Appendix B: Introduction to Microsoft Office Excel
Microsoft Office Excel is a spreadsheet program to store and analyze information.
We recommend its use due to the fact that it is widely available and has powerful
mathematical, statistical and graphical capabilities, with which all the numerical
examples in this book can be carried out. In this appendix, we outline main functions
and applications of Excel.
The outline of the appendix is as follows. Section B.1 presents the functions of
Excel and Section B.2 introduces Solver of Excel. We discuss simulation for
reliability analysis using Excel in Section B.3. Other relevant issues are briefly
outlined in Section B.4.
B.1 Built-in functions of Excel
Excel functions include the following categories:

Database functions

Date and time functions

Engineering functions

Financial functions

Information functions

Logical functions. They are “false”, “true”, “and”, “or”, “if”, and “not”.

Lookup and reference functions

Math and trigonometry functions

Statistical functions

Text functions, and

External functions.
Some important math functions are shown in Table B.1; some common statistical
functions are shown in Table B.2; and some important distribution functions are
shown in Table B.3. More details can be found from the user’s manuals of Excel or
using Excel’s “help”.
Table B.1 Math functions
Function
Description
abs(x)
Return the absolute value of x
ceiling(x)
Round x to the nearest integer
combin(n, k)
Return the number of combinations choosing k
items from n items.
gammaln(x)
Return the natural logarithm of  ( x )
exp(gammaln(x))
Return  ( x )
exp(x)
Return the value of the exponential function at x
fact(x)
Return the value of x!
floor(x)
Round x down, toward zero
int(x)
Round x down to a nearest integer
ln(x)
Return the natural logarithm of x
pi()
Return the value of 
product
Multiply its arguments
rand()
Return a pseudo random number between 0 and 1
round(x, j)
Round x to a number with j digits
sign(x)
Return 1, -1 or 0 if x > 0, < 0 or = 0
sum
Add its arguments
trunc(x, j)
Truncate x to a number with j digits
Table B.2 Statistical functions
Function
Description
average(a, …, b)
Return the average of (a, …, b)
correl(A, B)
Return the correlation coefficient between
datasets A and B
count
Return the number of nonblank cells in a range
kurt(a, …, b)
Return the kurtosis of (a, …, b)
large(A, k)
Return the k-th largest value in the dataset A
max(a, …, b)
Return the maximum value of (a, …, b)
median(a, …, b)
Return the median of (a, …, b)
min(a, …, b)
Return the minimum value of (a, …, b)
rank
Return the rank of a number in a list of numbers
skew(a, …, b)
Return the skewness of (a, …, b)
small(A, k)
Return the k-th smallest value in the data set A
stdev(a, …, b)
Estimate standard deviation of (a, …, b)
var(a, …, b)
Return the variance of (a, …, b)
Table B.3 Distribution functions
Function
Description
binomdist(x, n, p, true [false])
Return the cdf [pmf] at x
gammadist(x, a, b, true [false])
Return the gamma cdf [pdf] at x with the
mean parameter a and standard deviation
parameter b.
gammainv(p, a, b)
Return the inverse of gamma cdf.
lognormdist(x, a, b)
Return the cdf of lognormal distribution
with the mean parameter a and standard
deviation parameter b
Return the inverse of the lognormal
loginv(p, a, b)
distribution
Return the pmf of negative binomial
negbinomdist(x, n, p)
distribution
normdist(x, a, b, true [false])
Return the normal cdf [pdf] at x with the
mean parameter a and standard deviation
parameter b.
norminv(p, a, b)
Return the inverse of the normal cdf.
poisson(x, a, true [false])
weibull(x, a, b, true [false])
Return the Poisson cdf [pmf] at x with the
mean parameter a.
Return the Weibull cdf [pdf] at x with the
shape parameter a and scale parameter b.
B.2 Solver of Excel
“Solver” can be evoked to find the maximum or minimum of a function with a set
of constraints, or to solve an equation.
Excel will install the Solver by clicking Add-Ins on the Tools menu. Once the
add-in is installed, one can run Solver by clicking Solver on the Tools menu. The user
will need to input the required information in the Solver parameters dialog box. It
consists of four parts:

Target cell, which gives the value of a univariate or multivariate function

Type of the objective, which includes “max”, “min” or “equal to a specified
value”

Variables cells, and

Constraints (optional).
Example B.1: Find the mode of the gamma density function with the shape
parameter 5.6 and the scale parameter 9.3.
Referring to Table B.4, the computational process is as follows:

Key “Mode” into cell A1 and “Target” into cell A2.

Key an initial value of the mode by guessing (say 50) into cell B1.

Key “= gammadist(b1, 5.6, 9.3, false)” to cell B2.

Evoke “Solver” from “Tools” of Excel.

Fill “b2” to the target cell and select “Max” from the “Equal To” list.

Fill “b1” to the space of “by changing cells”.

Click “Solver” and then we will obtain the output shown in Table B.4. Namely,
the mode is at tm  42.78 with f (tm )  0.01964.
Table B.4 Spreadsheet of seeking the mode of the gamma pdf
Row \ column
A
B
1
Mode
42.78
2
Target
0.01964
B.3 Simulation for reliability analysis
Monte Carlo simulation for reliability analysis relies on pseudo random numbers
to generate random times to failure based on a given failure distribution F ( x) . A
pseudo random number between 0 and 1, p , is generated by Excel function rand(). A
random life x is given by
x  F 1 ( p) .
For the Weibull distribution, x is given by
x  [ ln(1  p)]1/   [ ln( p ')]1/ 
where p ' is also a random number between 0 and 1.
Example B.2: Assume that the time to failure follows the lognormal distribution
with l  1.0 and  l  0.5. Generate a failure point process, which is truncated at
t  20 .
Referring to Table B.5, the simulation process is as follows:

Key “xi”, “ti” and “Ti” into cells A1, B1 and C1, respectively.

Enter “=loginv(rand(), 1, 0.5)” to cell A2, and copy it to cells A3, A4, …..

Enter “=a2” to cell B2, type “=b2+a3” to cell B3 and copy this to cells B4, B5, ….

Enter “=min(20, b2)” to cell C2 and copy this to cells C3, C4, ….
The outputs are shown in Table B.5. It is noted that this simulation produces a
censored observation x7  20  19.3688  0.6312 . When pressing the key F9, all
values of failure times are updated and the outputs change.
Table B.5 A failure point process obtained from simulation
Row \ column
A
B
C
1
xi
ti
Ti
2
1.14408
1.14408
1.144076
3
2.56609
3.71017
3.710171
4
3.03061
6.74078
6.740785
5
6.17781
12.9186
12.9186
6
4.56061
17.4792
17.47921
7
1.88963
19.3688
19.36884
8
3.91215
23.281
20
B.4 Others
Excel has a number of other attractive functions such as “data analysis” tools,
including regression.
Microsoft Excel uses Visual Basic for Applications to create the macros for
automating re-calculation, variation of parameters, and collection of results. The
macros are particularly useful for solving relatively complex mathematical problems.
Excel can accept data in real time through several programming interfaces, which
allow it to communicate with many data sources.
Finally, graphical capabilities of Excel allow displaying various function relations
and creating various types of charts.
Math and Trigonometry functions
Function Description
ABS Returns the absolute value of a number
ACOS Returns the arccosine of a number
ACOSH Returns the inverse hyperbolic cosine of a number
ASIN Returns the arcsine of a number
ASINH Returns the inverse hyperbolic sine of a number
ATAN Returns the arctangent of a number
ATAN2 Returns the arctangent from x- and y-coordinates
ATANH Returns the inverse hyperbolic tangent of a number
CEILING Rounds a number to the nearest integer or to the nearest multiple of
significance
COMBIN Returns the number of combinations for a given number of objects
COS Returns the cosine of a number
COSH Returns the hyperbolic cosine of a number
DEGREES Converts radians to degrees
EVEN Rounds a number up to the nearest even integer
EXP Returns e raised to the power of a given number
FACT Returns the factorial of a number
FACTDOUBLE Returns the double factorial of a number
FLOOR Rounds a number down, toward zero
GCD Returns the greatest common divisor
INT Rounds a number down to the nearest integer
LCM Returns the least common multiple
LN Returns the natural logarithm of a number
LOG Returns the logarithm of a number to a specified base
LOG10 Returns the base-10 logarithm of a number
MDETERM Returns the matrix determinant of an array
MINVERSE Returns the matrix inverse of an array
MMULT Returns the matrix product of two arrays
MOD Returns the remainder from division
MROUND Returns a number rounded to the desired multiple
MULTINOMIAL Returns the multinomial of a set of numbers
ODD Rounds a number up to the nearest odd integer
PI Returns the value of pi
POWER Returns the result of a number raised to a power
PRODUCT Multiplies its arguments
QUOTIENT Returns the integer portion of a division
RADIANS Converts degrees to radians
RAND Returns a random number between 0 and 1
RANDBETWEEN Returns a random number between the numbers you specify
ROMAN Converts an arabic numeral to roman, as text
ROUND Rounds a number to a specified number of digits
ROUNDDOWN Rounds a number down, toward zero
ROUNDUP Rounds a number up, away from zero
SERIESSUM Returns the sum of a power series based on the formula
SIGN Returns the sign of a number
SIN Returns the sine of the given angle
SINH Returns the hyperbolic sine of a number
SQRT Returns a positive square root
SQRTPI Returns the square root of (number * pi)
SUBTOTAL Returns a subtotal in a list or database
SUM Adds its arguments
SUMIF Adds the cells specified by a given criteria
SUMPRODUCT Returns the sum of the products of corresponding array components
SUMSQ Returns the sum of the squares of the arguments
SUMX2MY2 Returns the sum of the difference of squares of corresponding values in
two arrays
SUMX2PY2 Returns the sum of the sum of squares of corresponding values in two
arrays
SUMXMY2 Returns the sum of squares of differences of corresponding values in two
arrays
TAN Returns the tangent of a number
TANH Returns the hyperbolic tangent of a number
TRUNC Truncates a number to an integer