Statistics and probability for better decisions in manufacturing

To make the best manufacturing decisions, an individual needs accurate data collected from a sample size of production that is most likely to represent the entire production run.

If you manage the manufacture of high-volume products, you also generate large volumes of data. Buried in that data are pieces of information that can direct you to make better decisions and improve your manufacturing efficiency. The key to reading your data lies in the mathematics of statistics.

If you’re like most people, you don’t remember statistics classes with fondness. Like most students, you probably wondered how calculus, rolling dice, and pulling marbles out of a jar were going to serve you in your career. If you paid attention and still understand the concepts you were taught, you probably know enough to begin using your production data to learn about your operations and improve your performance.

Play Ball!

Probably one of the best ways to introduce statistics and probability is through Major League Baseball. As with manufacturing statistics, baseball uses many mathematical calculations and can be equally nap-inducing. Using batting averages as an example, baseball fans gather statistics about a hitter’s base hits over his career, season, last month, and since the All-Star Game. A player’s batting average is the quotient of hits/at-bats. For every at-bat, we collect data about each instance. We then convert our accumulated data to meaningful information we can act upon. Was the pitcher left- or right-handed? Was it a home or away game? Was the batter healthy? Which field were they playing on? Did the batter get a hit? These quotients and their context are our statistics. Our statistics develop our knowledge of a given player’s capabilities.

Given his statistical knowledge, a manager can anticipate a player’s performance during a game. This knowledge allows managers to develop their lineup and make substitutions when needed. A manager’s actions during a game, a series, or a season are based on his statistical knowledge of a player’s performance and his understanding of the chance, or probability, of specific performance based on known variables. As an example, if a healthy player is hitting .300 against right-handed pitchers, the probability is that, given four at-bats during a game, that he will get at least one base hit if the opposing pitchers are right-handed.

Using Statistics to Improve Your Own Results

As in baseball, data about performance is collected from your plant floor. Data includes measured properties of received coils, press tonnage during forming, cycle rates, scrap rates, product rejection rates, vibration characteristics, hydraulic pressure, electrical measures, maintenance and repair activities, lubricant application rates, and so on. Raw data is meaningless without context and analysis. We use statistics to read what the data is telling us. As with our baseball analogy, statistics tells us about the performance of each “player” over a period of time and within a given set of production parameters. If you understand material properties and their variability, you can improve simulation data, resulting in fewer expensive die tryouts. If you can anticipate equipment failure through a process like Reliability Centered Maintenance, you can improve equipment and plant reliability.

Developing a statistical model from large volumes of data requires you select a representative sample from the population to analyze. The biggest challenges from sampling are selecting the correct population to sample and identifying a sample of observations that represents the entire population of interest. Selecting your population of interest requires a complete understanding of your operations and materials, as well as the impact of the variables you wish to study and their impact on your operation. Understanding and selecting your population is critical to your ability to support effective decisions.

Probably one of the best anecdotes of understanding a population was from the story of Abraham Wald. Wald worked with the Statistical Research Group during the World War II. He was assigned to a project to improve protection of bombers during battle. The project studied the distribution of bullet holes in the aircraft that returned after battle to determine which parts of the aircraft should be armored. The military’s inclination was to armor the parts of the aircraft that were most damaged. Dr. Wald, however, recognized that despite the extensive damage, the studied aircraft survived their mission and returned home. Dr. Wald recommended that aircraft be armored in the areas that were unscathed on returning aircraft, surmising that damage in those areas were most likely to bring the bombers down.

Understanding your population, you can then select a reasonable accurate sample of observations to study. Statistical analysis on a sample should provide a fairly accurate estimate of the properties of the entire population. This should lead you to better decision-making.

There is much about statistics and probability to understand and learn. Knowing your statistics, however, provides you with a foundation to estimate the probability of events occurring given a set of circumstances. Certain vibration characteristics may indicate a greater possibility of component failure. Certain material properties may lead to a greater frequency of wrinkling or splitting. Variability in tonnage meter readings may indicate issues with hydraulics or a misalignment of your dies.

There is no real magic to it. Statistical analysis can provide you with a greater level of awareness of your operations and anticipate events and performance for better results.