The overall tolerance for three components in series in an electrical circuit Is+ 10 Ω. Assuming normal, stable, capable processes produce the components, use stack tolerance techniques to find a set of tolerances for the three components.

For parts connected in series, the assembly value is the arithmetic sum of the individual values. Using the worst-case stack-up technique (required whenever the final value must never exceed the specification), the assembly half-tolerance equals the sum of the component half-tolerances: Tassembly = T1 + T2 + T3 10 Ω = T1 + T2 + T3 Among the listed sets, only 3 Ω + 3 Ω + 4 Ω satisfies this equality exactly, assuring that even at the extreme limits the total resistance will still be within ±10 Ω. Normal, stable, capable processes justify the assumption of independence, but do not remove the need to meet the worst-case requirement when the stack is purely additive.

B. 7 + 7 + 6 = 20 Ω, doubling the allowed stack and violating the overall ±10 Ω limit.
C. 8 + 8 + 8 = 24 Ω, far exceeds the permitted stack.
D. 10 + 10 + 14 = 34 Ω, more than triples the allowable assembly tolerance.

1. Bergman, T. & Gibbons, P. “The Certified Six Sigma Black Belt Handbook”, 3rd ed., ASQ Quality Press, 2018. Section 9.2.3, pp. 420-421: Eq. (9.2) defines worst-case stack as Tassembly = ΣTi.

2. MIT OpenCourseWare, Course 2.008 “Design & Manufacturing II”, Lecture Notes “Tolerance Analysis”, slide 16: worst-case chain stack = sum of component tolerances for additive dimensions.

3. Montgomery, D. C. “Introduction to Statistical Quality Control”, 8th ed., Wiley, 2020, p. 485: illustrates additive electrical resistances where assembly tolerance equals sum of individual tolerances in worst-case analysis.