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Chapter-wise Previous Year GATE Questions (With Solutions) Statistical Process Control 🔹 Chapter 1: Introduction to SPC GATE Question 1 (Conceptual – 1 Mark) Which of the following is the primary objective of Statistical Process Control? (A) Detection of defects (B) Prevention of defects (C) Sorting of products (D) Replacement of inspection ✅ Answer: (B) Solution SPC focuses on monitoring and controlling processes to prevent defects, not merely detecting them after production. 🔹 Chapter 2: Statistical Foundations for SPC GATE Question 2 (Numerical – 1 Mark) For a normally distributed process, approximately what percentage of observations lie within ±3σ? (A) 95% (B) 97% (C) 99.73% (D) 100% ✅ Answer: (C) Solution By the empirical rule : ±1σ → 68% ±2σ → 95% ±3σ → 99.73% GATE Question 3 (Numerical – 2 Marks) Five observations are: 10, 12, 14, 16, 18. Find the mean and range. ✅ Solution [ \bar{X} = \frac{10+12+14+16+18}{5} = 14 ] [ Range = 18 - 10 = 8 ] 🔹 Chapter 3: Proces...

GATE / AMIE / PSU Question Bank Statistical Process Control: A Step-by-Step Guide 🔹 Chapter 1: Introduction to SPC MCQs Statistical Process Control is primarily used to: (A) Inspect finished products (B) Improve process capability (C) Replace quality planning (D) Eliminate inspection Ans: (B) SPC is best described as a: (A) Corrective technique (B) Preventive technique (C) Detection technique (D) Sampling technique Ans: (B) Short Answer (1–2 marks) Define Statistical Process Control. State one objective of SPC. 🔹 Chapter 2: Statistical Foundations for SPC MCQs The measure most sensitive to extreme values is: (A) Mean (B) Median (C) Mode (D) Range Ans: (A) For a normal distribution, approximately what percentage of observations lie within ±3σ? (A) 95% (B) 97% (C) 99.73% (D) 100% Ans: (C) Numerical (GATE type) If σ = 2 mm, find process spread. Ans: 6σ = 12 mm 🔹 Chapter 3: Process Variation & Rational Subgrouping MCQs Variation inherent in a stable process is calle...

Solved Numerical Problems (Chapter-wise) Statistical Process Control: A Step-by-Step Guide 🔹 Chapter 1: Introduction to Statistical Process Control Problem 1.1 A process produces metal rods with varying lengths. Explain whether SPC should be applied for inspection or improvement. Solution SPC is applied for process monitoring and improvement , not merely inspection. It helps: Identify process variation Distinguish between common and special causes Reduce variability systematically ✅ SPC is preventive, not corrective. 🔹 Chapter 2: Statistical Foundations for SPC Problem 2.1 Five observations of a quality characteristic are: 12, 14, 15, 13, 16 Find the mean and range . Solution [ \bar{X} = \frac{12+14+15+13+16}{5} = \frac{70}{5} = 14 ] [ Range = 16 - 12 = 4 ] ✅ Mean = 14, Range = 4 Problem 2.2 If the standard deviation of a process is 2 mm, find the natural tolerance . Solution [ \text{Natural tolerance} = \mu \pm 3\sigma = \pm 6 ] ✅ Process spread = 6σ = 12 mm 🔹 Chapter 3...

Abstract: Statistical Process Control (SPC) is a data-driven methodology used to monitor, control, and improve processes by reducing variation, primarily through tools like control charts and process capability analysis.  Implementing SPC moves manufacturers from reactive, "after-the-fact" inspection to proactive prevention of defects .   SPC Implementation Steps Successful SPC implementation generally follows these steps: Identify Critical Process Parameters (CPPs):  Define which variables (e.g., temperature, weight, dimension) most affect product quality. Establish a Baseline:  Analyze the current process capability to determine if it is in a state of statistical control. Implement Control Charts:  Use X-bar and R charts or other, more sophisticated, charts to monitor process stability in real-time. Train Personnel:  Educate operators to identify and interpret out-of-control points to take corrective action. Continuous Monitoring and Action: ...

Abstract: Measurement System Analysis (MSA) is  a statistical method to evaluate the quality, accuracy, and precision of a measurement system  (gauges, methods, software, personnel, environment) to ensure it provides reliable data for decisions, identifying variation sources like repeatability, reproducibility, bias, linearity, and stability, and confirming it's fit for use before impacting product quality . MSA helps separate measurement error from actual product variation, preventing costly mistakes in quality control,  This video provides a detailed overview of Measurement System Analysis (MSA): Key Components & Concepts Accuracy  (Bias):  Difference between the average measurement and the true value. Precision :  How close repeated measurements are to each other. Repeatability:  Variation when the same operator uses the same gauge on the same part. Reproducibility:  Variation when different operators use the same gauge on the s...

Abstract  Acceptance sampling is  a statistical quality control method where a random sample from a production lot is inspected to decide whether to accept or reject the entire batch , balancing inspection costs with quality assurance by avoiding 100% testing, especially when testing is costly or destructive. A pre-defined sampling plan dictates the sample size and acceptance criteria (e.g., number of defects allowed), leading to lot acceptance or rejection, common in supply chains for balancing producer/consumer risks,    How it works Sampling Plan : A plan specifies sample size (n) and acceptance number (c) for a given lot size. Random Sample : A representative sample is drawn from the lot. Inspection : The sample is inspected for defects. Decision : If the number of defects is below 'c', the lot is accepted; otherwise, it's rejected.   Key concepts AQL (Acceptable Quality Level) : The maximum percentage of defects considered acceptable. OC Curve ...

Abstract: Using Statistical Process Control (SPC) tools  improves processes by using data to monitor, control, and reduce variation, leading to fewer defects, lower costs, and enhanced efficiency , primarily through techniques like  control charts , histograms, and process capability studies (Cp/Cpk) to detect "special cause" problems early, preventing waste, and enabling data-driven decisions for continuous improvement in manufacturing and beyond.   Key SPC Tools for Improvement Control Charts :  Monitor process stability over time (e.g., X-bar & R charts for variables, P/NP charts for attributes) to distinguish normal variation from assignable causes. Histograms :  Show the frequency distribution of data, revealing process shape and spread. Process Capability Studies  (Cp, Cpk):  Measure if a process can consistently meet specifications (e.g., capability indices like 1.33 or higher for good performance). Pareto Charts :  Identify...

Abstract: Process capability analysis (PCA) is  a statistical method to determine if a process consistently meets customer specifications by comparing its natural variation to required limits ( Specification Limits ) . It uses indices like  Cp  (potential capability) and  Cpk  (actual capability) to quantify this, assessing if the process is centered and its spread is narrow enough, often using data from control charts (like X-bar & R charts) and visualized with histograms, to guide quality improvement in manufacturing and other fields .   Key Concepts Specification Limits (USL/LSL):  Customer-defined upper (USL) and lower (LSL) limits for product characteristics. Control Limits:  Limits derived from process data (via SPC charts) showing natural variation, distinct from customer specs. Process Variation:  The inherent spread or variability of the process output (often measured by standard deviation, sigma). Cp  (Process C...

Abstract: Control charts for attributes in Statistical Process Control (SPC)  monitor quality when data is counted (pass/fail, yes/no) rather than measured, using charts like  P (proportion defective) ,  np (number defective) ,  C (number of nonconformities) , and  U (average number of nonconformities)  to distinguish common (natural) variation from special (assignable) cause variation, helping maintain process stability . These charts plot data over time, showing if a process is stable (in control) or has unusual patterns (out of control).   Types of Attribute Control Charts P-Chart  (Proportion Nonconforming):  Tracks the fraction of defective items in samples, suitable for varying sample sizes. np-Chart  (Number Nonconforming):  Monitors the actual count of defective items when sample sizes are constant. C-Chart  (Count of Nonconformities):  Used for the total number of defects per unit (e.g., scratches on a...

Abstract: Control charts for variables in Statistical Process Control (SPC) monitor measurable characteristics (like weight, height, diameter) using paired charts: an X-bar (mean) chart tracks the process average (centering) and an R (range) chart or S (standard deviation) chart tracks variability (spread) . These charts use Upper and Lower Control Limits (UCL/LCL) based on sample data to distinguish between normal process variation and significant shifts, helping identify issues like poor materials or machine problems.   Key Types of Variable Control Charts   X-bar (Mean) Chart : Plots the average of subgroups over time to check if the process is centered correctly. R (Range) Chart : Plots the range (max - min) within subgroups to monitor process spread (variability). S (Standard Deviation) Chart : Also monitors variability, often preferred for larger sample sizes over R charts. Individual & Moving Range (I-MR) Charts : Used for single observat...