3.7 Quality Tools and Techniques in Supply Chain

Here are some of the most common tools and techniques used to manage and monitor Quality in the Supply Chain.

Statistical Process Analysis is a powerful tool used in the field of Supply Chain Management to measure, control, and improve the quality of processes. It allows organizations to make informed decisions and predictions based on data, improving overall efficiency and customer satisfaction. The following are some of the crucial statistical concepts in process analysis:

• The Normal Distribution and Central Limit Theorem: In Supply Chain Management, many processes naturally follow a Normal Distribution – a bell-shaped curve that represents a large number of random variables added together. This distribution is characterized by its mean (the peak) and standard deviation (the width of the curve). The Central Limit Theorem is particularly important as it states that when an adequately large sample size is taken, the sampling distribution of the mean will approach normality, regardless of the shape of the population distribution. This property allows us to make predictions and inferences about the process under observation.
• Mean, Standard Deviation, Variance: Mean is the average value in a dataset, providing a glance at where values tend to cluster. Standard deviation is a measure of the spread of data points from the mean, and variance is the square of the standard deviation. In the context of a supply chain, these measures can help identify variability in processes, for instance, in delivery times, product quality, or production costs. High variability might signal a need for process improvement or better supplier management.
• Confidence Intervals: Confidence intervals provide a range in which the true population parameter is likely to lie with a certain degree of confidence. In Supply Chain Management, these are used to estimate parameters such as average delivery time, defect rate, or customer satisfaction level. This statistical method is essential when trying to make decisions under uncertainty.
• Applying Statistics to Make Predictions: Supply Chain Management often involves forecasting demand, predicting lead times, or anticipating defects. By leveraging statistical tools, organizations can predict future outcomes based on historical data. Techniques such as regression analysis, time series analysis, and predictive modeling play an essential role in these forecasting activities.
• The Importance and Selection of Sample Size for Statistical Significance: The sample size plays a critical role in statistical analysis. A larger sample size reduces the effect of random variation, providing a better estimate of the true population parameter and increasing the likelihood of achieving statistical significance in hypothesis testing. However, practical considerations, such as cost and time, also influence the decision on the sample size. In supply chain activities, like quality control or customer satisfaction surveys, determining an adequate sample size is crucial to make reliable decisions based on the data.

Statistical Process Analysis helps organizations maintain control over their processes, identify opportunities for improvement, and make informed, data-driven decisions in Supply Chain Management. By leveraging these statistical tools, supply chain managers can improve quality, reduce costs, and enhance customer satisfaction.

Process capability is a vital statistical measure used in Quality Management within the Supply Chain to assess the ability of a process to meet the specifications or customer requirements. It provides an objective measure of the inherent process variability and the potential for defects, making it an essential tool for continuous improvement.

Process Capability is a statistical measure that quantifies how well a process can deliver the output within the required specification limits set by the customer. It considers the variability of the process and the centeredness between the process mean and the desired target. This measurement is significant as it allows organizations to predict the future performance of their process, identify the causes of variability, and determine areas for process improvement.

Process Capability (Cp) and How to Determine It

Cp is a measure of the process capability, assuming the process is centered within the specification limits. It’s calculated by taking the difference between the Upper Specification Limit (USL) and Lower Specification Limit (LSL), divided by 6 times the standard deviation of the process.

Formula: [latex]C_p = \dfrac{USL - LSL}{6σ}[/latex]

For example, if a supply chain process has a USL of 10, an LSL of 4, and a standard deviation of 1, the Cp would be (10-4) / (6*1) = 1. This means the spread of the process fits exactly within the specification limits.

Adjusted Process Capability (Cpk) and How to Determine It

Cpk is an adjusted process capability index that takes into account the shift of the process mean from the center of the specification limits. It’s calculated by determining the minimum value of the quantity (USL – μ) / (3σ) and the quantity (μ – LSL) / (3σ), where μ is the process mean.

Formula: [latex]C_p = min[\dfrac{USL - μ}{3σ}, \dfrac{μ - LSL}{3σ}][/latex]

For example, if the process mean is 7, then the Cpk is [latex]min [\dfrac {(10 - 7)}{(3*1)}, \dfrac{(7 - 4)}{(3*1) }][/latex] = min [1, 1] = 1. This indicates that the process mean is exactly at the center of the specification limits.

Strategies and Tactics for Resolving Process Capability Issues

When a process is not capable (Cp or Cpk less than 1), actions are required to improve the capability. Here are the most common approaches to resolving this issue:

• Process Centering: If the process mean is not centered within the specification limits (Cp is high, but Cpk is low), efforts should be made to shift the process towards the center.
• Process Improvement: If the process variability is high (both Cp and Cpk are low), methods like Six Sigma, Lean Manufacturing, or Design of Experiments can be used to identify the root causes of variability and reduce them.
• Adjusting Specification Limits: In some cases, it might be possible to renegotiate the specification limits with the customers to make them more in line with the process capability.
• Supplier Management: In supply chain processes, supplier quality management can also help improve process capability by ensuring the quality of incoming materials.

By understanding and utilizing Cp and Cpk, supply chain managers can effectively control their processes, improve quality, reduce costs, and ensure customer satisfaction.  Finally, it should be noted that while a Cp or Cpk of greater than 1 indicates that the process is capable, most companies strive for a value of at least 1.33 [4 sigmas] or higher to ensure that the process will consistently deliver the desired results.  For critical requirements such as safety items, a value of greater than 1.5 is recommended.

Statistical Process Control (SPC) is a method of quality control that employs statistical methods to monitor and control a process, ensuring that the process operates at its full potential. SPC is widely used within Supply Chain Management to improve process capability, reduce variability, and enhance customer satisfaction.

The purpose of SPC is to provide a statistical signal when assignable causes of variation are present. These are variations that are not inherent to the process and can be identified and eliminated. By identifying these signals, an organization can focus its efforts on process improvement, thereby reducing waste and improving product or service quality. SPC can be applied in any context where processes are repeatable and can be measured, which includes virtually every aspect of Supply Chain Management, from manufacturing and logistics to procurement and customer service.

Examples of SPC in Business

In manufacturing, SPC can be used to monitor and control production processes. For instance, a company might use control charts to track the thickness of metal sheets, the weight of filled containers, or the delivery time of products. By identifying out-of-control conditions early, the company can take corrective action before defective products are produced, saving costs and protecting its reputation.

In service industries, SPC can also play a vital role. For example, a logistics company might use control charts to monitor package delivery times, aiming to identify and eliminate causes of delays. Similarly, a procurement department could use SPC to monitor supplier performance, ensuring that products and services meet specified quality criteria.

The Generic SPC Chart and Out-of-Control Patterns

A typical SPC chart, known as a control chart, includes a center line that represents the process mean, and upper and lower control limits that represent the expected range of process variation. Data points are plotted over time, allowing for visual inspection of the process behavior.

Several patterns might suggest out-of-control conditions:

• Point outside control limits: A single point outside the control limits is a strong signal of an out-of-control condition.
• Run of points on one side of the center line: Several consecutive points on one side of the center line suggest a systematic bias in the process.
• Trend: Several consecutive points steadily increasing or decreasing indicate a trend.
• Cycles: Repeating patterns of points suggest cyclical effects, perhaps linked to operational conditions or external factors.
• Instability: High variation, erratic behavior, or sudden shifts in process level can indicate instability.

By using SPC charts and recognizing these patterns, supply chain managers can monitor their processes in real time, identify process issues before they escalate, and continuously improve process performance, leading to enhanced quality and customer satisfaction.

SPC for Variable Data: X-bar and R Charts

For variable data, two kinds of charts are typically used: X-bar and R-charts. An X-bar chart monitors the process mean over time, while an R chart (Range chart) monitors variability. The X-bar chart helps detect shifts in the process mean, while the R chart identifies changes in process dispersion. Both charts are usually used together as a change in the dispersion can affect the process mean and vice versa.

Steps and Formulas to Create an X-Bar Chart

An X-bar chart is created using the following steps:

• Collect several samples of data from your process.
  The sample size (n) should be consistent for each sample.
• For each sample, calculate the average (X-bar). The formula is:
  [latex]\bar{X} = \dfrac{(ΣX)}{n}[/latex]
  Where ΣX is the sum of individual measurements within a sample.
• Plot these averages on the X-bar chart.
• Calculate the overall process average (the grand mean or X-double-bar) and draw a centerline at this value.
• Calculate the upper control limit (UCL) and lower control limit (LCL). These are typically set at 3 standard deviations above and below the centerline.
  For an X-Bar chart, the formulae are:
  [latex]UCL = \bar{\bar{X}} + A_2\bar{R}[/latex]
  [latex]LCL = \bar{\bar{X}} - A_2\bar{R}[/latex]
  Where A₂ is a factor depending on sample size, [latex]\bar{\bar{X}}[/latex] is the grand mean, and [latex]\bar{R}[/latex] is the average range.

Note: If the LCL_x is negative, it is set to zero, since you can’t have a negative sample average.

Steps and Formulas to Create an R Chart

An R chart is created using the following steps:

• Calculate the range (R) of each sample. The range is the difference between the maximum and minimum values in the sample.
• Plot these ranges on the R chart.
• Calculate the average range (R-bar) and draw a centerline at this value.
• Calculate the upper control limit (UCL) and lower control limit (LCL). These are typically set at 3 standard deviations above and below the centerline.
  For an R chart, the formulae are:
  [latex]UCL_r = D_4\bar{R}[/latex]
  [latex]LCL_r = D_3\bar{R}[/latex]
  Where D4 and D3 are factors depending on the sample size.

Note: If the LCLr is negative, it is set to zero, since you can’t have a negative range.

X-bar and R Charts Example

Let’s consider a specific scenario in which we’re inspecting the weight of packaged products in a warehouse. We’ll gather eight samples, each containing five observations, over an eight-hour shift:

Calculating X-bar and R Values for Each Sample

X-bar is the average of each sample, and R (Range) is the difference between the highest and lowest observations in the sample. Therefore, here are the calculated values:

Calculating X-double-bar and R-bar Centerlines

X-double-bar is the average of all X-bars, and R-bar is the average of all R values. Therefore, here are the calculated values:

            [latex]\bar{\bar{X}} = \dfrac{(21.6 + 22.4 + 23.2 + 23.6 + 24.8 + 25.4 + 25.6 + 25.6)}{8} = 24.1[/latex]

            [latex]\bar{X} = \dfrac{(3 + 3 + 2 + 3 + 2 + 3 + 3 + 3)}{8} = 2.75[/latex]

Calculating UCLx, LCLx, UCLr, and LCLr Control Limits

The formulas for these are as follows:

            [latex]UCL = \bar{\bar{X}} + A_2\bar{R},  LCL = \bar{\bar{X}} - A_2\bar{R}[/latex]

            [latex]UCL_r = D_4\bar{R},  LCL_r = D_3\bar{R}[/latex]

Where A₂, D₄, and D₃ are constants that depend on the sample size. For a sample size of 5, A₂ = 0.577, D₄ = 2.114, and D₃ = 0.

Here are the calculations for our example:

            UCL_x = 24.1 + 0.577 * 2.75 = 25.69;  LCL_x = 24.1 – 0.577 * 2.75 = 22.51

            UCL_r = 2.114 * 2.75 = 5.81; LCLr = 0 * 2.75 = 0

Drawing the X-Bar and R-Charts

Interpreting the X-Bar and R-Charts

The X-bar chart shows the average weight for each sample. The points should be plotted around the center line (X-double-bar) at 24.1, with upper and lower control limits at 25.69 and 22.51 respectively. If all points lie within these limits and no patterns are seen, it’s evidence the process is in control regarding its central tendency.

The R chart shows the range of weights for each sample. The points should be plotted around the center line (R-bar) at 2.75, with upper and lower control limits at 5.81 and 0 respectively. If all points lie within these limits and no patterns are seen, it’s evidence the process is in control regarding its dispersion.

Together, these charts provide a clear picture of process stability, both in terms of its average and variability. As a supply chain manager, this information is critical for identifying potential issues and implementing quality control measures.

Statistical Process Control (SPC) for Attribute Data: P Charts and C Charts

Unlike variable data, which are numerical and can be measured, attribute data are categorical and can be counted. In supply chain management, examples of attribute data could include the number of defective items in a shipment, the number of delayed deliveries in a month, or the number of customer complaints about a product.

SPC charts used for attribute data include P charts and C charts.

A P chart is used when we want to monitor the proportion of nonconforming units in different samples, where the sample size may vary. For example, we could use a P chart to track the proportion of defective items in daily shipments, where the number of items in each shipment varies.

A C chart, on the other hand, is used when we want to monitor the number of nonconformities in a constant-size sample. For example, we could use a C chart to track the number of defects found in every batch of 100 items inspected.

Creating a P Chart

To create a P chart, the following steps are undertaken:

• Calculate the proportion nonconforming (p) for each sample: [latex]p = \dfrac{number\ of\ nonconforming\ units}{sample\ size}[/latex].
• Calculate the average proportion nonconforming (P-bar): [latex]\bar{P} = \dfrac{sum\ of\ all\ p}{number\ of\ samples}[/latex]
• The control limits for a P chart are calculated as follows:
• Upper Control Limit (UCLp) = [latex]\bar{P} + 3 * \sqrt {\dfrac{\bar{P}(1-\bar{P})}{n}}[/latex]
• Lower Control Limit (LCLp) =  [latex]\bar{P} - 3 * \sqrt {\dfrac{\bar{P}(1-\bar{P})}{n}}[/latex]
• n is the sample size
  • In the case that the sample size varies, n in the formula would be the average sample size.

Note: If the LCL_p is negative, it is set to zero, since you can’t have a negative number of non-conformities.

Example: Creating and Interpreting a P chart

Consider a manufacturer that performs daily inspections for defective items, where due to variations in production, the sample size changes every day. The quality control team decides to use a P chart to monitor the proportion of defective items each day.

Here is a week of sample data:

– Day 1: 100 items inspected, 5 defective items found

– Day 2: 150 items inspected, 10 defective items found

– Day 3: 200 items inspected, 15 defective items found

– Day 4: 100 items inspected, 7 defective items found

– Day 5: 150 items inspected, 9 defective items found

– Day 6: 200 items inspected, 11 defective items found

– Day 7: 150 items inspected, 8 defective items found

Calculate the proportion nonconforming (p) for each sample

The proportion nonconforming is calculated as the number of defective items divided by the number of items inspected each day:

– Day 1: p₁ = 5/100 = 0.05

– Day 2: p₂ = 10/150 = 0.067

– Day 3: p₃ = 15/200 = 0.075

– Day 4: p₄ = 7/100 = 0.07

– Day 5: p₅ = 9/150 = 0.06

– Day 6: p₆ = 11/200 = 0.055

– Day 7: p₇ = 8/150 = 0.053

Calculate the average proportion of nonconforming (P-bar)

Step1: Calcuate P-bar as the sum of all proportions divided by the number of samples:

[latex]\bar{P} = \dfrac{p_1+p_2+p_3+p_4+p_5+p_6+p_7}{7}[/latex]

[latex]\hspace{0.55cm}=\dfrac{0.05+0.067+0.075+0.07+0.06+0.055+0.053}{7}[/latex]

Step 2: Calculate the average sample size (n-bar)

Since in this example we are with a P-chart where the sample size varies, the ‘n’ in the control limit formulas is replaced with the average sample size (n-bar).

To calculate the n-bar, we sum all sample sizes and divide by the number of samples as follows:

[latex]\bar{n} = \dfrac{100 + 150 + 200 + 100 + 150 + 200 + 150}{7} = 135.7[/latex]

Determine the control limits

Next, we calculate the control limits. The formula for the control limits is:

– Upper Control Limit (UCL_p) [latex]=\bar{P} + 3 * \sqrt {\dfrac{\bar{P}(1-\bar{P})}{n}}[/latex]

[latex]\hspace{6.6cm} = 0.06 + 3* \sqrt{\dfrac{(0.06)(1-0.06)}{135.7}} = 0.093[/latex]

– Lower Control Limit (LCL_p) [latex]=\bar{P} - 3 * \sqrt {\dfrac{\bar{P}(1-\bar{P})}{n}}[/latex]

[latex]\hspace{6.6cm} = 0.06 - 3* \sqrt{\dfrac{(0.06)(1-0.06)}{135.7}} = 0.027[/latex]

Creating and Interpreting the P Chart

To create the P chart, we plot the proportion nonconforming each day on the Y-axis, with the centerline at P-bar and the control limits at UCLp and LCLp. As with the C chart, we then examine the chart for any points outside the control limits or non-random patterns.

In this example, if all points fall within the control limits, it suggests the process is in control. However, a point outside the limits or a non-random pattern could indicate a special cause of variation. If such a point or pattern is found, it would require further investigation to identify and eliminate the special cause.

Creating a C Chart

For a C chart, the following steps are undertaken:

• Calculate the number of nonconformities (c) for each sample.
• Calculate the average number of nonconformities (C-bar): C-bar = sum of all c / number of samples.
• Determine the control limits as follows:
• Upper Control Limit (UCL_c) [latex]=\bar{C} + 3*\sqrt{\bar{C}}[/latex]
• Lower Control Limit (LCL_c) [latex]=\bar{C} - 3*\sqrt{\bar{C}}[/latex]

Note: If the LCLc is negative, it is set to zero, since you can’t have a negative number of non-conformities.

Example: Calculating, Creating, and Interpreting a C Chart

In the context of supply chain management, let’s consider a distribution center that processes 1000 packages each day. The quality control team conducts daily inspections to detect damaged packages. They want to create a C chart to monitor the number of damaged packages each day.

Here’s a week of sample data:

– Day 1: 15 damaged packages

– Day 2: 20 damaged packages

– Day 3: 16 damaged packages

– Day 4: 18 damaged packages

– Day 5: 17 damaged packages

– Day 6: 19 damaged packages

– Day 7: 21 damaged packages

Calculate the number of nonconformities (c) for each sample

In this case, the numbers of nonconformities are given above for each day.

Calculate the average number of nonconformities (C-bar)

To calculate C-bar, we add the number of damaged packages each day and divide by the number of days:

[latex]\bar{C} = \dfrac{(15+20+16+18+17+19+21)}{7} = 18[/latex]

Determine the control limits

Next, we calculate the control limits:

– Upper Control Limit (UCLc) [latex]=\bar{C} + 3*\sqrt{\bar{C}} = 18 + 3* \sqrt{18} = 29.7[/latex]

– Lower Control Limit (LCLc) = [latex]=\bar{C} + 3*\sqrt{\bar{C}} = 18 - 3* \sqrt{18} = 6.3[/latex]

Since the LCLc is not negative, we leave it as is. If it were negative, we would set it to zero.

Creating and Interpreting the C Chart

To create the C chart, we plot the number of nonconformities each day on the Y-axis, with the centerline at C-bar and the control limits at UCLc and LCLc.

We then examine the chart for any points outside the control limits, which would suggest a special cause of variation to be investigated. If all points are within the control limits, the process is considered statistically stable. However, we would also watch for non-random patterns, such as trends or cycles, that could suggest potential problems.

In this example, all the points would fall within the control limits, indicating that the process is in control. The variation in the number of damaged packages each day appears to be due to common causes rather than any special causes. The management can continue to monitor the chart daily to ensure the process remains in control.

DMAIC is a data-driven improvement cycle used for improving, optimizing, and stabilizing business processes and designs. The acronym stands for the five steps of DMAIC which are  Define, Measure, Analyze, Improve, and Control.

Here is a breakdown of each of these steps, as well as the tools used in these steps:

1. Define: Set the context and objectives for your improvement project.
2. Measure: Quantify the problem.
3. Analyze: Identify the cause of the problem.
4. Improve: Implement and verify the solution.
5. Control: Maintain the solution.

This entire process forms a cohesive strategy for tackling quality issues in supply chain management.

Let’s explore each of the DMAIC steps in detail with an example throughout to illustrate these concepts. We’ll use the example of a supply chain manager trying to reduce late deliveries in a logistics company.

1. Define

In this initial stage, you’re setting the scope, objectives, and deliverables for your project. You are defining what you hope to accomplish by outlining specific, measurable goals that align with both the project’s critical-to-quality elements and business objectives.

Tools and Methods

• Project Charter: Sets the scope, objectives, and stakeholders.
• SIPOC (Suppliers, Inputs, Process, Outputs, Customers) Diagram: Provides a high-level view of the process and its context.

In our example, the supply chain manager wants to reduce late deliveries by 20% over the next quarter to improve customer satisfaction and reduce costs associated with delays.

2. Measure

This step involves gathering data to establish baseline performance levels. This data will be used later to show how much the implemented improvements have affected performance.

Tools and Methods

• Flowcharts: To document the current process.
• Data Collection Sheets: To gather and organize data.

In the example, the manager collects data on delivery times for the past three months, using it to calculate the current rate of late deliveries as a baseline.

3. Analyze

The collected data is analyzed to identify the root causes of the problem. The aim is to understand why the problem occurs and to point toward possible solutions.

Tools and Methods

• Root Cause Analysis: Using methods like the 5 Whys or Fishbone Diagrams.
• Pareto Charts: To identify the most frequent causes of delays.

In the example, analysis shows that 70% of late deliveries are due to delays in the packing process, specifically due to a lack of packing materials.

4. Improve

This phase involves generating, selecting, and implementing a solution. The improvements are then tested to verify their effectiveness in solving the identified problem.

Tools and Methods

• Pilot Programs: To test the effectiveness of the solution.
• A/B Testing: To compare the new process against the old one.

In the example, the manager decides to maintain a larger stock of packing materials and trains the packing staff on more efficient methods. A pilot program shows a 15% reduction in late deliveries.

5. Control

This final step aims to make the new process standard and maintain the gains achieved by the improvement. Processes are set up to ensure ongoing control and to alert the team to deviations in performance.

Tools and Methods

• Statistical Process Control (SPC) Charts: For ongoing monitoring.
• Standard Operating Procedures (SOPs): To document the new process.

In our example, the new packing methods are standardized, and training materials are updated. SPC is used to monitor ongoing performance, which confirms that the rate of late deliveries remains low.