- 2.4.26E: The diameter of a rivet (in mm) is a random variable with probabili...
- 2.4.1E: Determine whether each of the following random variables is discret...
- 2.4.2E: Computer chips often contain surface imperfections. For a certain t...
- 2.4.3E: A chemical supply company ships a certain solvent in 10-gallon drum...
- 2.4.4E: Let X represent the number of tires with low air pressure on a rand...
- 2.4.5E: A survey of cars on a certain stretch of highway during morning com...
- 2.4.6E: The element titanium has five stable occurring isotopes, differing ...
- 2.4.7E: A computer sends a packet of information along a channel and waits ...
- 2.4.8E: After manufacture, computer disks are tested for errors. Let X be t...
- 2.4.9E: On 100 different days, a traffic engineer counts the number of cars...
- 2.4.10E: Micro processing chips are randomly sampled one by one from a large...
- 2.4.11E: Refer to Exercise 10. Let Y be the number of chips tested up to and...
- 2.4.12E: Three components are randomly sampled, one at a time, from a large ...
- 2.4.13E: Resistors labeled 100 ? have true resistances that are between 80 ?...
- 2.4.14E: Elongation (in percent) of steel plates treated with aluminum are r...
- 2.4.16E: A process that manufactures piston rings produces rings whose diame...
- 2.4.17E: Refer to Exercise 16. A competing process produces rings whose diam...
- 2.4.19E: The level of impurity (in percent) in the product of a certain chem...
- 2.4.20E: The main bearing clearance (in mm) in a certain type of engine is a...
- 2.4.23E: The thickness of a washer (in mm) is a random variable with probabi...
- 2.4.24E: Particles are a major component of air pollution in many areas. It ...
- 2.4.25E: The repair time (in hours) for a certain machine is a random variab...
Solutions for Chapter 2.4: Statistics for Engineers and Scientists 4th Edition
Full solutions for Statistics for Engineers and Scientists | 4th Edition
In a fractional factorial experiment when certain factor effects cannot be estimated uniquely, they are said to be aliased.
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 ( | ).
Chi-square (or chi-squared) random variable
A continuous random variable that results from the sum of squares of independent standard normal random variables. It is a special case of a gamma random variable.
Completely randomized design (or experiment)
A type of experimental design in which the treatments or design factors are assigned to the experimental units in a random manner. In designed experiments, a completely randomized design results from running all of the treatment combinations in random order.
Components of variance
The individual components of the total variance that are attributable to speciic sources. This usually refers to the individual variance components arising from a random or mixed model analysis of variance.
The variance of the conditional probability distribution of a random variable.
When a factorial experiment is run in blocks and the blocks are too small to contain a complete replicate of the experiment, one can run a fraction of the replicate in each block, but this results in losing information on some effects. These effects are linked with or confounded with the blocks. In general, when two factors are varied such that their individual effects cannot be determined separately, their effects are said to be confounded.
Another term for the conidence coeficient.
Continuous random variable.
A random variable with an interval (either inite or ininite) of real numbers for its range.
A graphical display used to monitor a process. It usually consists of a horizontal center line corresponding to the in-control value of the parameter that is being monitored and lower and upper control limits. The control limits are determined by statistical criteria and are not arbitrary, nor are they related to speciication limits. If sample points fall within the control limits, the process is said to be in-control, or free from assignable causes. Points beyond the control limits indicate an out-of-control process; that is, assignable causes are likely present. This signals the need to ind and remove the assignable causes.
A dimensionless measure of the linear association between two variables, usually lying in the interval from ?1 to +1, with zero indicating the absence of correlation (but not necessarily the independence of the two variables).
Defects-per-unit control chart
See U chart
Degrees of freedom.
The number of independent comparisons that can be made among the elements of a sample. The term is analogous to the number of degrees of freedom for an object in a dynamic system, which is the number of independent coordinates required to determine the motion of the object.
Deming’s 14 points.
A management philosophy promoted by W. Edwards Deming that emphasizes the importance of change and quality
The expected value of a random variable X is its long-term average or mean value. In the continuous case, the expected value of X is E X xf x dx ( ) = ?? ( ) ? ? where f ( ) x is the density function of the random variable X.
Extra sum of squares method
A method used in regression analysis to conduct a hypothesis test for the additional contribution of one or more variables to a model.
The distribution of the random variable deined as the ratio of two independent chi-square random variables, each divided by its number of degrees of freedom.
Finite population correction factor
A term in the formula for the variance of a hypergeometric random variable.
The harmonic mean of a set of data values is the reciprocal of the arithmetic mean of the reciprocals of the data values; that is, h n x i n i = ? ? ? ? ? = ? ? 1 1 1 1 g .