UNIT 4. MQA PYQ QUESTIONS
Q.1) Explain histogram or frequency distribution diagram
A histogram, also known as a frequency distribution diagram, is a graphical representation of data that displays the distribution of a dataset. It is commonly used in statistics to visualize the frequency or occurrence of different values or ranges within a dataset.
The horizontal axis of a histogram represents the range of values in the dataset, divided into equal intervals called bins or classes. The vertical axis represents the frequency or count of observations falling within each bin.
To create a histogram, the following steps are typically followed:
1. Data collection: Gather the data you want to analyze and determine the variable you want to represent on the horizontal axis.
2. Determine the number of bins: Decide on the number of intervals or bins you want to use to divide the range of values. The choice of the number of bins can affect the appearance of the histogram, so it's important to choose an appropriate number that captures the patterns and distribution of the data.
3. Calculate bin boundaries: Divide the range of values into the determined number of bins. The width of each bin is equal, and the boundaries represent the starting and ending points of each bin.
4. Count frequencies: Count the number of observations or occurrences falling within each bin. This involves determining how many data points fall within the range defined by each bin.
5. Plotting the histogram: Represent the frequency or count of each bin on the vertical axis, and the corresponding values or intervals on the horizontal axis. Typically, bars are used to represent each bin, with the height of the bar indicating the frequency or count of observations within that bin.
The resulting histogram provides a visual representation of the distribution of the data. It allows you to observe patterns, such as whether the data is skewed to one side, symmetric, or follows a specific shape, like a normal distribution. Histograms are particularly useful for exploring the shape of continuous numerical data and identifying any outliers or gaps in the data.
Histograms provide a concise summary of the data distribution, making it easier to interpret and analyze large datasets quickly. They are commonly used in various fields, including statistics, data analysis, quality control, and scientific research.
Q.2) What is cost of quality? Explain its types.
The Cost of Quality (COQ) is a concept used in business and project management to quantify the financial impact of both the conformance and non-conformance to quality requirements. It represents the total cost incurred by an organization to achieve and maintain a certain level of quality in its products or services.
The Cost of Quality can be divided into four main types:
1. Prevention Costs: These are the costs associated with activities and measures taken to prevent defects or quality issues from occurring in the first place. Prevention costs include activities such as employee training, process documentation, quality planning, supplier evaluation, quality audits, and quality improvement projects. By investing in prevention, organizations aim to minimize the occurrence of defects and reduce the overall cost of poor quality.
2. Appraisal Costs: These costs are incurred to evaluate and assess the level of quality achieved in products, services, or processes. Appraisal costs include activities such as inspection, testing, quality control activities, calibration of measuring equipment, and audits. These costs are necessary to identify and catch defects, ensuring that products or services meet the required quality standards before they reach the customer.
3. Internal Failure Costs: Internal failure costs arise when defects or quality issues are identified and corrected before the product or service reaches the customer. These costs include scrap and rework expenses, retesting, re-inspection, and the cost of dealing with customer complaints. Internal failure costs can also include the cost of downtime, inefficient processes, and wasted resources due to quality problems within the organization.
4. External Failure Costs: These costs occur when defective products or services are delivered to customers and subsequently identified or experienced by them. External failure costs can be significant and include activities such as warranty claims, product recalls, customer support, product returns or replacements, legal actions, damage to the organization's reputation, and the loss of customer trust. External failure costs can have a severe impact on an organization's profitability and market position.
The goal of managing the Cost of Quality is to strike a balance between prevention and appraisal costs to minimize internal and external failure costs. By investing in prevention activities and continuously improving processes, organizations can reduce the overall Cost of Quality and enhance customer satisfaction.
Q.3) Explain following SQC tools
i) X and R chart
ii) P chart
i) X and R Chart:
The X and R (average and range) chart is a statistical process control (SPC) tool used to monitor and control the variation in a process. It is commonly used when dealing with continuous data, such as measurements or dimensions.
The X chart tracks the average or mean of a process characteristic over time. It plots the average values of samples taken at regular intervals. The centerline of the X chart represents the overall process average, and control limits are typically set at three standard deviations above and below the mean. By monitoring the plotted values, any shifts or trends in the process average can be detected, indicating a need for investigation and potential process adjustment.
The R chart, on the other hand, tracks the range or dispersion of a process characteristic. It measures the difference between the highest and lowest values within each sample. The R chart helps assess the variability within the process and identify any special causes of variation. Control limits for the R chart are typically calculated using statistical formulas. If the range values fall outside these limits, it suggests an increase in process variability.
By using both the X and R charts together, it becomes easier to distinguish between common cause and special cause variation in a process. Common cause variation refers to the inherent variability that is present in a stable process, while special cause variation indicates the presence of external factors or unusual events affecting the process.
ii) P Chart:
The P chart, also known as the proportion chart, is another statistical process control tool used to monitor and control the proportion or percentage of non-conforming items or defects within a process. It is commonly applied when dealing with attribute data, where items are classified as either conforming or non-conforming based on specified criteria.
The P chart consists of a series of subgroups or samples taken from the process at regular intervals. Each subgroup is assessed for the presence or absence of non-conforming items, and the proportion of non-conforming items is calculated for each subgroup. The P chart then plots the proportion of non-conforming items over time.
Control limits for the P chart are typically calculated using statistical formulas based on the desired level of control. These control limits help determine if the process is in a state of control or if special causes of variation are present. If the plotted proportions fall outside the control limits, it suggests that the process is exhibiting an unusual level of non-conformities.
The P chart is useful for detecting changes in the proportion of non-conforming items, indicating potential issues or improvements in the process. By monitoring the chart over time, organizations can identify and address the sources of non-conformities, make necessary adjustments, and improve the overall quality of their products or services.
Q.4) Explain Process Capability Index
The Process Capability Index (Cpk) is a statistical measure used to assess the ability of a process to consistently produce output within specified tolerance limits. It quantifies the capability of a process to meet customer requirements and provides an indication of how well the process is performing in relation to its specification limits.
Cpk takes into account both the centering of the process and the spread or variation of the data. It compares the width of the process variation to the width of the specification limits. The higher the Cpk value, the more capable the process is in meeting the specified requirements.
The calculation of Cpk involves the following steps:
1. Determine the process average (mean)
2. Calculate the process standard deviation
3. Define the specification limits
4. Calculate the process capability indices
It is calculated using the formula:
1. Cpk = min((USL - mean) / (3 * standard deviation), (mean - LSL) / (3 * standard deviation))
2. Cp = (USL - LSL) / (6 * standard deviation)
Both Cpk and Cp values range from 0 to 1, with values closer to 1 indicating a higher process capability.
Q.5) The following table gives the number of missing rivets noted in a newly fabricated bus, construct c-chart and comment on process.
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