Statistical Process Control 101

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The Problem with Tampering

When a process is centered on target and is in state of statistical control, any adjustments to the process only increase variation. Adjusting a process that is in control is referred to as tampering.

The Funnel Experiment and Deming’s Four Rules

The classic analysis of the effects of tampering is Deming’s Funnel Experiment. In this experiment, participants drop marbles through a funnel suspended over a target. The funnel represents the process, the marble drop location is the feature being produced, and the target is the customer specification.

Deming described four approaches—also referred to as rules—that encompass the typical ways in which the experiment participants tamper with the funnel (Out of Crisis, 1986, p. 328).

Rule 1: No adjustment

The optimal approach is to leave the funnel fixed and aimed at the target, without making any adjustments. When a process is stable, centered, and shows only the inherent variation, there is no reason to make an adjustment.

The takeaway: Before attempting any process adjustment, you must gather enough data to make sure you understand the normal behavior of the process. Use a control chart to track variations, and then adjust the process only when special variations occur.

 

Rule 2: Adjustment from last position

Sometimes referred to as the “human nature” approach, some participants move the funnel after each drop, to try and compensate for the previous drop’s variation. In this approach, the funnel is moved the exact negative distance of the drop. Compensating for the “error” of the drop, might improve the on-target average but doubles the variation.

The takeaway: When participants compensate for error, the variation doubles—and remember, variation is the true issue. This problem is prevalent in gauge calibration when manufacturers adjust a gauge after taking one standard measurement.

 

Rule 3: Adjustment from target

Participants trying to take a “logical” approach also move the funnel to try to compensate for the previous drop. But in this instance, the funnel is moved not based on its last location, but on its distance from the target. For example, if the measurement of the previous drop was 5 units above the target, participants move the funnel 5 units below the target.

The takeaway: Although this approach seems logical, it results in an oscillating process.

 

Rule 4: Adjustment from last drop

In this approach, participants move the funnel to point at the previous drop rather than the target. In other words, at drop n, they set the funnel over the location of the n-1 drop. As you might expect, this approach creates a pattern that moves steadily away from the target.

The takeaway: Believe it or not, this approach occurs in calibration scenarios when one product is used to set up for the next production. This issue is typical in workplaces where on-the-job training is prevalent.

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Statistical Process Control 101

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Statistical Process Control (SPC) Implementation

Statistical process control is certainly not the only technique used to improve processes. But for our purposes here, we will focus on two of the tools used most in SPC:

  • Histograms
  • Control charts

LEARN MORE: SPC TOOLS FOR ANALYSIS

Histogram

Histograms can provide a quick view of process variation and are used to plot frequency distributions.

Control chart

Control charts are the best-known tools associated with SPC.

Control charts are used to determine whether a process is stable or unstable. There are many types of control charts that can be used to fit the nature of different types of data streams and sampling methods.

Below are examples of the most commonly used control charts:

  • Variable data
    • Xbar-S: Xbar and standard deviation
    • Xbar–R: Xbar and range chart
    • IX–MR: Individual X and moving range chart
  • Attribute data
    • c: Defect count
    • u: Defect count, normalized to sample size
    • p: Proportion defective
    • np: Proportion defective multiplied by sample size

Control charts are discussed further in the Process Behavior and SPC Control Charts section as well as in our Definitive Guide to SPC Charts.

LEARN MORE: DEFINITIVE GUIDE TO SPC CHARTS

Although SPC charts are revealing, today’s manufacturers increasingly recognize the benefits of moving away from manual SPC—conducted by recording data on paper and then running analysis via offline spreadsheets or statistical software—and instead using real-time SPC software.

SPC Software

Quality control software for manufacturing offers multiple benefits:

  • Surface relevant information more quickly
  • Filter data according to role (e.g., operator, quality manager) and location (e.g., the lines being worked on that day)
  • Faster, focused, and more detailed analysis
  • Additional means of evaluating data (e.g., grading and stream summary)
  • Directed alerts and notifications
  • Mobile, enterprise-wide visibility into operations

InfinityQS is the leading provider of SPC software and services for manufacturers, providing quality intelligence solutions that work in the cloud or on-premises, across the globe.

LEARN MORE: SPC SOFTWARE FOR MANUFACTURING

Remember: Using statistical process control just to “put out fires”—finding an out-of-control point on a control chart and then determining and removing the assignable cause—is not the same as creating continuous improvement. SPC can be fully realized only when you use it to improve processes and reduce variation.

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Statistical Process Control 101

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Statistical Process Control FAQs

Still have questions about statistical process control (SPC)? Click the links below to locate information about popular topics.

What is SPC (statistical process control)?

Statistical Process Control (SPC) is a scientific, data-driven methodology for quality analysis and improvement. In manufacturing, SPC is an industry-standard methodology for measuring and controlling quality during the manufacturing process.

LEARN MORE:  WHAT IS SPC?

What are the origins of SPC?

Dr. Walter A. Shewhart (1891–1967), a specialist in the use of statistical methods, was responsible for the application of statistical methods to process control. Up until Shewhart, quality control methods were focused on inspecting finished goods and sorting out the nonconforming product. As an alternative to inspection, Shewhart introduced the concept of continuous inspection during production and plotting the results on a time-ordered graph that we now know as a control chart.

LEARN MORE: SPC 101

How does SPC relate to quality control in manufacturing?

By using statistical process control, manufacturers can move from a detection approach to a prevention approach, reducing or eliminating the need to rely on sorting or inspection. SPC can increase productivity, reduce waste, and reduce the risk of shipping nonconforming products.

LEARN MORE: WHY USE SPC IN MANUFACTURING?

How can I implement an SPC measurement system?

Control charts are used to determine whether a process is stable or unstable. However, using statistical process control just to “put out fires”—finding an out-of-control point on a control chart and then determining and removing the assignable cause—is not the same as creating continuous improvement. SPC can be fully realized only when you use it to improve processes and reduce variation.

LEARN MORE: STATISTICAL PROCESS CONTROL IMPLEMENTATION

What are statistical process control limits?

Control limits are calculated from the process itself. Because control limits show how the process is performing, they are also referred to as the “voice of the process.” Control limits show how the process is expected to perform; they show the variation within the system or the range of the product that the process creates.

LEARN MORE: SPECIFICATION AND CONTROL LIMITS

What are specification limits?

Specification limits are boundaries set by a customer, engineering, or management to designate where the product must perform. Specification limits are also referred to as the “voice of the customer” because they represent the results that the customer requires. If a product is out of specification, it is nonconforming and unacceptable to the customer.

LEARN MORE: SPECIFICATION AND CONTROL LIMITS

What are Shewhart statistical process control charts?

All control charts have three common elements:

  • Plot points: Plot points usually represent individual measurements, averages, standard deviations, or ranges.
  • Centerline: The centerline is usually (but not always) the average of the points plotted on the chart.
  • Control limits: Control limits represent the amount of variability in the process.

There are four foundational guidelines to Shewhart statistical process control charts.

LEARN MORE: SPC CONTROL CHARTS

What’s the best use of SPC control charts?

Control charts are used to determine whether a process is stable or unstable. There are many types of control charts that can be used to fit the nature of different types of data streams and sampling methods.

LEARN MORE: STATISTICAL PROCESS CONTROL (SPC) IMPLEMENTATION

How should I use SPC charts to determine process capability?

Capability is calculated from existing data but can be used as a prediction of future performance. However, the capability results must come from an in-control process if the results are to be used to predict the process’s behavior in the future. The most commonly used measures of capability are Cp, Cpk, Pp, and Ppk.

LEARN MORE: PROCESS CAPABILITY

Why do SPC initiatives fail, and how can I help ours succeed?

Statistical process control can help manufacturers achieve continuous process improvement—when it is implemented properly. Watch out for obstacles that can sideline your SPC efforts.

LEARN MORE: OVERCOMING OBSTACLES TO EFFECTIVE SPC

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Why Use SPC in Manufacturing?

Today’s consumers expect the best quality products at the lowest price. Why do manufacturers use SPC? Because statistical process control can help you meet both these demands.

By using statistical process control, manufacturers can move from a detection approach to a prevention approach, reducing or eliminating the need to rely on sorting or inspection. SPC can increase productivity, reduce waste, and reduce the risk of shipping nonconforming products.

Statistical Process Control Reduces Scrap

For many years, the term quality control meant inspecting to remove nonconforming products. Products are produced, then inspected to determine whether they are fit to be shipped to the customer. Products that aren’t acceptable are either scrapped or reworked. Sorting products is not only expensive—you’re basically paying one employee to make the product and another to make sure that the product is right—it’s also not very accurate. Studies have shown that 100% inspection is approximately 80% effective.

Statistical process control helps manufacturers escape this inefficient cycle. SPC leads to a system of preventing nonconforming product during the production process instead of waiting until products are complete to determine whether they are acceptable. This reduces waste, increases productivity, makes product quality more consistent, and reduces the risk of shipping non-conforming products.

When statistical process control is properly implemented, manufacturers foster an environment in which operators are empowered to make decisions about processes. In this way, processes—and product quality—can be continuously improved.

SPC is a powerful tool—but success depends on regular and proper application. Management must support its implementation through trust and education of employees and a commitment to supply the necessary resources.

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Histogram

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What is a Histogram?

A histogram is a graphical frequency distribution of raw data values. Histograms reveal the distribution of data values, compare them with specification limits, and generate useful metrics and statistics that describe the data set in detail.

When analyzing data, histograms are often used with statistical process control (SPC) control charts. That is, the same data used to create control charts can be used to create histograms. While control charts display data in time sequence, histograms do not. Instead, histograms show individual data values summarized and compared to engineering specifications.

Using Histograms

Histograms communicate the central tendency and spread of a data set. When compared with specification limits, histograms reveal how close the average of the data is to the engineering target. In the histogram below, the average (represented by the black vertical line) falls to the right of the target value. This indicates that the process is not centered. This fact is also indicated by the yellow bars, which show that most of the data values fall to the right of the target.

Histograms also allow users to compare individual data values to both upper and lower engineering specification limits. This allows quality professionals to access a variety of different statistics and improvement metrics.

This histogram represents the measurements of a feature, “Location C,” from a specific part, revealing the following important information:

  • The mean value is larger than the target value.
  • Data values are “bunching up” against the upper specification limit.
  • The yellow bars do not seem to match the normal curve fit.
  • No data value falls below the lower specification limit.
  • If unchanged, the process is expected to generate a loss of about 4.8% above the upper specification limit.

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See the Histogram in Action

Histograms can be combined with other SPC tools and control charts to reveal important quality information and opportunities for improvement at a plant—and even across sites.

Modern SPC software solutions make these complex analyses possible. When data is centralized and standardized in a unified data repository, SPC software provides instant access to quality information, ensuring immediate attention to your greatest quality challenges.

See how InfinityQS® reveals valuable quality information and makes SPC easy.

 

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SPC Control Charts

All control charts have three common elements:

  • Plot points: Plot points usually represent individual measurements, averages, standard deviations, or ranges.
  • Centerline: The centerline is usually (but not always) the average of the points plotted on the chart.
  • Control limits: Control limits represent the amount of variability in the process.

The Four Foundations of Shewhart’s Control Charts

There are four foundational guidelines to Shewhart statistical process control charts:

  1. Shewhart statistical process control charts always use control limits that are set to 3 sigma units on either side of the central line. These 3-sigma limits are always based on the chart’s data and define when action should be taken on the process. Control limits are never based on any calculation using the specification limits. Specification limits are the customer requirements and define how to treat the product, not the process.
  2. Always use an average dispersion statistic or a median dispersion statistic when computing 3-sigma control limits. Using the average or median of several dispersion statistics increases the robustness of the chart.
  3. The conceptual foundation of Shewhart’s charts is the notion of rational sampling and subgrouping.
  4. Control charts are effective only to the extent that the organization can effectively use the knowledge gained to take action.
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Process Capability

Process capability is calculated from existing data but can be used as a prediction of future performance. However, the process capability analysis results must come from an in-control process if they are to be used to predict the process’s behavior in the future. The most commonly used measures of capability are Cp, Cpk, Pp, and Ppk.

Remember, in-control means that the process is showing primarily common cause variation and so is both stable and predictable. Also remember, a process can be within control limits and still be outside product specification limits.

What is Process Capability? Hearing Two Voices

As mentioned earlier, a 6-sigma range (+3 standard deviations) is the voice of the process and show only the expected variability of the process itself. Specification limits are the voice of the customer and represent what the customer expects. The graphic below shows a process that is consistently making product that is out of specification.

Process Capability

SPC Cp Index

The SPC Cp index shows how well the 6-sigma range fits into the specification range. This measurement is determined by dividing the specification limit (voice of the customer) by the control limit (voice of the process).

Formula for Cp calculation

To calculate Cp, use the following equation:

Process Capability

For example: A Cp value of 1 means that the process variation equals the specification limit range. The process is thus capable (but just barely) of meeting the customer’s criteria.

The Cp index does not consider how well (or how badly) the process is centered relative to the specification limit target. Therefore, the Cp is a measure of optimum capability (i.e., what the process is capable of if it were centered, not what the process might be doing).

SPC Cpk Index

Like the Cp index, the Cpk calculation shows the relationship of the 6-sigma spread to the specification limits, however, the Cpk considers the centering of the process. There are two Cpk values calculated, one that considers the upper specification limit and another that considers the lower specification limit. The reported Cpk, however, represents the lowest value of the capability against the upper or lower specification. Cpk shows where within the specification limits the process is currently producing, not what the process is capable of producing. To determine whether the process is capable, you must measure Cp.

Cp Versus Cpk

When the process is centered, the Cp and Cpk calculate to be the same number. However, as the process output deviates from the target value, so do the Cp and Cpk ratios. Some observations to consider looking at the graphic below:

  • The Cp value remains the same because the width of the distribution is constant.
  • Cpk = 0 when the process mean equals one of the specification limits.
  • Cpk < 0 when the process mean exceeds one of the specification limits.
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Quality Checks

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Use Data to Build Your Quality Manufacturing Strategy

At the most fundamental level, quality manufacturing hinges on quality checks. Data collected through quality checks is used to measure product and process quality, pinpoint places where operations can improve, and inform future strategies.

In order for quality checks to deliver meaningful insights, they have to be accurate, timely, complete, and appropriate. Leveraging statistical process control (SPC), manufacturers can hone in on the right metrics to watch and ensure data collection is consistent and precise—and that it’s providing needed information to make good business decisions.

InfinityQS SPC-based quality management solutions enable data collection options that help ensure key quality actions are attended to, whether that’s data collection, analysis, or investigation. With InfinityQS, operators are empowered to perform necessary quality checks and can take immediate steps to protect product quality.

Paper-based manufacturing quality checks are a costly option. Modernizing data collection saves more than you think.

How to Control Quality in Manufacturing? It Starts with Data

To make good decisions, you need good data. How do you collect the right information to assess and improve your quality manufacturing processes?

Compared to digital solutions, paper-based SPC data collection is expensive, inefficient, and even risky. Paper-based data collection is fraught with the potential for error and requires significant human resources to complete lower-value tasks, like managing supplies and filing or retrieving documents.

Gleaning usable information from a stack of papers—or dozens of spreadsheets—is costly too. Using paper, critical information is inaccessible, leading to missed opportunities to reduce risk, waste, or defects because the analytical process is too cumbersome and time-consuming.

QualityChecks_Check

Software Simplifies Data Collection

SPC-based quality software simplifies data collection and speeds up important quality checks, supporting streamlined data intake, reporting, and analysis with little to no IT involvement. In addition, modern quality solutions integrate into your existing quality workflows and manufacturing processes.

Because quality control in manufacturing is constantly evolving, modern quality management solutions allow for a mix of manual, semi-automated, and fully automated data collection.

  • Manual—Data collection can easily shift from pencil and paper to keyboards, touchscreens, or barcodes and become part of the “bigger picture.”
  • Semi-automated—Operators can use connected scales, calipers, gauges, and custom devices to collect quality information when they’re on the plant floor.
  • Fully Automated—Data from enterprise resource planning systems, automated test equipment, programmable logic controllers (PLCs) and “smart” sensors can feed directly into your InfinityQS quality improvement system without operator intervention.

No matter how or when data is collected, InfinityQS stores everything in a central data repository, along with the time, date, and shift. Once data is entered, anyone who’s responsible for quality—from operators to executives—can access, analyze, and act on the information.

Quality Alerts: Stay Focused on Quality, Not the Clock

Software brings standardization and consistency to quality checks, especially for time-based collections. Built-in alerts and scheduled reminders ensure that every timed check occurs on schedule, regardless of plant, shift, or machine. InfinityQS supports timed quality checks with:

  • countdown clocks that monitor the schedule
  • automatic notifications when checks are due
  • manager notifications when a check is missed
  • automatic assignment of rechecks or operator validation when data falls out of specification

Disciplined Data Collection, Flexible Management

When collection requirements or processes change, it’s easy to adapt digital collection processes and cascade that information throughout the organization. Managers simply adjust the data-collection requirements in the software, and they can include relevant information and instructions in the quality check notifications.

Testing requirements and standard operating procedures (SOPs) can be managed in the same way. Once the requirements and notification schedules are established, the software will trigger compliance workflows and automatically save data from the plant floor to a central repository.

Collect the Right Data, Right Now

Do you have the information you need to make strategic decisions and improve quality? InfinityQS software makes it easier to collect, access, and analyze the right information for your quality improvement journey.

Move Faster While Improving Product Quality in Manufacturing

When InfinityQS helped a semiconductor manufacturer transition from manual to software-based data collection, the company went from multiple, duplicate collection steps to one. Streamlining quality checks enabled the company to:

  • Save time and simplify operator processes
  • Improve the accuracy and timeliness of quality data
  • Quickly identify and correct errors
  • Improve operator morale
  • Identify opportunities to learn and improve

A manufacturing engineer at the company said the whole manufacturing atmosphere changed “from the drudgery of manually recording data and sending it into a black hole to a feeling of ownership as people instantly saw their names and the data they entered.”

“As the projects and operators advance, we only expect to move faster and faster—with the same integrity,” he said.

Read the Case Study

Proving Quality Check Compliance: Hit the “Easy Button” on Audits

Industry audits are high-stakes events. SPC software can ease some of the stress by making data collection, storage, and retrieval a cinch.

  • InfinityQS makes it quick and easy to prove that quality checks were completed correctly and on time.
  • Reports can be customized (e.g., by shift, day, or event) and produced in minutes, since all of your quality data are held in a centralized and standardized repository.
  • Information can be accessed from anywhere, anytime.

A purpose-built quality management solution can reduce audit prep and reporting time from days or weeks to mere minutes.

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Box-and-Whisker Plots

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What is a Box-and-Whisker Plot?

A box-and-whisker plot is a well-known statistical process control (SPC) comparative analysis tool that can help you eliminate process variation. Use box-and-whisker plots to compare product and process performance, even on different lines or in different plants.

Like a histogram, box-and-whisker plots reveal the distribution of data values. Instead of a histogram’s frequency distribution, box-and-whisker plots represent the distribution with percentiles.

Box-and-Whisker Plots Explained

Vertical lines on box-and-whisker plots represent percentiles. The leftmost point on each horizontal line (or “whisker”) represents the minimum value while the rightmost dot represents the maximum value. The line in the center of each box represents the 50th percentile. The box itself spans from the 25th to the 75th percentile. The vertical lines on the whiskers represent the 5th and 95th percentiles.

Use Box-and-Whisker Plots for Rapid Insights

In a screen display, box-and-whisker plots are more compact than histograms, enabling several plots to share the same screen space. This means you can easily compare multiple plots. You can quickly compare central tendency and variability for each data set represented by box-and-whisker plots.

Compare Against Specification Limits

To extract even more valuable information, box-and-whisker plots can be compared against specification limits. This allows the viewer to understand which data sets are generating the most (and least) out-of-specification issues. As a result, box-and-whisker plots are ideal tools for prioritizing quality activities and Six Sigma projects.

Compare Multiple Process Streams

Box-and-whisker plots are particularly useful for viewing the performance of multiple process streams in the same interface. This capability is useful in any industry that needs to compare performance between production lines, product codes, and shifts.

For example, in food packaging organizations, minimum fill weights are regulated. Underfilling can result in fines or sanctions; overfilling can significantly increase costs.

Box-and-whisker plots quickly reveal vitally important information such as:

  • Whether products are being filled to minimum required levels
  • The presence and amount of overfill
  • Which products run best on which production lines
  • Which production lines run the same product weights higher (or lower) than others
  • Whether different shifts fill consistently
  • Average fill volumes
  • Variability in fill volumes
  • Where out-of-specification issues occur the most

Take Another Look at In-spec Data

With the box-and-whisker chart, you can easily discover best practices and opportunities for improvement. Plus, you can examine in-spec data to find savings you might never have expected.

See the Box-and-Whisker Plot in Action

InfinityQS® SPC software solutions provide fast and easy access to box-and-whisker charts, without a great amount of time-consuming manual data entry or analysis. See how easy it can be to spot trouble—or opportunities—by surfacing this information from within SPC software.

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