An exhaustive IDDOV six sigma case study of an automated droplet coating system using MINITAB and QEtools
Identify and Define
A survey was sent to 7 main customers asking each customer to rank the following CR from least to most important (Least Important CR = 1; Most Important CR = 7).
Based on customer feedback and historical experience, the DFSS team identified the following Functional Requirements, and their relative importance, desired direction of improvement, target values, and upper/lower acceptance limits. Of note, for coating mass requirement, assume a target of 1000 mg for comparison analysis purposes. In actual practice, the new system must be able to change this nominal based on an individual customer application requirements.
Design
Objective was to identify the system flexible for different coating mass requirements. Coating mass may be modeled as a function of ‘flow rate’ and ‘pulse time’ (valve open to valve close time). The following chart shows the ideal function for Coating Mass where Coating Mass = flow rate * pulse time.
The pulse time is easy to adjust and maintain (may model as a fixed process setting). The challenge in controlling coating mass is the flow rate. Here, several factors may affect flow rate. The following P-Diagram summarizes these factors.
The primary noise factor for this process is the incoming material viscosity. Low viscosity allows for faster flow rates and thus typically more mass for a given pulse time. High viscosity has the opposite effect – slower flow rates and less coating mass for a given pulse time.
Optimize
Dynamic Taguchi Robustness DOE
These viscosity effects are widely known yet customers still require coating systems to be as robust as possible to inherent viscosity variation in order to lower their total operating costs. The operating range limits for viscosity in which the system must accept are 600 – 800. In other words, in making a final recommendation, you should assume that the system will need to operate with a material viscosity in this range. In other words, you may not recommend settings that fix the viscosity and thus you should not include this variable as a DOE term. To identify best settings for control factors, the company performs an L18 Taguchi Experiment.
The purpose of the Taguchi experiment is to determine which combination of control factor settings result in the best flow rate (meet functional requirement acceptance limits) for different pulse times and is the most robust to noise (i.e., viscosity). The team has identified a desired flow rate during the gathering of functional requirements (See Functional Requirements Matrix). So, if one is given a target mass coating size for a specific application, one simply needs to change the pulse time to hit the coating mass requirements with minimum variation relative to the inherent noise conditions (i.e., inevitable variation in viscosity).
Taguchi results
So, based on Taguchi’s DOE analysis, we recommend the optimal flow rate for either system to be at 271.53mg/sec with a standard deviation of 47.97
Reliability
System reliability is a metric derived by using experimental failure data, it is used to define warranty periods, generate spares forecast and maintenance scheduling. Through a small number of machines tested, the data is extrapolated and a Mean Time To Failure (MTTF) is established.
The data for the Penny Packer systems A & B indicates for all six machines, this is an uncensored dataset as there is no upper limit that is mentioned, hence when the distribution analysis is carried out, we should not take the warranty cycle as a censor. The cycles to failure for all six systems is greater than the specified warranty cycle, which to plain sight would mean, all products would last over the 150,000 cycles mark. However, when the Weibull distribution analysis is carried out, it accounts for the probability of the system surviving.
From the results below, it was found that System A had a probability of survival or reliability of 0.962737 and System B had the probability 0.977919.
The likelihood of System B failing is 1.5% lesser than System A. Hence the recommendation from the reliability analysis is System B as it would yield lower warranty costs.
Tolerance simulation analysis and design optimization
For Tolerance Analysis we consider three factors Viscosity, Temperature, and Pressure. The distribution for the three factors considered was taken to be Triangular Distribution. We ran a tolerance simulation to decide what control settings are needed to meet a final Mass Coating Specification of 1000 + 50 with the Desired Quality Yield > 99.95%. The Pulse Rate was selected such that Flow Rate* Pulse Rate=1000 (Flow Rate is 271.53 i.e value got by Taguchi DOE). The response equation for Coating Mass used was Coating Mass = (Flow Ratepulse time) + (Flow Ratetemperature %) + (Flow Rate*pressure %) + (viscosity effect).
We conduct the analysis for all possible combinations of control settings and assess the least expensive setting which achieves the desired quality of yield. The setting is where the temperature control setting is 1 and pressure is not controlled i.e. the tolerance for temperature is ∓5% and pressure is ∓10%.
Verification
We have selected 4 categories (Cost, Performance, Reliability and Maintenance) for our design scorecard and segregated the functional requirements into them.
System A: Total desirability =0.836
System B: Total desirability =0.88
Functional audit table
A functional audit Table is created to evaluate how well the two potential alternatives have met the functional requirements. Out of the two alternatives, B has higher system cost by $5,000. However, looking at the failure characteristics of the two systems over 150,000 cycles for 6 test units each, and performing a reliability analysis for the both we can conclude that system B has a better reliability than system A by 1.5182%. Also, after adding the cost of a new temperature module (option 2) to the system the per cycle operating cost for system B is lesser than that of A by $0.02.
Design Recommendation
The two new systems A and B are evaluated based on the parameters of Cost, Reliability, Performance and Cost. The importance ratings were obtained from the functional requirements that were provided. The total desirability index is the average of the sum product of importance and desirability.
Performance has the highest functional requirement, both Systems have a desirability score of 1.0 in this parameter. Equipment Reliability had the second highest functional requirement, the recommendation is to choose System B on this aspect as it has a desirability score of 0.80 compared to System A’s score of 0.55.In terms of Cost, although System A scores significantly better in system cost, score is affected by high operating costs. Desirability score of system A is higher for the cost parameter by 0.03. Hence from a cost point of view, System A is recommended. The last parameter is maintenance, both have equal desirability scores of 0.78.
Based on overall desirability score of 0.85, System B is recommended over System A which scored 0.77.