of 25 capacitors was randomly selected from a large population of such capacitors and the sample was TDDB stressed at a constant voltage and temperature until the timetofailure for each device was recorded. The timetofailure data for the sample was described well by a Weibull distribution with a characteristic timetofailure of (
t
_{63})
_{s} = 505 h and a Weibull slope of
β
_{s} = 1.82. What are the 90 % confidence intervals for the population
t
_{63} and
β?
1
2
3
Generally, in sampling theory, we round up the sample size requirement.
Note that this equation gives only single
point estimation for the
average failure rate over the interval
t. It does not tell us whether the failure rate is increasing, decreasing, or remains constant. To determine this, several sequential periods of time would have to be studied.
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 Titel
 Sampling Plans and Confidence Intervals
 DOI
 https://doi.org/10.1007/9783319936833_19
 Autor:

J. W. McPherson
 Sequenznummer
 19
 Kapitelnummer
 Chapter 19