How to calculate sample size for statistical control
Jo?o Leite
Engineering Manager, Program Manager, Tool & Die Expert +20 years experience in the ?? automotive industry
When we are implementing improvements in the process, or when we want to evaluate the current process, we have to carry out a control.
Normally we do not carry out a 100% control of the product due to time and cost issues, or in the case of destructive tests we would run out of product to ship.
In these cases we have to use Statistical Process Control (SPC) to control our product, using a sample to infer the result of the entire population.
The correct sizing of the sample size is extremely important to obtain a reliable result. That is, the population is properly represented by the sample.
In summary:
In many cases, one can easily determine the sample size needed to estimate a process parameter, such as the population mean.
Continuous data
Formula for calculating the sample size
n – sample size
σ – estimated standard deviation
Δ - precision or the level of uncertainty in estimation that one is willing to accept (expressed in %).
Discrete data
n – sample size
σ – estimated standard deviation
Δ - precision or the level of uncertainty in estimation that one is willing to accept (expressed in %).
P - is the defective percentage being estimated (expressed in %)
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Example
(1)
Given an estimated defective proportion of 5% to 15%, what sample size should we take to estimate the defective proportion within 4%?
P = (15% - 5%) = 10% = 0.10 Δ = 0.04
Using the formula for discrete data, we have
Sample size = 217
(2)
We want to estimate the average cycle time within 2 days.
The preliminary estimate of the population standard deviation is 6 days.
How many observations should we take?
Δ = 2 σ = 6 days
Using the formula for continuous data, we have
Sample size = 35
(transcribed and translated from my blog Iper - Industrial Performance)