Basic SixSigma Metrics

Hello everyone,

Today i'm going to share a topics which is related to SixSigma.

What i found from most of the enrgineers is that they dont have any idea about SixSigma, but in reality it is one of the criteria which determines one's potential about problem solving.

I'll would like to share few things about SixSigma from now so that it could brush up my knowlegde and also add something to the readers.

Today i've selected to post about the metrics of SixSigma i.e., the medium with which we are going to showcase our improvements which are done during a project.

The basics metrics that we use are DPO, DPU, DPMO, PPM, FPY, RTY & Sigma Level.

Lets see about these metrics one by one.

But before going into these topics, we need to understand the difference between defects and defectives.

Simply, Defect means not meeting a specific requirement or failing to achieve a specific customer CTQ (Critical To Quality). 

Defectives means a product or service with more than one defect and we call it as a rejected piece,

Often the product with defect can be accepted by customer but not the defectives.

Now, lets get into the calculation part with some examples.

i. DPU refers to Defects Per Unit

It helps to quantify individual defects on a unit or number of defects per manufactured unit.

DPU = Total defects / Total units produced

For an example, if we have manufactured 300 batches and out of 300 batches, total of 30 defects were identified, then the DPU = 30 / 300 = 0.1.

ii. DPMO refers to Defects Per Million Opportunities

Name itself indicates that if you consider one million opportunities, then the defects identified in that million opportunities refers to DPMO.

For an example, you have manufactured 300 batches and you have tested the sample for complete analysis and again lets consider that the complete analysis consists of 10 randome tests, which means there are 10 opportunities in a single batch to fail.

Hence for total of 300 batches, the number of opportunities to fail is 300 x 10 = 3000.

And lets say the identified defects are 30, so the DPO = 30 / 3000 = 0.01.

DPMO = DPO x 1000000 = 0.01 x 1000000 = 10000.

iii. PPM refers to Parts Per Million

To calculate the PPM we'll use defectives i.e., the rejected pieces

PPM is nothing but to count the number of defective parts per million produced.

For an example, lets say we have manufactured 300 batches and the rejected batches are 30.

So the percentage is going to be 30/300 = 0.1 and the PPM is going to be 0.1 x 1000000 = 100000.

iv. FPY refers to First Pass Yield

First Pass Yield helps us to identify the batches which are passed without any defects for the first time (i.e., without considering the reprocesses).

Lets say for an example, batches executed were 300 and the failed batches were 30,

So the FPY = (300 - 30) / 300 = 270 / 300 = 0.9 ~90%.

v. RTY refers to Rolled Throughput Yield

So, whenever we have multiple stages of product manufacturing, then we can use the Rolled Throughput Yield. RTY is a product of FPY for multiple stages.

Lets say, we have a product which is being executed in three stages and the FPY's of these three stages are 0.9, 0.85 & 0.95. So, the RTY = FPY1 x FPY2 x FPY3 = 0.9 x 0.85 x 0.95 = 0.72675 ~0.73

vi. Finally the Sigma level, this is the most commonly used metric.

Sigma level indicates available standard deviation between data points of a data set that we have collected. USing the sigma level we can calculate the DPMO and vice versa.

Below is the formula for calculating the sigma level.

Sigma level = normsinv(1-(D/O)) + 1.5, 1.5 refers to the sigma shift

** Use the formula in excel

Lets say, the total defects are 30 and opportunities are 3000, so

Sigma level = normsinv(1-(30/3000)) + 1.5 = 3.826 ~3.83

This is how we need to estimate the metrics of six sigma while executing any improvement projects.

Below is the simple related between sigma level and the DPMO, which is estimated based on the above formulas:

DPMO	Sigma-level	Yield, %
3.4	6	99.99966%
230	5	99.977%
6210	4	99.379%
66800	3	93.32%
308000	2	69.2%
690000	1	31%

For any queries in the above content, please feel free to contact me at pharmacalc823@gmail.com

Comments are most appreciated.... !!!

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Super Survey Maker About The Author

---

Hi! I am Ajay Kumar Kalva, Currently serving as the CEO of this site, a tech geek by passion, and a chemical process engineer by profession, i'm interested in writing articles regarding technology, hacking and pharma technology.
Follow Me on Twitter AjaySpectator & Computer Innovations

Estimation of orifice size for dosing of liquids

Good morning everyone....!!!

Hope everyone is safe and healthy, Today i wish to post about estimation of orifice sizing for dosing of liquids. Usually, this dosing of liquids is a pretty common scenario, as multiple operations require dosing of liquids like for semi batch reactions or any kind of anti-solvent isolation and to control the flowrate during these scenario's we'll prefer an orifice.

Though we can prefer certain kind of dosing pumps, but our first preference is always an orifice, because we feel it as "Less Lugguage More Comfort". However, at some junction in our mind we know that flow through orifice is not constant, but we'll still prefer an orifiice since it is being encouraged by management.

And coming to few drawbacks of using the orifice plates is that, the flow will reduce with time i.e., as the liquid level at source is reducing then the flow through orifice will also reduce and the second thing is making a hole of exact diameter is going to be difficult for the orificeplates.

Anyhow, lets get into the topic to check how to estimate the diameter for orifice...?

Before going into calculation part, lets take some time to get the basics and terms right.

What is Cd ?

Cd is referred as coefficient of discharge, it is the ratio of actual discharge to ideal discharge.

What is pressure drop ?

Pressure drop is the differnece between pressures i.e., difference between the pressure accumulated in the overhead space of the receiver from which the liquid is added and the pressure accumulated in the receiving end i.e., usually a reactor.

Lets start the calculation part through an illustration.

Case study:

For better understanding, i'll take the case of a semi batch reaction where there is an energy liberation of 500 KJ per Kg of starting material and there reaction is being executed in a 5 KL SS reactor (13.1 m2 heat transfer area) with an occupancy of 60% and the addition temperature is 20℃  , utility used to control the exothermicity is chilled water at ~5℃.

Soln.

In this case we need to perform controlled addition, hence proposed to use an orifice plate. The diameter to be estimated.

Before estimating the diameter, we need to understand the rate of addition.

To calculate the addition time, i'll prefer the energy balance approach.

Many engineers were asking me to demonstrate the energy balance, but the thing is whenever we are playing with heat loads, the energy balance is involved.

Demand from process = 500 x 500 = 250000 KJ = 59751.43 KCal

(Batch size considered is 500 Kg)

Cooling capacity required = 59751.43 / 3024 = 19.76 TR

Supply from jacket = U x A x LMTD

U (OHTC) = 250 KCal/hr.m2.C

A, effective = 13.1 x 0.6 = 7.86 m2

LMTD = ((20 - 7) - (20 - 11))/ln((20 - 7) / (20 - 11)) = 10.87 C

Supply rate = 250 x 7.86 x 10.87 = 21359.55 KCal/hr

Addition rate = 59751.43 / 21359.55 = 2.79 hours.

Now, lets come to the estimation of orifice size.

Lets say the volume of reagent is 400 L, (Density is 1500 Kg/m3)

To avoid the flow variations through orifice due to variations in liquid level, i'll prefer to maintain contsnt pressure in the addition vessel overhead space by closing the vent line and the pressure is 

~0.15 Kg/cm2.g = 14710 Pas.

Rate of addition (Q) = 400 / 2.79 = 143.37 L / hr = 3.98 E-05 m3/sec

Cross sectional area of orifice (A) = Q / (Cd x (2 x ΔP / ρ)^0.5) 

Cd is considered as 0.8 considering the physical symmetry 

= 3.98 E-05 / (0.8 x (2 x 14710 / 1500)^0.5) = 1.12 E-05 m2

Diameter of cross section (d) = (4 x 1.6419 E-05 / 3.141)^0.5 = 3.78E-03 m = 3.78 mm ~ 4 mm

This is how we need to estimate the orifice sizing for performing a liquid addition.

Hope you liked the illustration, for any queries please feel free to write us at pharmacalc823@gmail.com

Comments are most appreciated.....!!!

SuperSurvey

About The Author

---

Hi! I am Ajay Kumar Kalva, Currently serving as the CEO of this site, a tech geek by passion, and a chemical process engineer by profession, i'm interested in writing articles regarding technology, hacking and pharma technology.
Follow Me on Twitter AjaySpectator & Computer Innovations