# 3.2. Research of influence of variation of the mean errors of values of controllable parametres on magnitudes of errors of the first and second sort at indirect monitoring of availability index of product LTS

By working out of algorithm of calculation of tolerances on controllable parametres at the indirect control it is necessary to examine influence of a variation of the mean error of values of controllable parametres on value of magnitudes of errors of the first and second sort.

With a view of magnitude evaluation we will substitute in the formula (2.19) in

tegraly the sums of products of a frequency function of distributions of values of controllable parametres.

Then expression for definition rhjua (ft, AЈv)

It will be recorded:

r\*> «*. d =±, (z.z)

I

Where NA, Nb - value number in an array cell, corresponding to the lower and upper tolerance accordingly, where Nj - number of steps at integration of a composition of frequency functions of probability of values of controllable indexes, =?, (/) +Д and - the measured value of r thow controllable index.

For Pt (tk, A^z) expressions (2.20) will look as follows:

t i / (? «,)) r (< а,) - «) * (* With») - and (tk))) "Mu (TSk) - and (/,)),). TSTSk)... ^ (/d) to

By analogy, we receive expressions for calculation of values / ^ (g^d^i P7 (titAЈz) at the indirect control:

, (z.b)

M

In in

I? / №)) R (AT ': WITH *) "№> {Ok № (/„ D) = 1. (3.7)

Z? / (? ('* with *) - and с* »A> v with *))

».i and

For a case p controllable parametres the formula (2.21) will be recorded:

IN ft

Z Z ' «) i ¦ •• ¦? ('«) *) / »« * with ») - ^ с*» ¦; •••

p = And l

2.v, I • "," s, ft

ZZ J... J/... J/tf (/4);...; (3.8)

/ •I L cho-St

In operation  it is told, that in most cases apply two-sided the tolerance on controllable parametres; the same as it was marked earlier [1,2], for the specified tolerances it is expedient to use normal and uniform distributions of controllable parametres or their compositions.

For the purpose of study of influence of variation of the mean errors DLi id?. And

Positions of boundaries of fields of tolerances H |, X2..., Xn on magnitudes of errors of the first/> (/d, D? And the second P2 (tt, D?-) the dependences specified in rice have been constructed????. Evaluation/> (/, D??) and P2 (/ttA ^) it was spent in the conjecture, what controllable parametres, are linked with an index of quality dependence of an aspect? = AH, 2 + ВХ\provided that And =В=1 and? = 1.

On fig. (3.7) - (3.12) dependences D ^) and Р2 (/, D^i) from magnitudes ka and Ddon for a case of two parametres H | and Х2 for a combination of laws of distribution of values of controllable parametres H |, Х2 and errors of their measurement DH | and ДХ2 are displayed: "normal/normal"; «normal / uniform»; "uniform/normal"; "uniform/uniform"; «Vejbul - la / normal»; «vejbulla / Uniform». Graphic representations have been constructed for value of a total error??, =5 %, 10 %, 15 %, 25 %, 30 % from magnitude of a tolerance zone on controllable parametres.

Fig. 3.10. Dependence of errors of the first and second sort called additional from position of boundaries of fields of tolerances at a combination of laws of distribution of parametre and a variation of the mean error "uniform/uniform".

Fig. 3.9. Dependence of errors of the first and second sort called additional from position of boundaries of fields of tolerances at a combination of laws of distribution of parametre and a variation of the mean error "uniform/normal".

Fig. 3.8. Dependence of errors of the first and second sort called additional from position of boundaries of fields of tolerances at a combination of laws of distribution of parametre and a variation of the mean error "normal/uniform".

Fig. 3.7. Dependence of errors of the first and second sort called additional from position of boundaries of fields of tolerances at a combination of laws of distribution of parametre and a variation of the mean error "normal/normal".

Fig. 3.11. Dependence of errors of the first and second sort called additional from position of boundaries of fields of tolerances at a combination of laws of distribution of parametre and a variation of the mean error «vejbulla / Normal».

Fig. 3.12. Dependence of errors of the first and second sort called additional from position of boundaries of fields of tolerances at a combination of laws of distribution of parametre and a variation of the mean error «vsjbulla / Uniform».

After consideration of the received graphs it is visible, that the greatest values of an error of the first and second sort at influence of an additional making error, acquire at ravnoverojatnostnom the law of distribution of values inspected and errors. The maximum values of probability of errors of the first and second sort accept in range Kd more than 3 for a symmetric tolerance zone on controllable parametre and more than 1,5 for an one-sided tolerance zone. Thereof, in case of absence of the a priori information on laws of distribution of parametres and errors of their measurement it is recommended to use at the indirect multiple parametre control a combination of laws uniform/uniform for calculation of values of errors of the first and second sort, as the most worst case.