main()
{
extern long k, n;
extern double t;
double cumbin(), /* = function to calculate the cumulative binomial */
absol(); /* = function to calculate absolute value */
double p, /* = binomial parameter (component reliability) estimate */
pnew, /* = next estimate of binomial parameter */
v, /* = input system reliability */
s, /* = system reliability based on p, s is the estimate for v */
deriv, /* = derivative of the reliability curve at p */
eps; /* = input allowable error in the answer or the system rel. */
long count; /* = number of iterations to calculate p */
char yorn; /* = y to continue the program */
printf("This program calculates the common component reliability p\n");
printf("required to yield a given system reliability V of a k-out-of-n\n");
printf("system within a given error Epsilon.\n");
yorn = 'y';
while (yorn == 'y')
{
printf("Enter N = "); /* N2: Get input values to use within */
scanf("%ld", &n); /* the program. */
printf("Enter K = ");
scanf("%ld", &k);
printf("Enter V = ");
scanf("%lf", &v);
printf("Enter Epsilon = ");
scanf("%lf", &eps);
count = 1;
pnew = (k - 1.0) / (n - 1.0); /* N3: Start with inflection point. */
do /* N4: Iterate by Newton's method using */
{ /* pnew and cumbin() to get s and a */
p = pnew; /* new value of pnew. Repeat until */
s = cumbin(p); /* the error is acceptable. */
if (p >= 0.5)
deriv = k * t / p;
else
deriv = (n - k + 1.0) * t / (1.0 - p);
pnew = p - (s - v) / deriv; /* N5: The Newton step. */
count++;
}
while (absol(p - pnew) > eps || absol(s - v) > eps);
/* N6: Print the results. */
printf("\nThe required component reliability is %16.14lf\n", pnew);
printf("%ld iterations were required for the calculation.\n\n", count);
printf("Would you like to run another case (y or n)?");
scanf("%s", &yorn);
}
}
void cdfbin(int *which,double *p,double *q,double *s,double *xn,
double *pr,double *ompr,int *status,double *bound)
/**********************************************************************
void cdfbin(int *which,double *p,double *q,double *s,double *xn,
double *pr,double *ompr,int *status,double *bound)
Cumulative Distribution Function
BINomial distribution
Function
Calculates any one parameter of the binomial
distribution given values for the others.
Arguments
WHICH --> Integer indicating which of the next four argument
values is to be calculated from the others.
Legal range: 1..4
iwhich = 1 : Calculate P and Q from S,XN,PR and OMPR
iwhich = 2 : Calculate S from P,Q,XN,PR and OMPR
iwhich = 3 : Calculate XN from P,Q,S,PR and OMPR
iwhich = 4 : Calculate PR and OMPR from P,Q,S and XN
P <--> The cumulation from 0 to S of the binomial distribution.
(Probablility of S or fewer successes in XN trials each
with probability of success PR.)
Input range: [0,1].
Q <--> 1-P.
Input range: [0, 1].
P + Q = 1.0.
S <--> The number of successes observed.
Input range: [0, XN]
Search range: [0, XN]
XN <--> The number of binomial trials.
Input range: (0, +infinity).
Search range: [1E-100, 1E100]
PR <--> The probability of success in each binomial trial.
Input range: [0,1].
Search range: [0,1]
OMPR <--> 1-PR
Input range: [0,1].
Search range: [0,1]
PR + OMPR = 1.0
STATUS <-- 0 if calculation completed correctly
-I if input parameter number I is out of range
1 if answer appears to be lower than lowest
search bound
2 if answer appears to be higher than greatest
search bound
3 if P + Q .ne. 1
4 if PR + OMPR .ne. 1
BOUND <-- Undefined if STATUS is 0
Bound exceeded by parameter number I if STATUS
is negative.
Lower search bound if STATUS is 1.
Upper search bound if STATUS is 2.
Method
Formula 26.5.24 of Abramowitz and Stegun, Handbook of
Mathematical Functions (1966) is used to reduce the binomial
distribution to the cumulative incomplete beta distribution.
Computation of other parameters involve a seach for a value that
produces the desired value of P. The search relies on the
monotinicity of P with the other parameter.
**********************************************************************/
{
#define atol 1.0e-50
#define tol 1.0e-8
#define zero 1.0e-100
#define inf 1.0e100
#define one 1.0e0
static int K1 = 1;
static double K2 = 0.0e0;
static double K3 = 0.5e0;
static double K4 = 5.0e0;
static double K11 = 1.0e0;
static double fx,xhi,xlo,cum,ccum,pq,prompr;
static unsigned long qhi,qleft,qporq;
static double T5,T6,T7,T8,T9,T10,T12,T13;
/*
..
.. Executable Statements ..
*/
/*
Check arguments
*/
if(!(*which < 1 && *which > 4)) goto S30;
if(!(*which < 1)) goto S10;
*bound = 1.0e0;
goto S20;
S10:
*bound = 4.0e0;
S20:
*status = -1;
return;
S30:
if(*which == 1) goto S70;
/*
P
*/
if(!(*p < 0.0e0 || *p > 1.0e0)) goto S60;
if(!(*p < 0.0e0)) goto S40;
*bound = 0.0e0;
goto S50;
S40:
*bound = 1.0e0;
S50:
*status = -2;
return;
S70:
S60:
if(*which == 1) goto S110;
/*
Q
*/
if(!(*q < 0.0e0 || *q > 1.0e0)) goto S100;
if(!(*q < 0.0e0)) goto S80;
*bound = 0.0e0;
goto S90;
S80:
*bound = 1.0e0;
S90:
*status = -3;
return;
S110:
S100:
if(*which == 3) goto S130;
/*
XN
*/
if(!(*xn <= 0.0e0)) goto S120;
*bound = 0.0e0;
*status = -5;
return;
S130:
S120:
if(*which == 2) goto S170;
/*
S
*/
if(!((*s < 0.0e0) || ((*which != 3) && (*s > *xn)))) goto S160;
if(!(*s < 0.0e0)) goto S140;
*bound = 0.0e0;
goto S150;
S140:
*bound = *xn;
S150:
*status = -4;
return;
S170:
S160:
if(*which == 4) goto S210;
/*
PR
*/
if(!(*pr < 0.0e0 || *pr > 1.0e0)) goto S200;
if(!(*pr < 0.0e0)) goto S180;
*bound = 0.0e0;
goto S190;
S180:
*bound = 1.0e0;
S190:
*status = -6;
return;
S210:
S200:
if(*which == 4) goto S250;
/*
OMPR
*/
if(!(*ompr < 0.0e0 || *ompr > 1.0e0)) goto S240;
if(!(*ompr < 0.0e0)) goto S220;
*bound = 0.0e0;
goto S230;
S220:
*bound = 1.0e0;
S230:
*status = -7;
return;
S250:
S240:
if(*which == 1) goto S290;
/*
P + Q
*/
pq = *p+*q;
if(!(fabs(pq-0.5e0-0.5e0) > 3.0e0*spmpar(&K1))) goto S280;
if(!(pq < 0.0e0)) goto S260;
*bound = 0.0e0;
goto S270;
S260:
*bound = 1.0e0;
S270:
*status = 3;
return;
S290:
S280:
if(*which == 4) goto S330;
/*
PR + OMPR
*/
prompr = *pr+*ompr;
if(!(fabs(prompr-0.5e0-0.5e0) > 3.0e0*spmpar(&K1))) goto S320;
if(!(prompr < 0.0e0)) goto S300;
*bound = 0.0e0;
goto S310;
S300:
*bound = 1.0e0;
S310:
*status = 4;
return;
S330:
S320:
if(!(*which == 1)) qporq = *p <= *q;
/*
Select the minimum of P or Q
Calculate ANSWERS
*/
if(1 == *which) {
/*
Calculating P
*/
cumbin(s,xn,pr,ompr,p,q);
*status = 0;
}
else if(2 == *which) {
/*
Calculating S
*/
*s = 5.0e0;
T5 = atol;
T6 = tol;
dstinv(&K2,xn,&K3,&K3,&K4,&T5,&T6);
*status = 0;
dinvr(status,s,&fx,&qleft,&qhi);
S340:
if(!(*status == 1)) goto S370;
cumbin(s,xn,pr,ompr,&cum,&ccum);
if(!qporq) goto S350;
fx = cum-*p;
goto S360;
S350:
fx = ccum-*q;
S360:
dinvr(status,s,&fx,&qleft,&qhi);
goto S340;
S370:
if(!(*status == -1)) goto S400;
if(!qleft) goto S380;
*status = 1;
*bound = 0.0e0;
goto S390;
S380:
*status = 2;
*bound = *xn;
S400:
S390:
;
}
else if(3 == *which) {
/*
Calculating XN
*/
*xn = 5.0e0;
T7 = zero;
T8 = inf;
T9 = atol;
T10 = tol;
dstinv(&T7,&T8,&K3,&K3,&K4,&T9,&T10);
*status = 0;
dinvr(status,xn,&fx,&qleft,&qhi);
S410:
if(!(*status == 1)) goto S440;
cumbin(s,xn,pr,ompr,&cum,&ccum);
if(!qporq) goto S420;
fx = cum-*p;
goto S430;
S420:
fx = ccum-*q;
S430:
dinvr(status,xn,&fx,&qleft,&qhi);
goto S410;
S440:
if(!(*status == -1)) goto S470;
if(!qleft) goto S450;
*status = 1;
*bound = zero;
goto S460;
S450:
*status = 2;
*bound = inf;
S470:
S460:
;
}
else if(4 == *which) {
/*
Calculating PR and OMPR
*/
T12 = atol;
T13 = tol;
dstzr(&K2,&K11,&T12,&T13);
if(!qporq) goto S500;
*status = 0;
dzror(status,pr,&fx,&xlo,&xhi,&qleft,&qhi);
*ompr = one-*pr;
S480:
if(!(*status == 1)) goto S490;
cumbin(s,xn,pr,ompr,&cum,&ccum);
fx = cum-*p;
dzror(status,pr,&fx,&xlo,&xhi,&qleft,&qhi);
*ompr = one-*pr;
goto S480;
S490:
goto S530;
S500:
*status = 0;
dzror(status,ompr,&fx,&xlo,&xhi,&qleft,&qhi);
*pr = one-*ompr;
S510:
if(!(*status == 1)) goto S520;
cumbin(s,xn,pr,ompr,&cum,&ccum);
fx = ccum-*q;
dzror(status,ompr,&fx,&xlo,&xhi,&qleft,&qhi);
*pr = one-*ompr;
goto S510;
S530:
S520:
if(!(*status == -1)) goto S560;
if(!qleft) goto S540;
*status = 1;
*bound = 0.0e0;
goto S550;
S540:
*status = 2;
*bound = 1.0e0;
S550:
;
}
S560:
return;
#undef atol
#undef tol
#undef zero
#undef inf
#undef one
}