## Understanding 6sigma: Example-3 — Problem at a Soap Manufacturing Plant

Commodities products like soaps, detergents, potato chips etc. faces lot of cost pressure. Manufacturer has to ensure right quantity of the product in each pack to ensure his margins (by avoiding packing more quantity) and avoids legal issues from consumer forum (in case if less quantity is found in the pack).

Let’s take this example

A company is in the business of making soaps with a specification of 50-55 Gms/cake. Anything less than 50 Gms may invite litigation from consumer forum and anything beyond 55 Gms would hit their bottom line. They started the manufacturing and found huge variation in the mean weight of the cakes week after week (see figure-1, January-February period). They were taking one batch per week and producing 250000 soap cakes per batch. From each batch they draw a random samples of 100 soaps for weight analysis. Average weight of 100 samples drawn per batch for the month of Jan-Feb is given below.

In order to evaluate the performance of the process, a control chart is plotted with VOP & VOC (see below). Presently it represents the case-I scenario, Figure-6 where VOP is beyond VOC.

They started continuous improvement program to reduce the variability in the process using DMAIC process. They were able to reduce the variability to some extent but still majority of the soap cakes were out of specifications (March-April period, Figure-3). They continued their endeavor and reduced the variability further and for the first time the control limits of the process was within the specification limits (May-June period, Figure-3). At this point their failure rates were reduced as 95% of the soaps would be meeting the specifications.

We can further reduce the variability to reach the 6 sigma level where the failure rates would be 3.4ppm. But now, we need do a cost benefit analysis as improvement beyond a limit would involve investment. If 5% failure rate is acceptable to the management then we would stop here.

It is not always desirable to achieve 6 sigma level, a 3 sigma process is good enough. But there are cases where human life is involved like passenger aircraft, automobile brakes and airbags, medical devices etc. and in these cases it worth going to 6 sigma and beyond to ensure the safety of the human life.

## Understanding 6sigma: Example-2 — Getting Late for the Office

Our office timings is 8:30 AM to 5:00PM. Company requires us to reach the office between 8:00 and 8:30[1] otherwise it will lead to a pay loss of 1 hour if late for two consecutive days.

Following are the arrival time of my new colleague to the office for last 35 days.

What is “Voice of Customer” (VOC) Or the Customer’s Specifications?

Here customer is the company to whom we are providing our services and in return we are getting the salary. Now customer’s requirement is that we should be in the office between 8:00 to 8:30 AM. This is called as voice of customer or customer’s specifications. It can be represented as

 USL → Upper specification limits LSL→Lower specification limits Customers have right to demand anything in this world, but it is most important for us to recognize the current process capability or what we can deliver?

What is Voice of Process (VOP) or Process Control Limits?

Now we need to understand that the time my colleague took to reach the office is independent of the customer’s requirement. It is a different process by itself but it is desired that the output of this process (arrival time at office) or VOP should comply with the customer’s specifications (VOC).

Now he want to understand the efficiency of his current process (arrival time at office). Simply he wants to know what his routine or the current process can offer if he makes 100 trips to the office?

The statistical calculation shows that on 95 occasions out of 100, he would land in the office between 7:41 AM and 8:54 AM.[2] This is called as lower control limit (LCL) and upper control limit (UCL) of the process respectively. This is also known as voice of the process (VOP).

Overlap of the process efficiency (VOP) and the customer’s specification (VOC) is shown below in figure-3. It is clear from the chart below that the current process is incapable to meet the customer’s specification.

Now what we need to do is to analyze why his process is incapable of meeting customer’s requirement.

Where is the GAP?

It is evident from the figure-3 that the control limits of his process is way beyond the customer’s specifications. In other words there is a huge gap between customer’s expectation and his current process efficiency, it’s the time that he needs to improve his process by optimizing the following variables that can influence his arrival time to the office.

1. When he slept last night?
2. Did he had drinks last night?
3. When he woke-up?
4. When he started from the home?
5. How was the traffic in the morning?
6. How fast he was driving?
7. Which route he took?

How to Reduce the GAP?

Above mentioned variables were studied and optimized using DMAIC process,this enables him to improve his process so that on 95% of the occasions he would be landing in the office between 8:02 and 8:26 AM, hence he would be complying with the customer’s specifications as shown in figure-4. It is also evident that the control limits of the process is inside the customer’s specifications. But still on 5% of the occasions he would be outside the specification limits. Hence process needs further improvements. If the process is improved to such an extent that there is only 3.4ppm failures then it is called as six sigma process which means that if he make one million trip to office, then I will be late only on 3.4 of the occasions.

Arrival time after continuous improvement

## 7QC Tools: Scatter Plot

In general after preparing flow chart there is a brainstorming session, and the outcome of this brainstorming session is the fish-bone diagram which in-turn list down the probable parameters or causes that can affect your quality parameter. At this step all parameters thus collected are only suspects (unless proven guilty!) and their role in affecting the quality parameters needs to be proved in order to held them guilty. In this regard historical data of all suspects (probable parameters or causes) are collected and their effect on the quality parameter is evaluated using scatter plot.

This evaluation can be dome by expert using ANOVA, Regression etc. but a visual tool was required which can tell a shop-floor person that a given parameter is affecting the quality attributes or not? In this regard scatter plot comes handy where you plot a given parameter against the quality attributes.

In real case scenario, we end-up with huge data base as shown below, where X1 to X8 represents the process parameters (suspects) and y represents the quality attribute of interest.

By visual inspection of the above data, it becomes difficult to analyze the effect of X on Y, situation becomes worse if data is larger. Hence, scatter plot is a visual tool that gives qualitative correlation between X and Y.

Let’s look at the scatter plot of X1 and X2 Vs. Y

X-Axis represents X and Y-axis represents Y. we can see that in scatter plot of X1 Vs. Y, as the value of X1 increases, Y also increases. Whereas in X2 Vs. Y, there is no apparent correlation. Hence, we can conclude that X1 is affecting the Y and there is no effect of X2 on Y. We can also quantify the effect by calculating R2 values. R2 values can vary from -1 to +1. The values close to +1 indicates strong positive correlation whereas values close to -1 indicates strong negative correlation.

Scatter plot of all X Vs. Y are given below along with R2 values.

Looking at the scatter plot given above, any shop-floor person can tell that X1, X3 and X5 are affecting the Y in positive way whereas, X4 and X8 are affecting the Y in negative way. Also X2 and X6 doesn’t have any effect on Y.

Related Blogs

7QC Tools: Flow Chart, Know Your Process Thoroughly

7QC Tools: Fish Bone or Ishikawa Diagram

7QC Tools: How to Draw a Scatter Plot?

7QC Tools: Scatter Plot — Caution! Misuse of Statistics!

7QC Tools: Scatter Plot

7QC Tools — How to Prioritize Your Work Using Pareto Chart?

7QC Tools — How to Interpret a Histogram?

7QC Tools — How to Draw a Histogram?

7QC Tools — Histogram of Continuous Data

7QC Tools — Histogram of Discrete Data

7QC tools — Check List

Excellent Templates for 7QC tools from ASQ

What are Seven QC Tools & How to Remember them?

Also See

Car Parking & Six-Sigma

## 7QC Tools — Pareto Chart, How to Prioritize Your Work?

Pareto Principle: It has been found that 80% of the trouble (defects) are because of 20% of the reasons. Hence, 6sigma or continuous improvement program focuses on controlling these 20% of the causes so that 80% of the defects are under control. This helps in setting the priority (focus area) for a 6sigma project.

We have seen that the histogram provides the frequency (number of observations) in a given class. However, the classes are not arranged in descending order.

If the bars of a histogram are arranged in descending order of the frequency then that type of sorted histogram is called as Pareto Chart. Also, cumulative frequency is also plotted along with the frequency on the Pareto Chart.

In above example, if we can control reasons C, D and G then we can reduce the failures by 82% (see cumulative frequency).

Hence, Pareto Chart helps you in simplifying the bigger problem by identifying the vital few significant variables and enables you identify the focus on them with your limited resources.

Cumulative Frequency:

Related Blogs

7QC Tools: Flow Chart, Know Your Process Thoroughly

7QC Tools: Fish Bone or Ishikawa Diagram

7QC Tools: How to Draw a Scatter Plot?

7QC Tools: Scatter Plot — Caution! Misuse of Statistics!

7QC Tools: Scatter Plot

7QC Tools — How to Interpret a Histogram?

7QC Tools — How to Draw a Histogram?

7QC Tools — Histogram of Continuous Data

7QC Tools — Histogram of Discrete Data

7QC tools — Check List

Excellent Templates for 7QC tools from ASQ

What are Seven QC Tools & How to Remember them?

Kindly do provide feedback for continuous improvement

## Why & How Cpm came into existence? Weren’t Cp & Cpk enough to trouble us?

In the earlier post (see earlier post “what is Taguchi Loss function?”) we end up the discussion stating that Cp need to be penalized for the deviation of the process mean from the specification mean.

If you are producing goods near to LSL or USL hence, the chances of rejection increases which in turn increases the chances of reprocessing and rework thereby increasing the cost. Even if you manage to pass the quality on borderline then your customer has to adjust his process accordingly to accommodate your product thereby, increasing his set-up time and cost involved in readjusting his process. Moreover, the variance from your product and the variance from the customer’s process just get adds up to given final product with more variance (remember! Variance has an additive property).

It’s fine that we need to produce goods and services at the center of the specification, which means that we should know the position of process mean with respect to the center of the customer’s specifications. Hence another index was created called as Cpm was introduced which compensates for the deviation of process mean from the specification mean.

For calculating Cpm, the Cp formula is modified where the total variance of the system becomes

Where μ = process mean & T = specification mean or target specification

Hence, Cp formula

is modified to

This is necessary because if I can keep the process mean and the specification mean near to each other, the chances of touching the specification limits would be less which in turn would reduce the chances of reprocessing and we can control the process in a better way.

If μ = T, then Cpm = Cpk = Cp

Related Posts

What Taguchi Loss Function has to do with Cpm?

Car Parking & Six-Sigma

What’s the big deal, let’s rebuild the garage to fit the bigger car!

How the garage/car example and the six-sigma (6σ) process are related?

Now Let’s start talking about 6sigma

What do we mean by garage’s width = 12σ and car’s width = 6σ?

Kindly provide feedback for our continuous journey

## 7QC tools — Check List

Check list is a method of data collection in a tabular or graphical form. We can collect historical data, make a format for new data collection etc.

In summary we need to make a check list in the form of tabular or graphical form (user friendly format) so that the data collection becomes easy even for shop-floor people.

For example

Check sheet for collecting the data of average temperature for the month of July, 2016.

Check sheet for collecting the data about type of defects in production

Check sheet for collecting the data about type of defects in production in two shifts

Related Blogs

7QC Tools: Flow Chart, Know Your Process Thoroughly

7QC Tools: Fish Bone or Ishikawa Diagram

7QC Tools: How to Draw a Scatter Plot?

7QC Tools: Scatter Plot — Caution! Misuse of Statistics!

7QC Tools: Scatter Plot

7QC Tools — How to Prioritize Your Work Using Pareto Chart?

7QC Tools — How to Interpret a Histogram?

7QC Tools — How to Draw a Histogram?

7QC Tools — Histogram of Continuous Data

7QC Tools — Histogram of Discrete Data

Excellent Templates for 7QC tools from ASQ

What are Seven QC Tools & How to Remember them?

Kindly do provide feedback for continuous improvement

## You just can’t knock down this Monster “Variance” —- Part-3

If x & y are two variables, then irrespective of whether you add or subtract them the variance will always add up.

A store wants to know the mean and the variance of sales made by male and female customers in a day. He also wants to see the variance in case sales by both gender are added in pair randomly. Lastly he wants to analyze the mean and variance because of the gender effect (i.e. difference of means and variance). Data of sales in hundred dollars is given below

Using Excel Sheet Mean is calculated by typing formula  =average(array)

Variance is calculated by typing formula  =var.s(array)

Array = column of data, Var.s = variance of sample

But most surprising element is that, irrespective of whether you add or subtract the data, variance always increases. This monster will always raise its head. This is indicated by the resultant variance which is always greater than the individual variances.

In general, the variance always gets added irrespective of whether we are adding or subtracting the individual variances.

where ρ is the correlation coefficient between two variables.

If two random variables are not correlated or they are independent then, ρ = 0 and above formula will get reduced to

Try to calculate the variance for x+y and x-y, are you getting little bit different answer? use correlation coefficient into the equation!

Calculating correlation coefficient (ρ) in excel

Type formula in a cell  =correl(array1, array2)

array1 = column x, array2 = column y

Understanding the Monster “Variance” part-1

Why it is so Important to Know the Monster “Variance”? — part-2

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## Why it is so Important to Know the Monster “Variance”? — part-2

Variance occupies the central role in the six-sigma methodology. Any process whether from manufacturing or service industry has many inputs and the variance from each input gets add up in the final product.

Hence variance has an additive property as shown below

Note: you can add two variances but not the standard deviations

Consequence of the variance addition and six sigma

Say if a product/services which is the output of some process, which in turn have many inputs. Then the variance from the input () and from the process () adds up to give the final variance () in the product/services.

DMAIC methodology of 6Sigma try to identify the inputs that contributes maximum towards the variance in the final product and once identified, its effect is studied in detail to minimize the variance from the input. This is done by reducing the variance in the input itself.

Example: if the quality of a input material used to manufacture a product is found to be critical, then steps would be taken to reduce the fluctuation of the quality of that input material from batch to batch either by requesting/threatening the vendor or by performing the rework of the input material at your end.

Related articles:

Understanding the Monster “Variance” part-1

You just can’t knock down this Monster “Variance” —- Part-3

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