Q 472. Some professionals claim that "Sigma Level for a process cannot be calculated if there are zero defects". Is that a correct statement? Explain your response using continuous data as well as discrete data.   

 

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Process sigma for discrete data

Defects per million opportunities (DPMO) of a process is the total defects / total defect opportunities, multiplied by 1 million

Defect 7, Opportunity = 5, Unit : 3

Defect Per opportunity = Defect/(Unit X 1000000)

DPO = 7/(5 x 3) = 0.46

Excel = normsinv(0.46)+1.5 = 1.399

If the Defect is 0 , then DPO = 0/(5X3) = 0

 

Process Sigma for Continuous Data

For continuous data we need to know the Cpk

Upper Specification Limit : 50

Lower Specification Limit : 25

Task needs to be completed with 10 sec

Mean is 8 sec, Standard Deviation is 5

Cpk = USL – X/3 Sigma

Cpk = 50 – 8/3*5 = 2.8

Process Sigma = 3X2.8

 

The main aim of Six sigma is achieve 3.4 defect per million opportunities. Its not possible to attain zero defects however we can minimize or keep the defects minimum to achieve process stability.

Sigma level represents number of defects per million opportunities. If there are no defects, then there is no way we can calculate the sigma level for a process.

Yes, it can be calculated we can easily calculate it by CPk*3= Sigma level 

The Six Sigma level represents zero defects as 3.4 DPMO. Sigma level 6 and greater is considered generally an excellent process. But true zero defect is not possible. So I agree that Sigma level for a process can’t be calculated if there are zero defects.

1.    Let’s take an example by using Continuous Data:

Suppose, we have height data of African country citizens and based on sampling the average height is 6.7 Ft with standard deviation 0.153 and we are interested in Upper limit only and say USL is 8. What is the Sigma Level and whether is it feasible?

X Bar – 6.7

s – 0.153

USL – 8

We are Skipping Area 2 as there is no LSL limit

Determine Area 2: N/A

As highlighted in the circle, Sigma Level couldn’t be calculated as UCL is very far away from the mean means close to zero defects.

  99.9996% Yield @ 6 Sigma Level. Hence, 100% pragmatically not possible so as Sigma level also can’t determine.

 

2.    Let’s take an example by using Discrete Data:

Suppose we are HRC (Hot rolled coil) steel manufacturing company and our target to meet or exceed customer expectations. Steel market in India is booming and customer have lots of choices. So management decided to stringent the target which is zero defect. Before processing, they want to check Sigma level at zero defects and also current Sigma Level.

No of Unit (N) – 500 Coils

Total Defects (D) – 57

Defect opportunities per unit (O) – 3

DPMO = (D*1000000)/(N*O)

            = 38000

Sigma Level from Conversion Table – 3.27

If suppose defect is zero than calculate Sigma Level:

 

Hence proved that if defect is zero, Sigma Level couldn’t be calculated. So Company will look to increase Sigma Level from 3.27 to 4 at the initial stage.

 

 

Edited May 18, 20224 yr by Saurabh Dhaked
Deleting Duplicate image

Yes. It is true .Sigma level for a process can not be calculated if there are ZERO defect. 

 

For Discrete data  & Continuous data 

 

Suppose example of 100 units ,There are ZERO defectives. The Yield will be 100 %. Sigma level overall will be Infinity 

 

Hence Sigma level for a process can not be calculated 

 

 

            Six Sigma is a data driven approach which aims at reducing the variation in a process. As per the Measure of Central Tendency, mean and SD are the 2 important parameters that helps to characterize a process.

            Mean helps to define how far the process is performing from the specification (target), whereas Standard Deviation helps to define the Spread or Variation in the proces. In general, we assume that the process data is normally distributed.

           From the Normal distribution curve, the distance between the Process mean and the Specification mean can be measured by counting the number of Standard deviations between them, which is denoted by Z (Sigma level).

A 6-Sigma process has the specification limits which are 6 standard deviations from the specification mean (as shown below).

 

In a process, any value that lies between the Specification mean and the Specification Limits (USL & LSL), is called a defect.

              Sigma level can be calculated for both the continuous data and Discrete data available from the process.

Continuous Data – anything that can be measured. Eg – Weight, Length, Diameter, Temperature etc.

Discrete Data – anything that can be counted or classified. Eg – number of products, number of samples, number of pallets, Classification of Good products & defective products etc.

 

Sigma Calculation for Continuous Data:

 

To calculate the Sigma Level for Continuous data, we need to calculate the CpK.

 

                                                        CpK = Min [(USL-Xbar)/3σ, (Xbar-LSL)/3σ]

Process Sigma = 3 * CpK

 

Example:

Specification Mean = 50 mm

Upper Specification Limit = 50.1 mm

Lower Specification Limit – 49.8 mm

Standard Deviation = 0.02 mm

 

CpK = Min [(50.1-50)/(3*0.02), (50-49.8)/(3*0.02)]

CpK = Min [1.67,3.33]

CpK = 1.67

 

Process Sigma Level = 3*1.67 = 5

 

Conclusion:

If the number of defects are Zero means, all the measured values are falling within the specification limits. But that doesn’t mean that the Process mean is equal to Specification mean.

 

The normal curve which we draw for the continuous data is an asymptote – which never touches the X-axis and the area of the curve can never be 100%. Hence it is not possible to calculate the Sigma level for zero defects , in other words, it is practically not a feasible situation to get zero defects, even in a stable and consistent process.

 

Sigma Level Calculation for Discrete Data:

In order to calculate the Sigma Level, the following steps can be followed:

1)      Define the number of Opportunities (O) – which is the number of lowest defects noticeable by the customer

2)      Define the number of Defects (D) - which is the number of values that deviate the specification limits in actual

3)      Calculate Yield = [(D)/((U)*(O))]

4)      Look up for the Sigma Level from the Yield to Sigma Conversion Table.

 

 

Example:

# Opportunities = 10

# Defects = 5

# Units = 4

 

DPO = 5/(10*4) = 0.125

DPMO = DPO *1000000 = 0.125*1000000 = 125000

 

From the chart, we can find the Sigma level = 2.65

 

We can also calculate the sigma level in excel using the formula below:

Sigma Level = -NORMSINV(DPO)+1.5

Sigma level = -NORMSINV(0.125)+1.5 = 2.65

 

Note : This formula accommodates the 1.5 Sigma shift that happens in any stable process over a longer term.

 

In this case, lets assume that, number of defects as Zero.

# Opportunities = 10

# Defects = 0

# Units = 4

 

DPO = 0/(4*10) = 0

DPMO = DPO * 1000000 = 0

 

Conclusion:

This usually happens when we collect samples over a shorter period of time or sometime when the samples are biased. This will give a false indication that the process is very good. In fact, this is only possible because we did not have a sufficient sample size.

Hence Sigma level cannot be calculated for a process with Zero defects or in other words, zero defect process doesn’t exist on a longer time period and we need to collect sufficient sample size.

This seemingly simple question has proved to be very challenging.

 

The statement - "Sigma Level for a process cannot be calculated if there are zero defects" - is only true for Discrete Data. This statement does not hold good for Continuous Data. For Continuous Data, Sigma Level can be calculated (without knowing the actual defect count) and it indicates the probability of getting defects (DPMO). For Discrete Data, we first calculate DPMO / DPU / Yield% (with the actual defect count) and then convert them to Sigma Level. Hence, if defects are 0, there is no Sigma Level for Discrete Data.

 

While there are a few answers which seemed to be moving in the right direction, however no answer is completely correct. Hence, there are no winners for this question.