How to Draw Oc Curve for Single Sampling Plan

The calculation of sample size, n, and disquisitional distance, chiliad, depends on the number of specification limits given and whether standard deviation is known.

Single specification limit and known standard deviation

The sample size is given by:

The disquisitional distance is given past:

where:

Unmarried specification limit and unknown standard deviation

The sample size is given by:

The critical distance is given by:

The standard divergence is estimated from the sample data:

Double specification limits and known standard deviation

Kickoff Minitab calculates z:

Then Minitab finds p* from the standard normal distribution every bit the upper tail area corresponding to z. This is the minimum probability of defective outside 1 of the specification limits.

The method Minitab uses for the adding of sample size and critical altitude depends on this value of p*.

Let p₁ = AQL, p_two = RQL

• If 2p* ≤ (p₁/ 2), then the ii specifications are relatively far apart and calculations follow the unmarried limit plans.
• If p₁/ 2 < 2p* ≤ p₁, then the 2 specifications are not relatively far autonomously, but are still not then shut that the minimum probability of defective can be institute for certain mean values. Minitab performs an iteration to find sample size and disquisitional distance.

Let

μ = μ₀+ m * h, where h = σ/100

Let grand = ane, 2, ...300. For each μ calculate:

where Φ is the cumulative distribution function of the standard normal distribution. If Prob (Ten<L) + Prob (X>U) is extremely close to p₁, and so Minitab uses the larger value between Prob (Ten<L) and Prob (10>U) to find sample size and accept number.

Suppose Prob (X<50) is the larger value, permit p_L = Prob (X<L).

The sample size is given by:

The critical distance is given by:

where:

Z_pL = the (1 – p_L) * 100 percentile of the standard normal distribution

• If p_i < 2p* < p₂, then the specifications of the plans must be reconsidered because the minimum probability defective adamant by the two specification limits and the standard deviations is larger than the acceptable quality level p₁. Consider a program with a slightly larger probability of defective than p₁.
• If 2p* ≥ p₂, and so the lot should be rejected; the minimum probability of defective determined by the 2 specification limits and the standard deviation is larger than the rejectable quality level. You can reject the lot without testing any products.

Double specification limits and unknown standard deviation

Start Minitab lets the critical altitude be the value as given in the case of two divide unmarried-limit plans:

Then Minitab finds the upper tail surface area from the standard normal distribution, p*, corresponding to the k as the percentile; and the percentile Zp** from the standard normal distribution corresponding to upper tail area of p* / 2.

The maximum standard departure (MSD) is given by:

The estimated standard deviation is given by:

Minitab tests whether the estimated standard difference, south, is less than or equal to the MSD.

If the estimated standard deviation, due south, is less than or equal to the MSD, then:

The sample size is given by:

The disquisitional distance is given past:

If the estimated standard divergence, south, is not less than or equal to the MSD, so the standard departure is too large to be consequent with acceptance criteria and you lot must refuse the lot.

Note

Term	Description
Z1	the (1 – p1) * 100 percentile of the standard normal distribution
p1	Acceptable Quality Level (AQL)
Z2	the (i – p2) * 100 percentile of the standard normal distribution
ptwo	Rejectable Quality Level (RQL)
Zα	the (1 – α) * 100 percentile of the standard normal distribution
Zβ	the (1 – β ) * 100 percentile of the standard normal distribution
Xi	the ith measurement
	the hateful of actual measurements
L	lower specification limit
U	upper specification limit
σ	known standard deviation

hulmetrame1994.blogspot.com

Source: https://support.minitab.com/en-us/minitab/18/help-and-how-to/quality-and-process-improvement/acceptance-sampling/how-to/variables-acceptance-sampling-create-compare/methods-and-formulas/methods-and-formulas/