Solutions for Chapter 2: Frequency Distributions and Graphs

In a fractional factorial experiment when certain factor effects cannot be estimated uniquely, they are said to be aliased.

The arithmetic mean of a set of numbers x1 , x2 ,…, xn is their sum divided by the number of observations, or ( / )1 1 n xi t n ? = . The arithmetic mean is usually denoted by x , and is often called the average

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.

An estimator for a parameter obtained from a Bayesian method that uses a prior distribution for the parameter along with the conditional distribution of the data given the parameter to obtain the posterior distribution of the parameter. The estimator is obtained from the posterior distribution.

The tendency of data to cluster around some value. Central tendency is usually expressed by a measure of location such as the mean, median, or mode.

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.

A correction factor used to improve the approximation to binomial probabilities from a normal distribution.

A method to derive the probability density function of the sum of two independent random variables from an integral (or sum) of probability density (or mass) functions.

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).

A square matrix that contains the correlations among a set of random variables, say, XX X 1 2 k , ,…, . The main diagonal elements of the matrix are unity and the off-diagonal elements rij are the correlations between Xi and Xj .

A control chart in which the point plotted at time t is the sum of the measured deviations from target for all statistics up to time t

A subset of effects in a fractional factorial design that deine the aliases in the design.

A continuous random variable that is the sum of a ixed number of independent, exponential random variables.

The difference between an estimated value and the true value.

The numerical value of a point estimator.

A type of experimental design in which every level of one factor is tested in combination with every level of another factor. In general, in a factorial experiment, all possible combinations of factor levels are tested.

A random variable that generalizes an Erlang random variable to noninteger values of the parameter r

The geometric mean of a set of n positive data values is the nth root of the product of the data values; that is, g x i n i n = ( ) = / w 1 1 .

In general, the agreement of a set of observed values and a set of theoretical values that depend on some hypothesis. The term is often used in itting a theoretical distribution to a set of observations.

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 .