Probability of Miscounts on Counting Many Parts with Counting Scale and with Roberval Balance

Abstract

There are two common methods for counting many small machine parts using a balance.
One of these consists of using a counting scale which has a large mechanical advantage l, and the other consists of repeatedly using a Roberval balance which has equal arm lengths. The former method counts (l+1)N parts directly, and the latter method counts 2ⁿN parts after using the balance n times, where N is the initial number of parts.
The present paper is concerned with the analysis and with the comparison of the probability of miscount in these methods. The analysis is based on the assumptions that the distribution function of population of these many machine parts is always a normally distributive function which has a mean value w and a standard deviation σ, and that both types of balance are always accurate.
As a result of fundamental analysis based on elementary statistics, it becomes evident that the probability of miscount is far larger in using the counting scale than in using the Roberval balance. The probability of miscount in relation to the rsesultant number of parts is presented graphically for each type of balance.