3. Calculate the estimate of the slope of the regression line
$m
:$ ( ) These Sums of Squares are calculated the same as those used for the correlation coefficient:
SS x x x x
( )
4. Finally, calculate the estimate of the y-intercept,$b
:$ $
b = − y mx
5. Plot the regression line on the scatter diagram. Visually check the line to see if it is a good fit and that no calculation errors were made.
Note: If you think a regression analysis will help your project, see your Black Belt. First, they will have access to software that will make the job easier. Second, there are some regression assumptions that they will check for your. Ask them about “residuals analysis.”
5. CAUSE & EFFECT
Cause and Effect is a critical element of quality improvement. Throughout this manual, the concepts of process factors and process output have been discussed over and over. The process (methods, machines, materials, personnel, environment, and information) produces your products and services.
To improve quality, we must understand the factors that contribute to variation in quality. Through this path we can identify countermeasures that have a high probability of improving the quality of our products and services. It’s easy to “jump to solutions,” harder to understand the real factors that affect performance.
Here are two examples of where this thinking was not applied and the subsequent consequences:
The Case of the Leaky Pump Seal: A nuclear power plant was having problems with the seal on a pump required for plant safety. The seal would begin to leak after only 1100 hours (on average) of operation. A “brief” analysis led to the conclusion that the seal’s design needed changing. $40,000 and six months later, the new seal was installed. After 100 hours of pump operation, the new seal was leaking just like the old.
A more thorough cause and effect analysis revealed that the pump motor’s thrust bearing was not being properly aligned during overhaul.
Correction of this problem resulted in no more leaky seals. The cost of the new change: just the revision of one procedure!
The Case of the Clinical Assistants - At one large hospital, a new role, the Clinical Assistant, had been established as part of cost and service-quality improvement efforts. The Clinical Assistant was a multi-function role, including clinical duties, housekeeping, nutrition and environmental services. Unfortunately, after a few months, administration found that the turnover rate for these assistants was high in some units of the hospital.
The hospital’s Business Leaders met one week to “fix” the problem. They concluded that the Clinical Assistants did not like to do the housekeeping duties, and so their “countermeasure” was to create a new position, the Unit Assistant, to perform the “undesirable” duties. Three months later, the Clinical Assistants were still leaving the same units of the hospital. The problem still exists today.
5.1 CAUSE AND EFFECT ANALYSIS
Cause and Effect Analysis is designed to focus on the causes, rather than the symptoms of the quality problem. The Cause and Effect Diagram is often used to help identify and evaluate the potential causes of quality problems.
Cause and Effect Analysis consist of two basic steps:
1. Develop an Understanding of the Potential Causes of a Problem, and 2. Determine or Verify which Potential Causes are the Actual Causes.
Sometimes, Cause and Effect Analysis will put you in the role of a detective. You will look for “clues” from your process, trying to discover which of the process factors are responsible for the quality problems or variation.
• A railroad conducted a root cause analysis of locomotive engine leaks. They discovered that the wrong size bolts were being used that connected a “Y-pipe” to the engine block. The bolts were too long, allowing the “Y-pipe” to flex, resulting in leaks.
• A hospital conducted an investigation of a high infection rate for cardiac surgery patients. They found that antibiotics were being administered too early in the surgery preparation process. During the actual surgery, the antibiotics were significantly reduced in their effectiveness.
Cause and Effect Analysis can also put you in the role of a scientist. Here, you will design experiments to determine which factors are important to the quality of your products and services and what are the best “levels” to set these factors.
• A manufacturer of plastic components was experiencing excessive “flash” - extra plastic on the component formed when plastic squeezed between the injection mold halves. They conducted experiments to determine the optimal injection pressure that would produce a quality component without flash.
• Utility customers were experiencing outages during lightning storms. Utility engineers suspected that changing the time delay on a certain protective relay could prevent many of these outages. They conducted experiments to determine the optimal time delay for the relay and reduced the interruptions.
5.2 THE CAUSE & EFFECT DIAGRAM Purpose
The Cause and Effect Diagram (sometimes called the Fishbone or Ishikawa Diagram) is used as the starting point of a Cause and Effect Analysis.
Here the Diagram is used to develop hypotheses about the causes of variability or poor performance of the product or service. The Cause and Effect Diagram is also used to record data and to note “discoveries” made during the verification step of Cause and Effect Analysis.
The advantage of the Cause and Effect Diagram is that it provides you with a picture of all the possible causes. Ideas from many different people can be captured on the diagram and the search for important causes then planned systematically. The Cause and Effect Diagram helps you avoid the tendency to think of only one possible cause at a time and go searching for that one cause.