Six Sigma in a Sterilization Central: Design of Experiments (DoE) for improving Process Efficiency

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This article investigates the application of Six Sigma, a process improvement methodology typically associated with manufacturing, to the example of a centralized sterilization process in a hospital network, specifically the use of Design of Experiments (DoE), a systematic approach to investigating how various factors influence a process outcome.

In the bustling world of hospitals, sterilization plays a paramount role. Imagine a central sterilization department, responsible for a vast array of surgical instruments, each having their own unique needs and challenges. In recent times, healthcare professionals have found an unexpected ally in their quest to optimize this crucial process and reduce the number of surgical instruments that cycle through their sterilization system. This ally comes in the form of an approach developed in the manufacturing industry: Six Sigma, and specifically, a powerful tool within its repertoire, Design of Experiments (DoE).

At its heart, Six Sigma is a disciplined methodology aimed at improving processes by reducing errors and variability. One might ask how a method bred in the world of manufacturing relates to healthcare, and in particular, hospital sterilization. Well, just as a production line churns out products, a hospital churns out sterilized surgical instruments. The fundamental objective in both scenarios is the same: create an efficient, reliable, and high-quality process.

What is the Design of Experiments (DoE) method?

Design of Experiments (DoE) is a particular tool used within Six Sigma that allows teams to learn more from their processes and make educated improvements. It’s like a master detective kit for processes, enabling us to scientifically and systematically determine how different factors are influencing our outcomes.

In the case of hospital sterilization, let’s consider the variety of surgical instruments to be sterilized as one factor. Others might include the type of sterilization method used, the number of sterilization cycles, the duration of sterilization, and even the sterilization technician’s experience. Each of these factors can be tweaked or adjusted, a bit like adjusting the dials on a control panel.

Here’s where DoE becomes critical. Rather than randomly adjusting the ‘dials’ and hoping for the best, DoE allows us to plan and execute a series of experiments. We methodically change the factors and observe the results. For example, we might change the type of sterilization method for a specific set of instruments and see if it reduces the number of instruments requiring sterilization.

Design of Experiments (DoE) is a statistical tool used in a structured and systematic way to investigate the relationship between factors affecting a process and the output of that process. The goal of DoE is to understand these effects in order to optimize process variables, with an emphasis on efficiency, reliability, and quality control.

When using DoE, the process variables, or factors, that could influence the outcome are varied in a planned and structured manner. These factors can be anything that can be manipulated in the process. For instance, in a manufacturing setting, it could be temperature, pressure, or raw material composition. In a hospital sterilization process, factors could include the type of sterilization method, the duration of sterilization, the type of instrument being sterilized, the training level of the technician, etc.

By systematically varying these factors, DoE allows us to study their effects on the outcome. It helps us identify which factors have a significant impact on the outcome, which ones do not, and whether there are any interactions between factors that influence the outcome.

By analyzing these results, we can start to understand the relationship between the different factors and the outcome we’re trying to influence—the number of surgical instruments going through sterilization. We might discover that certain types of instruments are more effectively sterilized with a specific method or that adjusting the sterilization cycle duration can improve efficiency for some instruments but not for others.

This new-found knowledge helps us tune our process dials to their most effective settings. With continued application and adjustment, we can streamline our sterilization process, reducing the number of instruments requiring sterilization and increasing the overall efficiency of our hospital network’s sterilization centers.

Setting up the experiments

Setting up an experiment in the framework of Design of Experiments (DoE) involves a systematic approach. Here’s a step-by-step guide to the process:

• Define the Problem and Objectives: The first step is to clearly define the problem you are trying to solve and the objectives of the experiment. The objectives should be SMART (Specific, Measurable, Achievable, Relevant, and Time-bound).
• Choose the Response Variable: The response variable (also known as the output or dependent variable) is what you’re interested in studying. It should be quantifiable and directly related to the objective of the study. In a hospital sterilization process, for instance, the response variable could be the sterilization effectiveness or the sterilization time.
• Identify the Factors Factors: Also known as input or independent variables, these are the variables you think might influence the response variable. They could be controllable factors like sterilization temperature, duration, and method, or uncontrollable factors like room temperature, humidity, etc.
• Determine the Levels of the Factors: For each factor, decide on the levels you’ll test during the experiment. Levels are the different values that a factor can take. If you’re testing the effect of sterilization temperature, for instance, you might choose three levels: low, medium, and high temperatures.
• Select the Experimental Design: Choose an appropriate design that suits your objective, number of factors, and resource availability. Common designs include full factorial (where all possible combinations of factors and levels are tested), fractional factorial (where only a subset of combinations is tested), and response surface designs (used for optimizing a process).
• Conduct a Pilot Study (Optional): A small-scale pilot study can be useful to test the feasibility of the experiment, identify potential problems, and get an estimate of the variability in the response variable.
• Randomize: Randomization is a crucial aspect of any experiment as it helps to minimize the impact of uncontrolled or unknown variables. Ensure that the order in which experimental runs are performed is randomized.
• Conduct the Experiment: Perform the experimental runs as per the chosen design, ensuring that conditions are kept as consistent as possible across runs. Record the data meticulously.
• Analyze the Data: Once you have collected the data, use statistical analysis methods to determine the effects of the factors, their significance, and potential interactions.
• Validate the Findings: Conduct additional experiments at the optimized settings to ensure the process performs as predicted and to validate the experimental model.

Evaluate the most important factors

A number of statistical methods are used to analyze the results of a Design of Experiments (DoE) to determine the significance of the effects of different factors and their interactions. Some of these methods include:

1. Analysis of Variance (ANOVA): This is one of the most common methods used in DoE. ANOVA is used to determine whether there are significant differences between the means of several groups. In the context of DoE, these groups are defined by the different levels of each factor. The outcome of the ANOVA analysis can tell you whether any of the factors had a significant effect on the response.

2. Regression Analysis: Regression analysis is often used in conjunction with ANOVA in DoE. A regression model is built using the factors and their interactions as predictors and the response variable as the outcome. The coefficients in the regression model represent the effects of the factors and their interactions, and statistical tests can be used to determine which effects are significant.

3. Factorial Effects and Interaction Plots: These are graphical methods used to visualize the effects of factors and their interactions. A main effects plot shows the effect of each factor on the response variable, and an interaction plot shows the effect of two factors simultaneously.

4. Pareto Charts of the Effects: A Pareto chart can be used to visually represent the magnitude and significance of the effects. The chart consists of bars that are proportional to the absolute value of the effect estimates and ordered so that the largest effects are on the left. A reference line is often added to the chart to indicate the level of significance (usually 0.05). Effects that extend past this line are considered statistically significant.

5. Response Surface Methodology (RSM): This is a collection of statistical and mathematical techniques used for developing, improving, and optimizing processes. RSM uses regression modeling to create a mathematical model that represents the process, which can then be used to find the optimal settings.

A practical example

The task is to identify factors affecting the number of non-conforming surgical instruments during a sterilization process. The factors identified are:

1. Transport time (trans_t): The time it takes to transport surgical instruments from the operating room to the sterilization unit. It’s categorized into three levels: short, medium, and long (so, me, lo).
2. Container Condition (st_of_cont): The physical state of the surgical instrument transport containers. This is categorized into two levels: new and old.
3. Water Quality (w_qual): The water quality used in the sterilization process. It’s categorized into two levels: treated and untreated (tr, untr).
4. Operator Experience (op_exp): The level of experience of the sterilization process operators. This is categorized into two levels: experienced and inexperienced (exp, inexp).

import numpy as np
import pandas as pd
import statsmodels.api as sm
import statsmodels.formula.api as smf

# Define the levels of the factors
trans_t = ['sh', 'me', 'lo']
st_of_cont = ['new', 'old']
w_qual = ['tr', 'untr']
op_exp = ['exp', 'inexp']

# Generate hypothetical data
np.random.seed(0)  # for reproducibility
data = pd.DataFrame({
    'trans_t': np.random.choice(transport_time, 100),
    'st_of_cont': np.random.choice(state_of_containers, 100),
    'w_qual': np.random.choice(water_quality, 100),
    'op_exp': np.random.choice(operator_experience, 100),
    'non_conf': np.random.choice([0, 1], 100)  
               # 0: conforming, 1: non-conforming
})

# Convert the categorical variables into dummy/indicator variables
data_encoded = pd.get_dummies(data, drop_first=False)

In the Python code above, we first generate some hypothetical data based on these factors. We then convert these categorical factors into a form suitable for analysis using a technique known as one-hot encoding. This process creates new binary (0 or 1) columns for each category of each factor. The naming convention used is to take the original factor name and append the category after an underscore.

So, transport_time becomes transport_time_medium and transport_time_long (with transport_time_short being the baseline category that's dropped), state_of_containers becomes state_of_containers_old (with state_of_containers_new as the baseline), and so on.

# show the first 10 rows of data 
# both the original and the enconded data for comparison.

from tabulate import tabulate

print(tabulate(data[:10], headers='keys', tablefmt='psql'))

print(tabulate(data_encoded[:10], headers='keys', tablefmt='psql'))

original data

Encoded data

We then use logistic regression to model the probability of a non-conformance (i.e., a surgical instrument failing to meet quality standards) based on these factors. Logistic regression is a type of statistical model used for predicting the probability of categorical outcomes, in this case, conforming (0) or non-conforming (1).

The logistic regression model is then fitted using the one-hot encoded data, and a summary of the model fit is printed out. This summary provides information about the effect of each factor on the likelihood of non-conformance, the statistical significance of each factor, and the confidence intervals for the effect sizes.

By examining the results, one can understand which factors significantly affect the likelihood of non-conformance and therefore need to be controlled or modified to improve the overall quality of the sterilization process.

Specify the logistic regression model
model = smf.logit('non_conformance ~ transport_time_medium + 
                  transport_time_long + state_of_containers_old + 
                  water_quality_untreated + operator_experience_inexperienced',
                  data=data_encoded)

Fit the model
result = model.fit()

Print the summary
print(result.summary())

Analysis

Each row in the output represents one of the factors in the model, and the columns provide different pieces of statistical information about each factor. Let’s go through the important parts:

1. coef (coefficient): This column shows the effect size for each factor. The coefficients represent the change in the log-odds of a non-conformance for a one-unit increase in the corresponding predictor variable, holding all other predictors constant. For example, the coefficient forwater_quality_untreated is 0.8118, indicating that using untreated water (compared to treated water) is associated with an increase in the log-odds of a non-conformance by about 0.8118, all else being equal.
2. P>|z| (p-value): This column shows the p-values for the tests of the null hypothesis that each coefficient is zero, given that the other predictors are in the model. A small p-value (usually less than 0.05) indicates strong evidence that the coefficient is different from zero. For example, the p-value for water_quality_untreated is 0.059, which is slightly higher than the common threshold of 0.05, suggesting that the water quality may not have a significant effect on the probability of non-conformance at a 5% significance level.
3. [0.025, 0.975] (Confidence Interval): These two columns show the lower and upper bounds of the 95% confidence interval for each coefficient. This interval provides an estimated range of values that is likely to include the true unknown parameter in the population based on the observed data from our sample. For example, the confidence interval for the water_quality_untreated coefficient is from -0.031 to 1.655. Since this interval includes zero, it indicates that we can't be confident at the 95% level that the water quality has a non-zero effect on the probability of non-conformance.

Based on this output, none of the factors appear to have a statistically significant effect on the likelihood of non-conformance at a 5% significance level, as all p-values are greater than 0.05. However, water_quality_untreated has the smallest p-value and could potentially be significant at a higher significance level.

Also, note that the p-value for the overall model (LLR p-value) is 0.4879, suggesting that the model as a whole does not provide a significantly better fit to the data than an intercept-only model.