<p>diff(ATI(x,n,N),x) Golden ratio </p>

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sample size
reject size n 10 : c 2 : 21 sys

Poisson [1] parameter λ - exp λ t^* t! /

Discrete Poisson [2] parameters p PAp n p * - exp n p * (i^i! / i 0 c sum * :

Alternate forms x c 10 x ≤ cases : u 0 x ≤ (x 1 ≤ (* : 21 sys

Poisson probability of accepance

x PAp u / n x * - exp x c * 2 1 sys

PAp(p) ... part poly expand n p * (i^i! / i 02 sum 2 n 2^p 2^* + 2 n * p * + 2 / ≡

n routine sample size ≡ c NO pass testing count per say: cost factor 21 mat ≡ 21 line

3. Average Total Inspection ATI ==============================

ATI => Average Total Inspection p n N ATI p PAp n * 1 p PAp - (N * + :

3. Average Total Inspection

Another quantity of interest is the average number of items

in each lot that are inspected. This average total inspection

is one measure of the cost of the sampling procedure.

A sample of size n is drawn from every lot, but if the lot is

rejected, the rest of the lot must also be inspected. Thus,

the average total inspection ranges between n and N and takes

on these extreme values when p is 0 or 1.

Assume that for a lot of size N, n components are sampled

in those lots that pass and N components must be inspected

for those lots that fail ... the average total inspection curve is

calculated below ... suite of this project.

ATI depends upon governing Poisson in PAp

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Define lot size N 50 :

Define Poisson sample size n n : 10

plot scale factor s c n / :

u f s u n N ATI u diff (* :

x c 10 x ≤ (x 1 ≤ (& cases :

<= observe the relationship
max diff(ATI(x,n,N),x) max c n / : 0.2

<p>diff(ATI(x,n,N),x) Golden ratio </p>

The hyperfast Golden-Ratio search [min/max]

x f x n N ATI x diff : a b G 32 / b * 12 / a * - 12 / 5 sqrt * a b - (* + : 21 line

Code adapted from Valery Ochov Mathcad 11 f a b test TOL Extrema y1 y2 ≥ max in range ≡ y1 y2 ≤ min in range ≡ x1 a b G eval : y1 x1 f eval : x2 b a G eval : y2 x2 f eval : 41 line iter 0 : iter 1000 < a b - abs TOL ≤ break test b x2 : x2 x1 : y2 y1 : x1 a b G eval : y1 x1 f eval : 51 line a x1 : x1 x2 : y1 y2 : x2 b a G eval : y2 x2 f eval : 51 line if iter iter 1 + : 21 line if while a b + 2 / iter 21 mat 61 line :

1. All modules/functions in "Symbolic" optimiz. 2. Once in target: shrink the range 3. respect the search y1≥y2≡"max in range" y1≤y2≡"min in range"

Ex f 0 0.5 y1 y2 ≥ 1012 -^Extrema 1 el :

Ex Ex : 0.2

cost Ex n N ATI : 22.9

Cost factor from ATI analysis [N,n,c]. 'cost' printed at 'Ex' on ATI(Ex,n,N)

s x f * n + 0 f - ( x c * x n N ATI x c * n Ex cost o 9 blak 1 5 mat Ex 50 Ex 25 - 2 2 mat 5 1 sys

s x f * n + 0 f - (x c * x n N ATI x c * n Ex cost o 9 blak 15 mat Ex 50 Ex 25 - 22 mat 51 sys

1. blue: Average Outgoing Quality [AOQ] 2. red: Average Total Inspection [ATI]

For firms of mass producion of constant n/N ATI is a good indication of miscellaneous parameters governing production ... [robotics, employees incentive, raw products, working conditions, sickness ...] As the quality increases, i.e: QA department reports less proportion rejected 'c' in 'n' the cost factor ATI decreases. In this scheme, the Production Manager plays a important role wrt all intrants.

data char size clr plotG k 1 data rows range r3 k el char : r4 k el size : r5 k el clr : 31 line for data r3 r4 r5 augment 21 line :

cost 1 20.6 2 22.9 3 24.1 4 24.8 42 mat :

Z-score

A column of sampled data can be standardized to a set of data with mean of zero and a standard deviation of one.

Z-score transform v Zscore v v Mean - v StdDev / 11 line :

v cost 2 col :

v Zscore 1.3571 - 0.1086 - 0.5429 0.9229 41 mat

U cost 1 col v Zscore augment :

Manager U o 7 red plotG :

Happy Manager ... c ≤ 2

U Manager 2 1 sys

n c U 31 mat 1021 1.3571 - 2 0.1086 - 3 0.5429 4 0.9229 42 mat 31 mat

c_day 1122334254627172 mat :

week c_day 1 col c_day 2 col Zscore augment :

weekreport week o 7 red plotG :

week weekreport 2 1 sys