How to calculate sample size for statistical control

How to calculate sample size for statistical control

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:

  • Samples that are too large can waste time, resources and money,
  • Samples that are too small can lead to inaccurate results.


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

No alt text provided for this image

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

No alt text provided for this image

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 %)


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

  • n = (1.96 / 0.04)^2 * (0.10)*(1-0.10)
  • n = 2401 * 0.09
  • n = 216.09


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

  • n = (1.96 x 6 / 2)^2
  • n = 34.57


Sample size = 35


(transcribed and translated from my blog Iper - Industrial Performance)

#qualityimprovement ; #continuousimprovement ;#processimprovement

要查看或添加评论,请登录

Jo?o Leite的更多文章

  • Repeatability & Reproducibility - R&R Study

    Repeatability & Reproducibility - R&R Study

    The problem In the world of industry, there are often situations where there is a dispute between the customer and the…

  • Tolerance Stackup Analysis

    Tolerance Stackup Analysis

    In the article “Process Performance (capability)” we talk about process performance indicators (aka “capability”)…

  • Optimization of Production Batches vs SMED

    Optimization of Production Batches vs SMED

    When analysing the cost of production we normally focus on optimizing the cycle time. But let's verify the impact of…

  • Sourcing die sets overseas

    Sourcing die sets overseas

    More than a decade ago, I heard a globally influencer on the automotive industry saying “The question is not "if" we…

  • Free magazines, technical articles and webinars

    Free magazines, technical articles and webinars

    Sometimes the biggest limitation of a self-taught person is the budget (sometimes called "time") they have to do…

  • Kinetic energy and the Sheet Metal Stamping

    Kinetic energy and the Sheet Metal Stamping

    Let’s try to use Kinetic energy to understand and improve reliability on sheet metal stamping dies. Kinetic Energy…

    1 条评论
  • Productivity vs Average Income

    Productivity vs Average Income

    Since I started working on the end of last century, the global market as changed a lot. Since then, I hear about Toyota…

  • Production line balancing Yes or No

    Production line balancing Yes or No

    The “fundamentalists” of lean and the Toyota Production System are always defending line balancing. Line balancing…

  • Relationship between Cpk and Tolerance Interval

    Relationship between Cpk and Tolerance Interval

    When we are making feasibility analysis or designing a new product it’s easy to misevaluate our capacity to attend the…

  • Who is The Swiss Army Knife in Switzerland

    Who is The Swiss Army Knife in Switzerland

    Everybody knows the swiss army knife, but perhaps nobody thought of who is currently being the multipurpose tool on…

社区洞察

其他会员也浏览了