- 10.2.3.4.1: Assume that CPU activity is being probed and let the ith observatio...
- 10.2.3.4.2: Returning to the text example of inspection of a lot of RAM chips, ...
- 10.2.3.4.3: Obtain a distribution-free confidence interval for population media...
- 10.2.3.4.4: In order to estimate the fault-detection coverage c of a fault-tole...
Solutions for Chapter 10.2.3.4: Sampling from the Bernoulli Distribution.
Full solutions for Probability and Statistics with Reliability, Queuing, and Computer Science Applications | 2nd Edition
2 k factorial experiment.
A full factorial experiment with k factors and all factors tested at only two levels (settings) each.
A formula used to determine the probability of the union of two (or more) events from the probabilities of the events and their intersection(s).
Adjusted R 2
A variation of the R 2 statistic that compensates for the number of parameters in a regression model. Essentially, the adjustment is a penalty for increasing the number of parameters in the model. Alias. In a fractional factorial experiment when certain factor effects cannot be estimated uniquely, they are said to be aliased.
A study in which a sample from a population is used to make inference to a future population. Stability needs to be assumed. See Enumerative study
The portion of the variability in a set of observations that can be traced to speciic causes, such as operators, materials, or equipment. Also called a special cause.
Average run length, or ARL
The average number of samples taken in a process monitoring or inspection scheme until the scheme signals that the process is operating at a level different from the level in which it began.
An equation for a conditional probability such as PA B ( | ) in terms of the reverse conditional probability PB A ( | ).
When y fx = ( ) and y is considered to be caused by x, x is sometimes called a causal variable
A horizontal line on a control chart at the value that estimates the mean of the statistic plotted on the chart. See Control chart.
Conditional probability mass function
The probability mass function of the conditional probability distribution of a discrete random variable.
If it is possible to write a probability statement of the form PL U ( ) ? ? ? ? = ?1 where L and U are functions of only the sample data and ? is a parameter, then the interval between L and U is called a conidence interval (or a 100 1( )% ? ? conidence interval). The interpretation is that a statement that the parameter ? lies in this interval will be true 100 1( )% ? ? of the times that such a statement is made
Continuous uniform random variable
A continuous random variable with range of a inite interval and a constant probability density function.
The value of a statistic corresponding to a stated signiicance level as determined from the sampling distribution. For example, if PZ z PZ ( )( .) . ? =? = 0 025 . 1 96 0 025, then z0 025 . = 1 9. 6 is the critical value of z at the 0.025 level of signiicance. Crossed factors. Another name for factors that are arranged in a factorial experiment.
Another name for factors that are arranged in a factorial experiment.
Defects-per-unit control chart
See U chart
A subset of effects in a fractional factorial design that deine the aliases in the design.
A study in which a sample from a population is used to make inference to the population. See Analytic study
Estimate (or point estimate)
The numerical value of a point estimator.
A subset of a sample space.
A model that contains only irstorder terms. For example, the irst-order response surface model in two variables is y xx = + ?? ? ? 0 11 2 2 + + . A irst-order model is also called a main effects model